Assessment and the logic of instructional practice in Secondary 3 English and mathematics classrooms...

Assessment and the logic of instructional

practice in Secondary 3 English and

mathematics classrooms in Singapore

David Hogan*, Melvin Chan, Ridzuan Rahim, Dennis Kwek,Khin Maung Aye, Siok Chen Loo, Yee Zher Sheng andWenshu LuoNational Institute of Education, Singapore

By any measure, Singapore’s educational system has generated an extraordinary record of achieve-

ment over the past two or three decades. In this article, we report on one key component of a

broader three year investigation into why Singapore has done so well, and explore the logic,

strength, resilience and limits of the underlying pedagogical model and policy framework that have

helped secure this record of achievement. Specifically, we draw on data we collected in 2010 to ana-

lyze the pedagogical organization of four theoretically specified ‘models’ of instructional strategy–

traditional instruction, direct instruction, teaching for understanding, and co-regulated learning

strategies–in Secondary 3 mathematics and English. In the course of our analysis, we develop three

arguments. The first is the single-minded performative orientation of instructional practices gener-

ally–and instructional strategies specifically–in Singaporean classrooms that rarely deviated from a

logic of curriculum coverage, knowledge transmission and assessment. Second, while we found sub-

stantial evidence of a pervasive performative orientation to instruction, we also found that teachers

in Singapore draw from a variety of instructional perspectives in ways that reflect a pragmatic,

instrumental fit-for-purpose approach and broader performative orientation. Third, we found that

the national high stakes assessment system, by virtue of its considerable institutional authority, both

shaped the pattern of instructional practice at the classroom level and constrained opportunities for

instructional improvement. In the conclusion, we review related findings from the research program

on the impact of instructional practice on student achievement in Singapore.

Introduction

By any measure, Singapore’s educational system has generated an extraordinary

record of achievement over the past two or three decades. Not the least of these

achievements has been its record in international assessments, including TIMMS

and PISA (Table 1). It is now recognized as one of the leading educational systems in

the world and the object of envy and emulation. In this article we report on one key

component of a broader three year investigation into why Singapore has done so well

and explore the logic, strength, resilience and limits of the underlying pedagogical

*Corresponding author: National Institute of Education, 1 Nanyang Walk, Singapore 637616,

Singapore. Email: [email protected]

Review of EducationVol. 1, No. 1, February 2013, pp. 57–106

DOI: 10.1002/rev3.3002

© 2013 British Educational Research Association

model and policy framework that have helped secure this widely admired and envi-

able record of achievement.

Specifically, we draw on data we collected in 2010 to analyze the pedagogical orga-

nization of four theoretically specified ‘models’ of instructional strategy—traditional

instruction, direct instruction, teaching for understanding, and co-regulated learning

strategies—in Secondary 3 mathematics and English. We do not report, however, on

other key features of instructional practice in Singapore—the design and enactment

of instructional tasks, classroom organization, interaction and talk, the use of high

leverage instructional strategies (including checking for prior knowledge, the commu-

nication of learning goals and performance standards, monitoring, feedback, learning

support and knowledge representation) and the overall relationship between the pre-

scribed and the enacted curriculum—that our larger research program has addressed.

In the course of our analysis we will develop three arguments and intimate two

others that we have developed in our broader research program. The first is the sin-

gle-minded performative orientation of instructional practices generally—and

instructional strategies specifically—in Singaporean classrooms that rarely deviated

from a logic of curriculum coverage, knowledge transmission and reproduction

(assessment). We think this partly reflects the influence of underlying cultural

assumptions and institutional rules about education, teaching and learning—what

Jerome Bruner (1996) and David Cohen (1988) have separately termed a ‘folk peda-

gogy’—and the very considerable institutional authority of the national high stakes

assessment system in a society where the nexus between credentialing and social

mobility is unusually tight and the accountability system renders teachers unusually

susceptible to parent credentialing anxieties. Indeed, we think this deeply instrumen-

tal performative orientation largely explains the essential hybridity of instructional

practice in Singapore.

Second, while we found substantial evidence of a pervasive performative orienta-

tion to instruction, we also found that instructional practices did not conform to a par-

ticular theoretical or normative model of pedagogical practice. Teachers in Singapore

are not, by and large, sectarian or tribal in their instructional commitments—that is,

they do not tend to see themselves as members of a particular pedagogical sect or tribe

(traditional, constructivist) or, for that matter, East Asian or Western. Instead, they

Table 1. 2009 PISA results

Rank Country Overall reading Overall math Overall science

1 Shanghai, China 556 600 575

2 Korea 539 546 538

3 Finland 536 541 554

4 Hong Kong 533 555 549

5 Singapore 526 (5) 562 (2) 542 (4)

6 Canada 524 527 529

7 New Zealand 521 519 532

8 Japan 520 529 539

9 Australia 515 514 527

10 Netherlands 508 526 522

Source:OECD (2010).

58 D. Hogan et al.


pragmatically mix and match, drawing from a variety of instructional perspectives in

ways that reflect their pragmatic, instrumental fit-for-purpose approach and broader

performative orientation. However, this non-sectarian pragmatism and hybridity is

neither culturally or institutionally innocent but reflects the play of powerful vernacu-

lar discourses (ability, readiness, meritocracy, nation-building, social harmony) and

the complex articulation of instructional practices in response to the national high

stakes assessment system and cross-cutting institutional and organizational processes

that variously support or constrain the alignment of instruction with assessment. On

balance though, the forces of alignment and institutional isomorphism have prevailed

decisively until now, although this is likely to slowly change in the years ahead as the

professionalization of teaching, might, if appropriately organized, offer at least some

protection of teaching and learning practices from these pressures.

Third, we found, like others before us, that the national high stakes assessment sys-

tem exercised considerable institutional authority over Singapore’s pedagogical sys-

tem through its unparalleled ability to shape the pattern of instructional practice at

the classroom level. In Singapore, the Ministry of Education administers three high

stakes national assessments: at the end of primary school (the Primary School Leaving

Examination [PSLE]) regulating access to secondary school and to the curriculum

streams within them, at the end of secondary school (the Cambridge O levels) regu-

lating access to post-secondary education, and at the end of Year 12 for those enrolled

in junior colleges hoping for admission to a university (the Cambridge A levels). The

national high stakes assessment system is intended to serve a number of objectives—to enhance the quality of teaching and learning, to provide a public, transparent, reli-

able and politically acceptable quality assurance and accountability mechanism, and

to provide a clearly meritocratic process for the allocation of students into school

streams and the social division of labour more broadly. This is a considerable politi-

cal, educational and ideological burden for any assessment system to bear. Not sur-

prisingly, it has long been the subject of close scrutiny by local commentators. Cheng

(1996, p. 9), for example, argued that the ‘examination is the soul of the ethos about

education in East Asian societies’ and ‘the goalkeeper to the quality of education out-

put’. Two years later, Cheah (1998, p. 4), similarly concluded that the teaching of

English language in Singapore was ‘driven by an “examination-type literacy”’ and

that teachers ‘teach in the way they believe will help more students pass their examin-

ations’. The trouble with this pedagogical arrangement, as Cheah goes on to con-

clude, is that the tight coupling or calibration of instruction and assessment has had

unfortunate and unintended consequences. He notes in particular that the introduc-

tion of a key pedagogical reform in English in the 1990s—process writing—was ‘ham-

pered by the emphasis on examinations in the school system’. More recently,

Anneliese Kramer-Dahl (2008), in her research on the implementation of the 2001

English syllabus in Singapore in 2006 and 2007, similarly reports that the English

teachers she and her colleagues studied closely repeatedly retreated from the innova-

tive pedagogy of the 2001 EL syllabus and fell back instead to the default position of

an examination-driven instructional regime in order that their students be properly

prepared for school-based and national high stakes assessments. ‘Indeed’, she writes,

‘“exams”, “practice” and “back to basics” were keywords reiterated over and over in

our interviews and in the classroom, often juxtaposed against what they see as an all-

Assessment and the logic of instructional practice 59


too-unrealistic “advanced thinking and literacy” discourse of the syllabus’. One of her

two subjects, Elise, explained her teaching choices this way:

There’s the syllabus and there’s the exam. I feel a lot of the curriculum is controlled by the

exam. I’m building the kids up to a last final outcome, with lots of practice and drill…Ulti-

mately on paper, you have to have your exams and your tests. Making the link between

school and real life? I think for our students that’s not a salient incentive. You need to link

it to the exams, right? That’s the carrot that dangles. ‘You learn this because exams are

gonna have that’. For lots of our teenagers exams have become life. You can’t draw the

line, not in the Asian context, because it’s very very obvious, you know. (Kramer-Dahl,

2008, p. 94)

Still, it is fair to say that Singapore’s national high stakes regime has had both posi-

tive and negative consequences for the quality of teaching and learning. On the one

hand, it goes a long way towards explaining the clear-eyed focus, coherence and effec-

tiveness of instructional practice and the underlying performative pedagogical orien-

tation that underwrites it in Singapore. On the other hand, we also think that the

national high stakes assessment system has resulted in a pedagogy that is intractably

didactic rather than dialogical, compromised the epistemic quality and the transpar-

ency or ‘visibility’ (Hattie, 2009, 2012) of learning processes during lessons,

restricted the opportunities of students to engage in knowledge building work in class,

and constrained the ability of the system to successfully introduce substantial and sus-

tainable pedagogical improvements despite a strong policy commitment to doing so

as reflected in the two key policy documents of the past 15 years—Thinking schools,

learning nation (TSLN, 1997) and Teach less, learn more (TLLM, 2004). We consider

these very high opportunity costs to pay and to reflect a considerable lack of align-

ment between policy and practice in the system, even though at the same time they

reflect a very high degree of pedagogical alignment between assessment and instruc-

tion. Indeed, our findings suggest a very considerable tension, if not outright contra-

diction, between the teaching for understanding and twenty-first century learning

objectives of recent policy statements (especially Teach less, learn more) and the

continuing commitment of the government to its national high stakes assessment

regime. When all is said and done, these findings raise important questions about

whether the current pedagogical model, originally developed in the late 1970s, has

now more or less run its course and needs substantial modification of its basic design

principles if the system is to have any real hope of achieving the policy priorities set

out in TSLN and TLLM. Tinkering around the edges—a little bit more feedback and

formative assessment here, a little bit more teaching for understading there, a little

more PD everywhere—is unlikely to achieve the outcomes the system desires.

In short, over the course of our article we develop three key arguments—one regard-

ing the overall performative orientation of instructional practice in Singapore, the sec-

ond regarding the pragmatic hybridity of instructional practice, and the third the tight

coupling or alignment of national high stakes assessment system and classroom

instruction. We think these arguments go some way towards explaining why Singa-

pore’s educational system has achieved extraordinary success in a very short period of

time, accelerating from a standing start in 1965 as a third world education system to

one of themost successful 40 years later.We think this remarkable achievement can be

explained, in part, by the single-minded instrumentalist focus of the system on devel-

60 D. Hogan et al.


oping a highly effective performative pedagogy using a high stakes national assessment

system to lift standards and ensure quality. Of course, there are other factors as well

that have contributed to Singapore’s success, including a high quality curriculum

framework, exceptional leadership of a tightly integrated and centralized system, the

quality and commitment of its teaching corps, and highly supportive cultural orienta-

tions to education that in part reflects Singapore’s Confucian heritage and in part the

tight nexus between educational credentialing and status attainment in Singapore. But

our evidence also suggests that the basic design principles of the pedagogical system

that have served Singapore sowell over the course of the developmental phase of its his-

tory now appear, ironically enough, to constrain the ability of the system to successfully

support substantial and sustainable pedagogical improvement in line with its own pol-

icy preferences. This has important implications for other systems that have recently

made it their business to emulate or imitate some key features of Singapore’s system.

Data andmethods

The data we report in this study draws from a nationally representative sample of over

4000 Secondary 3 students and their teachers in approximately 120 mathematics and

English classes across 32 secondary schools in Singapore conducted in 2010. Our first

interim report (Hogan et al., 2011) includes detailed discussions of the statistical proce-

dures specification and theoretical issues involved in the construction of all of the

instructional methods scales. However, it is appropriate now to briefly discuss some

details of our sampling strategy and the reliability of students as raters. In order to

maximize the analytical scope of key pedagogical practices and individual student

characteristics, we employed a split-half multi-level strategy in which 50% of the total

student samples within each class in the sample were randomly assigned to a 230-item

survey focused on students’ perceptions of instructional practices. The other half of

the samples were assigned to a survey in which students answered a similar number of

questions about their family background, learning orientation, motivation, self-beliefs

and so on. In addition, all the students in each class sampled completed an hour-long

assessment in mathematics or English. This design permits us to model the logic of

instructional practice at the classroom level and to model the impact of domain spe-

cific classroom practices on student outcomes. In this article, however, we draw

exclusively on the classroom level survey data only, apart from limited interview data

with teachers concerning their views on assessment.

While relatively few studies have been conducted of primary and secondary school

students as raters of instructional practices, the studies that have been completed

indicate that elementary and secondary school students can effectively differentiate

among various types of instructional practices (Urdan & Midgley, 2001; Wolters,

2004; Assor et al., 2005). In any case, there are compelling statistical reasons to use

the multiple data points from student reports at the class level to model instructional

practices rather than the single data point provided by the class teacher.

While we report a range of descriptive statistics in the analysis that follows, analyti-

cally the greater part of the heavy lifting is undertaken by structural equation model-

ling (SEM). SEM is a powerful multivariate statistical technique used to examine

whether the hypothetical relationships specified by the researcher can be empirically



supported by the sampled data. One of its key strengths is its ability to specify latent

variables as robust measures of theoretical constructs. Unlike traditional factor ana-

lytic approaches where theoretical variables of interests are often assumed to be mea-

sured without error, measures assessed using confirmatory factor analysis (the

measurement approach of SEM) are corrected for biases attributable to random and

unexplained measurement error that often result in more precise estimates of struc-

tural relationships (Bollen, 1989). Another strength of SEM is the availability of good-

ness-of-fit statistics that allow researchers to evaluate the relative strength of the

hypothesized model against the baseline structure. In this study, evaluation of good-

ness-of-fit statistics is based on the classical chi-square test (v2) where a non-signifi-

cant v2 at a specified alpha level of p < .05 indicates that there is no statistically

significant discrepancy in the covariance structure between the observed data and the

hypothesized model. However, since the v2 can be sensitive to sample size and model

complexity, we also report a range of alternative fit statistics together with the v2 testthat take these issues into account. Based on the conventional guidelines by Hu and

Bentler (1999), the recommended thresholds of a good fitting model are as follows:

comparative fit index (CFI) and Tucker–Lewis index (TLI) should have values above

0.95, root mean square error of approximation (RMSEA) should have values less than

0.05, and standardized root mean square residual (SRMR) should have values less

than 0.08.

Although researchers would typically like to develop empirical models that are suf-

ficiently complex so that they are closer to explaining the truth as observed in the real

world, this is often challenging as complex models can result in unstable parameter

estimates (Bandalos & Finney, 2001). One strategy often employed (and the one

employed in this article) is the use of composite variables or ‘item parcels’ as proxies

for the estimated latent variable. As composite variables reduce the number of param-

eters that must be estimated by the model, complex analyses requiring a larger pool of

variables become less demanding. This, happily, reduces sampling and measurement

error, thus resulting in more accurate estimates. In this study, a single-item latent

composite variable is constructed by assigning a pre-calculated regression and error

constraint estimated from a proportionally weighted composite score. Given that uni-

dimensionality is an important condition for latent composite models (Sass & Smith,

2006), all instructional variables presented in this article are psychometrically reli-

able. Construct reliability ranged from .79 to .90, and all over-identified latent mea-

surement models achieved a non-significant chi-square (p < .05), except for one

(p = .001). The general approach to this procedure is explained in more detail by

Chan (2012). Similar approaches to this procedure has been established previously as

total aggregation method with reliability correction (Coffman & MacCullum, 2005),

equivalent composite measures (Landis et al., 2000), latent composite variables (Ste-

phenson & Holbert, 2003), one-factor congeneric measurement model (J€oreskog,1971) and one-factor congeneric measurement model (Rowe, 2002).

The analysis of instructional methods and student achievement reported in this

article is part of a larger three year study (the Core 2 Research Program) focused on

mapping, measuring and modelling instructional practices in Singaporean classrooms

and their impact on wide variety of student outcomes (Hogan et al., 2011). We have

already published a number of papers that focus on instructional tasks, classroom talk

62 D. Hogan et al.


and student motivation (Hogan et al., 2011, 2012a, b; Luo et al., 2011a, b; Rahim et

al., 2012) and will not address these issues here. This particular article focuses, as the

title suggests, on the logic of instructional strategies where we understand these to be

composed of sets or arrays of instructional methods loosely organized as very general

instructional strategies—‘traditional instruction’, ‘direct instruction’, ‘teaching for

understanding’ and ‘co-regulated learning strategies’. We recognize that only the

more theoretically self-conscious of teachers will frame their teaching in these broad

strategic terms (let alone even broader theoretical frameworks), and that they are far

more likely to understand their practice in somewhat more disaggregated and discrete

terms. Our theoretical models then function as methodological heuristics that allow

us to explore the relationships within and between nominally independent sets of

instructional strategies. Intriguingly, however, statistically speaking, the clusters of

discrete instructional practices associated with particular strategies exhibit relatively

high levels of covariance and therefore constitute relatively coherent clusters of

instructional practice that we might well consider empirically established latent theo-

retical models of instructional practice. However, we hasten to add that the covari-

ances between the sets of instructional practice are not so low that teachers, at least in

Singapore, feel compelled to choose between them rather than combine them in ways

that they believe are pragmatically ‘fit for purpose’. We also recognize the theoretical

risks in treating instructional strategies separate from instructional tasks, lesson

organization, curriculum materials, classroom management, learning environment

and talk but treating all of them simultaneously in one publication places impossible

demands on editors of academic journals.

A taxonomy of instructional methods

Traditional instruction. One common stereotype of East Asian pedagogy is that it is

characterized by ‘traditional’ forms of instruction and that this is a major part of the

explanation of why East Asian students have done so well in international assess-

ments like TIMMS and PISA. In its cruder forms the East Asian thesis is that drill

and practice supports memorization and memorization develops understanding;

more sophisticated versions suggest that drill and practice develops both procedural

skills and conceptual understanding as well, although this version of the thesis is

unclear about the nature of the causal relationships involved. Although by no means

the first to do so, Frederick Leung describes the stereotypical image (particularly in

the West) of the teaching style in mathematics in East Asia in the following terms.

Mathematical classes, he writes, are seen as ‘rather traditional’. Teaching is ‘predom-

inantly content orientated and exam driven. Instruction is very much teacher domi-

nated and student involvement minimal’. Teaching is ‘usually conducted in whole

group settings, with relatively large class sizes’. There is ‘virtually no group work or

activities, and memorization of mathematics is stressed’ and ‘students are required to

learn by rote’. Students are ‘required to engage in ample practice of mathematical

skills, mostly without thorough understanding’ (2001, pp. 35–36; see also Biggs &

Watkins, 2001; Cai et al., 2004; Wong, 2004; Leung, 2006). Leaving aside whether

this is an accurate picture in East Asia, is it an accurate guide to teaching in

Singapore?



Our particular specification of what we call ‘Traditional Instruction’ (TI) focuses

on five first order constructs or single indicators: a focus on worksheets and work-

books (‘How often does your mathematics/English teacher ask you to do worksheets

or workbooks?’); a focus on textbooks (e.g., ‘How often does your mathematics tea-

cher asks you to answer questions from the textbook?’); drill and practice of basic

facts, rules and procedures (e.g., ‘How often does your mathematics/English teacher

ask you to drill and practice on basic facts, rules or procedures?’); a focus on memori-

zation (e.g., ‘How often does your mathematics teacher ask you to remember formu-

lae or rules?’); and exam preparation (‘my teacher emphasizes studying problems that

may occur in the exams’; ‘my teacher spends a lot of class time preparing for exams’;

‘my teacher teaches us test-taking strategies’; and ‘my teacher emphasizes practicing

past year exam papers’). Initially, we also included an item ‘teacher talks/lectures a

lot’ on the grounds that theoretically at least it ought to fit the TI model, but when we

subjected the model to further statistical analysis using confirmatory factor analysis

(CFA) to test the reliability of the TI scale, teacher talk/lecture did not load well on

the TI second order construct in either English or mathematics. Accordingly, we did

not include it in our final model. Some of the measures in the TI scale are made up of

single indicators measures: we recognize that this is far from optimal statistically (we

would have preferred three or four), but the post hoc nature of our analysis of the TI

scale (and some other measures) gave us little choice.

Table 2 reports the results of the CFA models of mathematics and English. Factor

loadings range from the moderately high (.790, .841) to, in the case of English, the

relatively low (.426). The CFA models indicate quite different factor structures for

the two subjects. In mathematics, textbook focus has the strongest loading, followed

by memorization and drill and practice. By contrast, in English, textbook focus has

the lowest factor loading of all; conversely, memorization has the strongest factor

loading, followed by drill and practice and exam preparation. The re-specified model

includes a theoretically sensible correction for an error covariance in both models:

Table 2. CFA higher order factor loadings and goodness-of-fit statistics: traditional instruction,

Secondary 3 mathematics and English

Mathematics English

Respecified higher order model Respecified higher order model

Higher order factor loadings

Textbooks focus (2) .790 (.035) .426 (.034)

Memorization (1) .784 (.023) .841 (.022)

Drill and practice (1) .771 (.023) .800 (.022)

Worksheets focus (1) .648 (.027) .573 (.030)

Exam preparation (4) .611 (.027) .784 (.022)

Goodness-of-fit statistics:

Chi-square/df/p-value 48.115/24/.0024 30.143/18/.0361

CFI/TLI .993/.989 .996/.993

RMSEA (90% C.I.) .029 (.017–.041) .026 (.007–.041)SRMR .021 .016

64 D. Hogan et al.


between exam preparation and drill and practice in mathematics, and between text-

book focus and drill and practice in English.

The mean scores, standard deviations and Cronbach’s alphas for the scales are

reported in Table 3. The overall mean scores for traditional instruction in both Eng-

lish and mathematics are relatively high, although there are important differences

across subjects—mathematics teachers especially are far more likely to employ tradi-

tional instructional techniques in general than English teachers. However, the rank

ordering across the two subjects differs slightly: in mathematics, memorization, fol-

lowed by focus on worksheets and workbooks and focus on textbooks, are dominant;

in English, focus on worksheet sand workbooks, memorization and focus on exam

preparation led the field.

The mean scores tell us about the relative frequency of instructional events; what

they cannot tell us about are the strength of the relationships between the five mea-

sures. CFA modelling of course provides a measure of patterns of covariance; the

CFAs reported in Table 1 indicate reasonably strong levels of covariance. A closely

related statistic—correlation coefficients—provides a second. These are reported in

Table 4 and again indicate moderately strong relationships, although the strength of

the relationships varies between subjects, but with particularly strong correlations in

both subjects between exam preparation and focus on drill and practice.

Table 4. Latent correlation matrix: traditional instruction for mathematics and English

(mathematics to the left of the diagonal; English to the right)

EXPR MEM DRILL WKSF TXBF

Focus on exam preparation .65 .62 .45 .37

Focus on memorization .45 .68 .50 .32

Focus on drill and practice of basic

facts, rules and procedures

.53 .59 .44 .35

Focus on worksheets and workbooks .39 .51 .50 .40

Focus on textbooks .44 .67 .58 .51

Note: All correlations significant at p < .01.

Table 3. Traditional instruction, Secondary 3 mathematics and English

Mathematics English

Mean (1–5) SD Mean (1–5) SD Cohen’s d

N 1166 1027

Traditional Instruction (TI)

Scale (alpha: .758, .726)

3.78 .65 3.46 .65 .49

Focus on memorization 4.06 .91 3.47 .93 .64

Focus on worksheets and

workbooks

3.93 .95 3.63 .95 .32

Focus on textbooks 3.83 .82 3.35 .97 .54

Focus on drill and practice on

basic facts, rules and procedures

3.59 .97 3.39 .92 .21

Focus on exam preparation 3.51 .86 3.45 .82 .07



Neither CFA nor bivariate correlations, however, tell us much about the pattern of

causal relationships between variables. Is it the case, for example, as pedagogical folk-

lore in Singapore suggests, that instructional practices in Singapore are more or less

dominated by the institutional authority of the assessment system? To even begin to

answer this question we need a kind of statistical analysis that can estimate the

strength of ‘causal’ pathways between variables controlling for the influence of con-

founding factors. The statistical procedure of choice these days to answer this kind of

question is structural equation modeling (SEM). SEM models allow researchers to

precisely measure the pattern and strength of relationships between the different

instructional practices (technically, ‘constructs’) by estimating regression coefficients

for the pathways between the constructs. These regression coefficients predict how

much of the variance in the outcome variable (the construct into which the arrow

goes) is accounted for by variations in the predictor variable (the construct from

which the construct leaves) controlling for the influence of other variables on the

outcome variable.

SEM models proceed by first specifying a theoretical model of the relationships

that researchers hypothesize exists in the real world, and then tests to see how well the

real world empirical data ‘fits’ the model. The better the fit, the better the model. In

addition, SEM models estimate the strength of relationships (pathways) between

variables and report the results in terms of regression coefficients. A pathway regres-

sion coefficient of .47, for example, between exam preparation and textbook focus

means that for every unit increase in exam preparation, teachers will increase their

focus on textbooks by .47 of whatever unit metric is being used, as in the SEMmodel

for Secondary 3 mathematics below (Figure 1). This means that a focus on exam

preparation is directly predictive of textbook focus (with a strong regression coeffi-

cient of .47). In addition, exam preparation is predictive of a focus on worksheets and

workbooks (.18), and the drill and practice of basic facts, rules and procedures (.34).

We believe that the strength of these coefficients underscores the institutional ability

of the assessment system, through its classroom proxy (exam preparation), to shape

Note: Values represent unstandardized estimates significant at p < .01

Goodness-of-fit statistics:Chi-square/df/p-value 1.902/1/.1679CFI / TLI .999/.993RMSEA (90% CI) .028 (.000–.089)SRMR .006

TextbookFocus

DrillExam

Preparation

Worksheet Focus

.34(.04) .25(.05)

.31(.05)

.21(.04)

Memorization

.18(.04)

.47(.04)

.15(.04).43(.05)

.46(.06)

Figure 1. SEMmodel for traditional instruction (mathematics)

66 D. Hogan et al.


classroom practice. But, in addition, all three of these strategies in turn have direct

pathways to a focus on memorization, with a particularly strong pathway from text-

book focus to memorization (.46). Further, there are a series of indirect pathways

from exam preparation to memorization. All together these indirect pathways add up

to a substantial effect size of .42 if we multiply out and add up all the individual coeffi-

cients ((.47*.46) + (.34*.25) + (.18*.15) + (.18*.21*.25) + (.47*.31*.25) + (.47.

*43*.15) + (.47*.43*.21*.25)). Effect sizes of this kind should be interpreted in much

the same way as Cohen’s d; in this case, an effect size of .42 is, by convention, consid-

ered a small to moderate effect size. As a standard SEM convention, unstandardized

estimates are reported throughout this article (see Brown, 2006; Kline, 2011).

Although standardized coefficients are often used to infer the magnitude of parameter

estimates, there is no reason why unstandardized estimates cannot be interpreted as

effect sizes since all measures adopted a similar response metric (i.e., 1 to 5) (see

Preacher & Kelley, 2011). Moreover, as single-item latent variable models were used,

comparisons between standardized estimates found no appreciable differences, and

even if differences were observed, they were often found at the second or third deci-

mal point.

In Secondary 3 English (Figure 2), model fit is also very good (although not quite

as good as in mathematics). Exam preparation, similarly, has a pervasive and

substantial impact on all other traditional instruction practices: textbook focus (.38),

a focus on worksheets and workbooks (.35), drill and practice of basic facts, rules and

procedures (.54), and memorization (.32). Exam preparation, drill and worksheet

focus in turn have direct pathways to a focus on memorization (.32, .41 and .17,

respectively). In addition, there are a series of indirect pathways from exam prepara-

tion to memorization via textbook focus, worksheet focus and drill. All together these

direct and indirect pathways from exam preparation to memorization add up to a very

large effect size of .66 if we multiply out and add up all the coefficients (.32 +(.38*.28*.17) + (.38*.28*.20*.41) + (.54*.41) + (.35*.17) + (.35*.20*.41)). This

result underscores the very substantial leverage exam preparation has over TI prac-

tices more generally.


Goodness-of-fit statistics:(N = 1027)Chi-square/df/p-value 5.569/2/.0617CFI/TLI .997/.985RMSEA (90% CI)/SRMR .042 (.000–.085)/.012

TextbookFocus

DrillExam

Prepara on

Worksheet Focus

.54(.04) .41(.04)

.20(.04)

Memoriza on

.35(.04)

.38(.04)

.17(.04).28(.04)

.32(.04)

Figure 2. SEMmodel for traditional instruction (English)



Direct instruction. Direct Instruction (DI) has a well-established and well-deserved

track record for its ability to promote student learning for a broad variety of learning

tasks, including the acquisition of content knowledge and procedural skills, and the

execution of relatively straight forward cognitive tasks (Desforges, 1995; Good &

Brophy, 2003, Chapter 9; Hattie, 2003, 2009; Rowe, 2003, 2006; Purdie & Ellis,

2005; NMAP, 2008, Chapter 4). Hattie (2009), however, claims the efficacy of direct

instruction across a broader range of tasks (with a Cohen’s d effect size of .59),

although he also employs a relatively broad conception of direct instruction that is

conceptually close to related notions of mastery learning and active teaching. Our

specification of DI is narrower and includes five first order constructs: a four-indica-

tor measure of maximum learning time (e.g., ‘The teacher makes sure that pupils

focus on the lesson’); a four-indicator measure of review (e.g., ‘The teacher checks

that pupils understand the lesson’); a six-indicator measure of structure and clarity

(e.g., ‘The teacher clearly states the objectives of the lesson’, ‘The teacher organizes

information in an orderly way’, ‘The teacher explains things very clearly’); a single

indicator measure of time on practice (‘We spend a lot of time practicing what we

learned’); and a one-indicator measure of frequency of questioning (‘The teacher asks

the class lots of questions’). The last two scales, having only one indicator each, are

rather thin and far from what we would like to have, but our modelling of the con-

structs indicates that they behave sensibly and usefully, statistically speaking.

The results of the confirmatory factor analysis, reported in summary form in

Table 5, indicate good fit statistics in both subjects. Factor loadings in both subjects

range from the high (.918, .958 respectively in mathematics and English) to the mod-

erately low (.587, .586). There was only one significant error covariance in either sub-

ject between the sole frequency of questioning indicator (‘the teacher asks the class

lots of questions’) and the sole indicator of the frequency of practice.

The mean scores, standard deviations, alphas and effect sizes for the DI scales are

reported in Table 6. In both mathematics and English, maximum learning time

Table 5. CFA higher order factor loadings and goodness-of-fit statistics: direct instruction,

Secondary 3 mathematics and English

Mathematics English


Higher-order factor loadings:

Revision (4) .918 (.015) .958 (.015)

Structure and clarity (6) .849 (.015) .838 (.016)

Maximum learning time (4) .828 (.016) .859 (.015)

Time on practice (1) .677 (.023) .689 (.024)

Frequency of questioning (1) .587 (.026) .586 (.027)



CFI/TLI .991/.989 .985/.981

RMSEA (90% C.I.) .031 (.023–.038) .041 (.034–.049)SRMR .020 .024

68 D. Hogan et al.


scores the highest mean values, followed by structure and clarity and review. These

are important findings that highlight key strengths of Singaporean pedagogy and play

important roles in shaping the overall structure of instructional methods.

As we did before with Traditional Instruction, we can also examine the strength of

the relationships between the DI measures by looking at correlation coefficients

(Table 7). Again, the coefficients are sensible and slightly higher in general in English

than they are for mathematics. However, the absolute values of the coefficients are

generally higher than they are in TI.

But, as with TI, correlation coefficients do not help us understand the strength of

the relationships between the practices controlling for the confounding influence of

other practices. Again, we can represent the strength of these relationships with struc-

tural equation models (Figures 3 and 4). The DI SEM model for both English and

mathematics fit the data exceptionally well, although the model fit is not quite as

strong in English as it is for mathematics. Still, the internal pathway structure of the

two broad instructional strategies are very similar, although not identical, in that DI

for English includes a non-recursive relationship between teacher revision and fre-

quency of practice missing in mathematics. All the structural relationships repre-

sented by the model are strong and statistically significant. On balance, coefficients

are slightly higher in English. In our construction and interpretation of both the math-

ematics and English models we drew upon conventional conceptions of direct

instruction and John Hattie’s (2009) account of visible teaching and learning to

Table 6. Direct instruction, Secondary 3 mathematics and English

Mathematics English

dMean (1–5) SD Mean (1–5) SD

N 1166 1027

Direct instruction

(alpha: .844, .850)

3.61 .668 3.53 .65 .12

Maximum learning time (4) 3.89 .767 3.84 .78 .06

Structure and clarity (6) 3.61 .812 3.56 .78 .06

Teacher revision (4) 3.59 .835 3.52 .77 .09

Frequency of practice (1) 3.49 .952 3.30 .94 .20

Frequency of questioning (1) 3.47 .946 3.44 .91 .03

Table 7. Latent correlation matrix: direct instruction for mathematics and English (mathematics

to the left of the diagonal; English to the right)

MLT REV SNC FOQ FOP

Maximum learning time .85 .72 .48 .53

Teacher revision .78 .78 .55 .67

Structure and clarity .70 .77 .53 .64

Frequency of questioning .47 .55 .51 .58

Frequency of practice .53 .60 .62 .61

Note: All correlations significant at p < .01.



hypothesize that structure and clarity would perform a similar structuring or organizing

role in direct instruction as exam preparation does in traditional instruction. Accord-

ingly, we have treated it as an exogenous variable in both models.

In mathematics, for example, there are strong pathways from structure and clarity

to maximum learning time (.70), indicating that teachers who have structure and

clarity in their lessons are very likely to maximize learning time in their classes. In

English the pathway is slightly stronger (.72). Structure and clarity also has a strong


Goodness-of-fit statistics:(N = 1166)Chi-square/df/p-value 2.296/3/.5134CFI/TLI 1.00/1.00RMSEA (90% CI) .000 (.000–.04)SRMR .006

Teacher Revision

Structure & Clarity

MaximumLearning

Time

Frequency of Ques oning

.70(.03) .43(.04) .30(.04)

.48(.04)

Frequency of Prac ce

.31(.06)

.43(.04).39(.06)

Figure 3. SEMmodel for direct instruction (mathematics)


Goodness-of-fit statistics:(N = 1027)Chi-square/df/p-value 4.421/2/.1097CFI/TLI .999/.994RMSEA (90% CI) .034 (.000–.079)SRMR .008

TeacherRevision

Structure &Clarity

MaximumLearning T

Frequency ofPrac ce

.72(.03)

.27(.05)

.33(.05)

.58(.04)

Frequencyof

Ques oning

.14(.05)

.37(.05)

.47(.07)

.23(.08)

Figure 4. SEMmodel for direct instruction (English)

70 D. Hogan et al.


direct pathway to teacher revision in mathematics (.43) (a measure of the extent to

which teachers revise the work they have done with students previously), and a some-

what weaker pathway to teacher revision in English (.27), a finding consistent with

the conventional folk wisdom about the relative importance of revision in mathemat-

ics. The pathway from structure and clarity in mathematics to frequency of practice is

also strong (.39), and even stronger in English (.47), which probably reflects the

greater attention in English to practicing genre-based work rather than drilling. All

three of these pathways are theoretically and practically sensible in both subjects. In

mathematics both teacher revision (.30) and frequency of practice (.43), in turn, have

direct pathways to frequency of questioning, our key outcome measure in the model.

In English, the two pathways to frequency of questioning have coefficients of .33 (tea-

cher revision) and .37 (frequency of practice) respectively.

Intriguingly, there are no statistically significant direct pathways from structure and

clarity to frequency of questioning in either mathematics or English. Instead, the

effect of structure and clarity on frequency of questioning is indirect in both subjects,

with a total, and very substantial, effect size of .495 in mathematics and .490 in

English. This is an important finding, underscoring the complementary role that tea-

cher questioning can play in enhancing the structure and clarity, and hence the visibil-

ity of teaching and learning, to both teachers and students. In English there is also a

non-recursive relationship between teacher revision and frequency of practice, with a

coefficient of .23 for the pathway from teacher revision to frequency of practice, and a

weaker but still significant pathway from frequency of practice to teacher revision

(.14). This too makes pedagogical sense, in that it suggests that not only do teachers

use revision as a springboard to practice, as we would expect teachers to do, but they

also respond to practice with additional revision if they feel that the students do not

quite understanding what they need to learn. In mathematics the relationship is one

way, from teacher revision to frequency of practice (.30), suggesting in this matter at

least, that mathematics teachers could learn a thing or two from their English

colleagues.

Note: Values represent unstandardized es mates significant at p < .01

Goodness-of-fit sta s cs:(N = 1166)Chi-Square / df / p-value 38.300 / 19 / .0054CFI / TLI .996 / .990RMSEA (90% CI)/ SRMR .030 (.016-.043) / .012

ExamPrepara on

TeacherRevision

Structure &Clarity

MaximumLearning Time

Frequency ofQues oning

.34(.05)

.46(.04)

.10(.04)

.17(.05)

.23(.04)

.13(.05)

.19(.05).28(.05)

.14(.05)

.16(.05)

Frequency ofPrac ce

TextbookFocus

Drill

WorksheetFocus

Memoriza on

.25(.06)

.48(.04)

.18(.04)

.43(.05)

.34(.04)

.33(.05)

.25(.05)

.16(.04)

.45(.06)

.20(.04)

.44(.04)

.31(.05)

.17(.06)

.56(.03)

.29(.04)

.13(.04)

Figure 5. SEMmodel for traditional and direct instruction (mathematics)



The next step in our analysis was to examine the relationships between the TI and

the DI models. We first conducted an integrated CFA of the two sets of measures

followed by an integrated SEM model that incorporated both TI and DI practices

(Figures 5 and 6). We only report the SEM results here. A number of features of the

integrated SEMmodels should be highlighted.

First, the internal structure of the two sets of instructional strategies remained

remarkably stable in the models, with almost identical networks of pathways in the

integrated models that we achieved separately and discussed above. Second, there is

significant asymmetrical interaction between the TI and DI instructional strategies.

Indeed, in mathematics, all the TI constructs have pathways leading to DI constructs,

but none in the reverse direction. This is true as well of English with but one excep-

tion. We tested models that reversed the relationship between DI and TI, as well as

looked for non-recursive relationships (that is, feedback loops) from DI to TI con-

structs. In mathematics this was to no avail. Instead we found that our best fitting

models were ones that ran the pathways from TI to DI. In English, however, we did

identify one pathway from a DI practice to a TI practice: from revision to textbook

focus (.25), indicating that teachers often, at least in English, follow up a revision ses-

sion with a textbook session.

Third, we concluded that the asymmetrical relationship between TI and DI is prin-

cipally a function of the institutional leverage exam preparation has over instructional

practices in Singapore in both subjects. Indeed, there are multiple direct and indirect

paths from exam preparation to other traditional instructional methods and to direct

instructional methods. Because we have positioned it (after testing a number of alter-

native models) as an exogenous variable in the model, it has no pathways into it. But

in mathematics it has a total of seven pathways leading from it towards other TI vari-

ables and all but one of the DI measures as well (maximum learning time). Three of

the coefficients are quite strong—textbook focus (.48), structure and clarity (.46) and

drill (.34)—but most are small to modest. In English, there are six direct pathways


Goodness-of-fit statistics:(N = 1027)Chi-square/df/p-value 47.613/20/.0005CFI/TLI .994/.986RMSEA (90% CI) .037 (.023–.050)SRMR .015

ExamPreparation

TeacherRevision

Structure &Clarity

MaximumLearning

Time

Frequency ofQuestioning

.26(.05)

.52(.04)

.16(.04)

.14(.04)

.34(.04)

.19(.06)

.13(.03)

.17(.05)

.24(.05)

Frequency ofPractice

TextbookFocus

Drill

WorksheetFocus

Memorization

.22(.07).21(.06)

.37(.04).25(.04)

.54(.04)

.42(.04).14(.04)

.18(.04)

.49(.04)

.25(.05).23(.08)

.67(.04)

.30(.04)

.27(.06)

.20(.03)

.15(.06)

Figure 6. SEMmodel for traditional and direct instruction (English)

72 D. Hogan et al.


from exam preparation to TI and DI practices. However, in English, there are no

pathways from exam preparation to teacher revision or frequency of questioning,

indicating that the direct institutional leverage of the examination system over DI

instructional practices in English is slightly lower than it is in mathematics. But for

both subjects, all of the pathways are theoretically sensible, and attest to the institu-

tional authority of the assessment regime over instructional practices in a way that

strengthens the alignment—or, to change the metaphor, tightens the coupling—of

classroom instruction and the national assessment regime.

Fourth, in integrating the two instructional strategies, we positioned the DI out-

come variable, frequency of questioning, as the outcome variable for the integrated

model for both subjects. We did so for three reasons: it worked well statistically in our

SEM model of DI, the importance of teacher questioning and classroom talk more

generally as a gateway to the co-construction of meaning and conceptual understand-

ing, and the fact that we were unable to get as good a fitting model with memorization

as the outcome measure. This is not to say that teachers did not value or employ

memorization as an instructional strategy—but they employed it rather differently in

the two subjects. In mathematics, as we know from Table 3, memorization had the

highest mean score of all the TI instructional practices (4.06), indicating that teachers

relied on it a lot to promote a particular kind of learning that we can assume reflects

their preoccupation with exam preparation. Indeed, it is notable that memorization is

causally dependent on three other instructional methods within TI ensemble: from

worksheet focus (.16), from textbook focus (. 45) and from drill and practice of basic

facts, rules and procedures (.25). But while mathematical teachers clearly find memo-

rization useful as a follow up to other traditional instructional methods, they do not

find it particularly useful as a platform to scaffold further instructional strategies.

Rather, they are more likely to use it as a means of completing a teaching–learningsequence than begin a new one. In English, on the other hand, the mean score (3.47)

indicates that English teachers rely relatively less on memorization than mathematics

teachers do, but they also view it as more potent, instructionally generative and

instrumentally useful than their mathematics colleagues.

Fifth, overall, the total effect size, including both direct and indirect pathways from

exam preparation to frequency of questioning, our key outcome practice, for mathe-

matics is .53 (.17 + .36). For English, it is .48 (indirect effect only as the direct path

was not statistically significant).

Sixth, in Table 3 we reported that focus on textbooks has a relatively high mean

score (3.83) in Secondary 3 mathematics and a relatively low score in English (3.35).

In the SEMmodel for mathematics, textbook focus has only one pathway leading into

it—from exam preparation—but it is highly generative in its impact on other instruc-

tional practices, with seven pathways leading from it to other instructional practices.

Three of these are to other TI practices (drill (.33), memorization (.45) and work-

sheet focus (.43). All of these coefficients are substantial and theoretically meaning-

ful, indicating that the use of textbooks is a prelude to (and therefore predicts) the

other three TI practices. Four other pathways from textbook focus in mathematics

lead to four DI practices: structure and clarity (.13), maximum learning time (.19),

frequency of practice (.28) and frequency of questioning (.13). Overall, the total

effect size of the pathways from textbook focus to frequency of questioning is .17. In



English, the textbook focus is much less strong and pervasive in its impact. Like

mathematics, it only has one pathway into it, from exam preparation (.21), but unlike

mathematics, it only has three (rather than seven) pathways leading from it: to work-

sheet focus (.25), frequency of practice (.13) and frequency of questioning (.14). This

suggests that English teachers rely less on textbooks to shape their instruction than

teachers do in mathematics. However, the SEM model indicates that there is moder-

ately strong feedback loop from teacher revision (.27) back into textbook focus, indi-

cating that teachers often follow up a revision session with a return to the textbook in

use, and so the cycle begins again.

Seventh, two DI practices play structurally important roles generatively: structure

and clarity, and teacher revision. In mathematics, structure and clarity is predicted by

three TI practices, two of them with substantial coefficients: textbook focus (.13),

drill (.29) and exam preparation (.46). This is an important finding, attesting to

the causal importance of TI, particularly exam preparation, given the size of its

coefficient, to the enactment of DI practices. In English, structure and clarity is pre-

dicted by three TI practices: drill (.30) and exam preparation (.52). No DI practices

predicted structure and clarity in either mathematics or English. In turn, as a predic-

tor variable, in both mathematics and English, structure and clarity has three path-

ways from it to other DI practices: maximum learning time (.56 and .67 respectively),

teacher revision (.31 and .25 respectively) and frequency of practice (.25 and .22

respectively). There is no statistically significant pathway from structure and clarity to

frequency of questioning in either mathematics or English, replicating our finding of

the SEM model of DI above. But structure and clarity does have an indirect effect on

frequency of questioning through four pathways in mathematics and English—from

structure and clarity to maximum learning time (MLT) to teacher revision to fre-

quency of questioning; from structure and clarity to teacher revision to frequency of

questioning; from structure and clarity to teacher revision to frequency of practice to

frequency of questioning; and from structure and clarity to MLT to teacher revision

to frequency of practice to frequency of questioning. The combined indirect effects

sum up to a moderate effect size of .21 in mathematics and .23 in English. This again

is an important finding, in that it underscores not only the multiplier effects that

structure and clarity has on other instructional practices, but its ability to help gener-

ate ‘visible’ teaching and learning.

Eighth, a second DI practice, teacher revision, also plays a pivotal role in the inte-

grated model. In mathematics, revision is predicted by three practices: two fraternal

DI practices—MLT (.44) and structure and clarity (.31)—and one first cousin TI

practice, the ubiquitous exam preparation (.23). Teacher revision in turn predicts fre-

quency of questioning through two pathways: directly (.16) and indirectly through

frequency of practice (.17*.34) for a total effect size of .22 for mathematics and .25

for English. In English, we observed some similar but also some unique pathways into

and out of revision. Similar to mathematics, revision is predicted by maximum learn-

ing time (.49) and structure and clarity (.25). However, a unique predictor of revision

found in English, but not mathematics, is memorization (.20). Revision goes on to

predict frequency of questioning directly (.19), but also indirectly through frequency

of practice (.23*.26) for a total effect size of .25. However, we found a significant

effect for a feedback loop connecting revision and textbook focus (.27), and again the

74 D. Hogan et al.


cycle repeats itself—through worksheet focus, drill and memorization, including

some other indirect pathways through structure and clarity and maximum learning

time—resulting in an increased effect size of .30 from revision to frequency of ques-

tioning. This feedback is unique to English and together with the effect of memoriza-

tion on teacher revision which we found earlier, they suggest that perhaps traditional

instruction is more visible as a pedagogical practice among English teachers.

Finally, in mathematics, frequency of practice is predicted by two DI practices and

two TI practices: structure and clarity (.25), teacher revision (.17), textbook focus

(.28) and exam preparation (.14). In turn it has a solitary but relatively substantial

pathway from it to frequency of questioning (.34). In English, it is predicted by three

instructional practices: memorization (.17), textbook focus (.13) and exam prepara-

tion (.15), but it in turn predicts frequency of questioning (.26), indicating that teach-

ers often follow up a practice session with more questioning, surely sensible.

Overall then, the SEM for TI and DI mathematics generates a good fitting model

with a dense, asymmetrical network of pathways leading from the TI ensemble of

instructional practices, exam preparation above all, to the DI instructional practices

with a high value instructional practice, frequency of questioning, as the key outcome

variable. However, the density and strength of these pathways casts considerable

doubt on the idea that we can view TI and DI as discrete instructional categories and

underscores the wisdom of viewing them, at the construct level, as constituting an

integrated, theoretically meaningful hybridic model of instructional practice and that

underscores the exceptionally strong institutional leverage of the assessment system

over instructional practice in Singapore. In English, likewise, the SEM model for TI

and DI is very strong but it also generated a slightly less asymmetrical model between

TI and DI because of the non-recursive feedback from teacher revision to textbook

focus. In addition, English teachers appear to make much greater instrumental use of

memorization focus to leverage additional instructional practices than do mathemat-

ics teachers.

Teaching for understanding (TfU) and co-regulated learning strategies. In this section we

want to consider two quite closely related scales: a teaching for understanding scale

that draws substantially on existing teaching for understanding frameworks, and a co-

regulated learning strategies scale that draws heavily on research on metacognitive

self-regulation. Initially, we considered the latter an aspect of the former, but confir-

matory factor analysis and a number of theoretical considerations convinced us to

consider them separately, although the two are, if not identical twins, closely related

siblings, theoretically speaking.

What we have called the teaching for understanding (TfU) framework shares a

common intellectual sensibility (if not identical constructs) with Harvard Univer-

sity’s Project Zero’s Teaching for Understanding framework (Perkins, 1993) and

Good and Brophy’s expansive account of ‘teaching for understanding’ that draws in

turn on a variety of intellectual resources particularly constructivist (and particularly

social constructivist) models of knowledge, learning and teaching (Brophy, 2002,

2004; Good & Brophy, 2003, Chapter 10). But we have also drawn on other theo-

retical resources as well: the Understanding by Design framework developed by Wig-

gins and McTighe (2005); the ‘authentic pedagogy’ of Newmann and his



colleagues at the University of Wisconsin (Newmann et al., 1995); conceptions of

‘thoughtful discourse’, ‘dialogical teaching’ and ‘understanding talk’ variously

developed by Douglas Barnes (1992, 2008), Robin Alexander (2001, 2008), Neil

Mercer and his colleagues (Mercer, 1992; Mercer & Littleton, 2007; Hodgkinson &

Mercer, 2008), Courtney Cazden (Cazden, 1988), Lauren Resnick (Resnick et al.,

2010), Sarah Michaels and colleagues (Michaels et al., 2002, 2004, 2008),

Nystrand and colleagues (Nystrand et al., 1999, 2001) and John Hattie’s recent and

important account of ‘active teaching’ and ‘visible learning’ (2009, 2012). Our

attention to co-regulated learning strategies (CRLS) reflects a research judgment

reached over the past couple of decades that metacognitive self-regulation is a

strong determinant of academic achievement and a key capacity for successful nego-

tiation of twenty-first century institutions (OECD, 1999; Good & Brophy, 2003;

Galton, 2007; James et al., 2007; Hacker et al., 2009; Hattie, 2009, 2012; Zimmer-

man & Schunk, 2011).

Our initial specification of the teaching for understanding (TfU) framework

focused on the following 12 scales, subsequently reduced to 11 when we combined

the 3rd and 4th indicators because of very high collinearity:

(1) An effective focus on developing on understanding (six indicators; e.g., ‘The tea-

cher’s explanations really help me understand the topic’; ‘Class discussions

really help me understand the topic’).

(2) Asking high quality questions designed to prompt students to think about their

learning (four indicators; e.g., ‘The teacher asks good questions to see if we

really understand’; ‘The teacher’s questions help us to think deeply’; ‘The tea-

cher asks lots of questions that open up discussion’).

(3) Communicating learning goals (four indicators; e.g., ‘The teacher tells us the learn-

ing objectives of the lesson’).

(4) Communicating performance standards (four indicators; e.g., ‘The teacher explains

the standard of good performance in our tests and exams’).

(5) Actively attempting to engage students in the work of the class by exciting student

interest and curiosity (five indicators; e.g., ‘The teacher makes mathematics/

English really interesting’).

(6) Flexible teaching: adjusting instructional methods when appropriate as the task or

levels of student engagement require (three indicators; e.g., ‘The teacher tries

different kinds of teaching to help us understand better’; ‘The teacher changes

the speed of the lesson’).

(7) Engaging students in meaningful class discussions (one indicator; e.g., ‘The tea-

cher supports long class discussions about topics’).

(8) Support for collaborative group work (two indicators; e.g., ‘The teacher encour-

ages students to work as a team in group work’).

(9) Teacher scaffolding of group work to ensure that students work together collabora-

tively rather than simply alongside each other (three indicators; e.g., ‘The

teacher shows us how to work together in groups’).

(10) Continuous teacher monitoring of student learning—i.e., feedback from the stu-

dent to the teacher (four indicators; e.g., ‘The teacher asks the class questions to

see how well we understand the topic at the beginning of the class’).

76 D. Hogan et al.


(11) Regular personal feedback from teachers to students about the quality of their

work (five indicators; e.g., ‘The teacher gives me personal comments on my

homework’).

(12) Regular collective feedback from teachers to students about the quality of their

work (five indicators; e.g., ‘The teacher gives the class detailed comments on

exams or tests’).

We report the results of the TfU CFAs for mathematics and English in Table 8. Fit

statistics are very good for both subjects. In addition, in both subjects, quality of ques-

tioning and focus on learning have the highest factor loadings. This is an especially

important finding, indicating that both of these constructs are close to the centre of

the covariance structure of the larger TfU construct. The strength of flexible teaching

is also notable, emphasizing the pivotal importance of flexible teaching to the TfU

framework and supporting the decision to include it in the TfU scale rather than the

DI scale. The strength of the monitoring of student learning aligns very well with the

arguments of Hattie (2009, 2012) and others regarding the critical contribution of

monitoring to visible teaching and learning. Factor correlations fall within an accept-

able range (Table 10), except for two (focus on learning and quality of questioning,

and monitoring student learning and quality of questioning) which are both high and

Table 8. CFA higher order factor loadings and goodness-of-fit statistics: teaching for

understanding, Secondary 3 mathematics and English

Mathematics English


Higher-order factor loadings:

Quality of questioning (4) .906 (.011) .919 (.010)

Focus on learning (6) .882 (.013) .933 (.010)

Communicating learning

goals and performance

standards (8)

.873 (.011) .885 (.011)

Monitoring student

learning (4)

.851 (.013) .880 (.014)

Flexible teaching (2) .820 (.019) .854 (.019)

Collective feedback (4) .572 (.024) .487 (.028)

Collaborative group

work (2)

.570 (.027) .699 (.022)

Curiosity and interest (4) .565 (.024) .518 (.026)

Teacher scaffolding of

group work (3)

.549 (.024) .737 (.019)

Whole class discussion (1) .545 (.026) .686 (.022)

Personal feedback (4) .528 (.026) .427 (.029)



CFI/TLI .966/.964 .974/.972

RMSEA (90% C.I.) .033 (.031–.035) .029 (.027–.032)SRMR .034 .028



statistically significant, indicting substantial error covariance. However, we thought

all the error covariances theoretically justified and adjusted for them in the final

respecified model.

In English, the strong factor loadings were led by focus on learning (.933), quality

of questioning (.919), communicating goals and standards (.885), monitoring stu-

dent learning (.880) by and flexible learning (.854).The stronger factor loadings for

focus on learning and quality of questioning in English than in mathematics are espe-

cially notable—and not a little surprising. Inter-factor correlations are all reasonable

(see Table 10), as are error covariances. Finally, apropos our decision to include flexi-

ble teaching in the TfU rather than the DI scale, it is worth noting that flexible teach-

ing has the strongest factor loadings in both mathematics and English.

In Table 9 we report the mean scores and standard deviations for the two TfU

scales in both subjects. Overall, the mean scores for TfU were substantially lower

than the mean scores for TI and DI for both subjects: 3.38 in mathematics, and 3.43

in English. However, within subjects mean scores differences between scales are quite

large. In mathematics, for example, the mean scores range from a low 2.79 for teacher

scaffolding of group work to 3.59 for collective feedback. In English, mean scores var-

ied from a low of 3.21 for whole class discussion to a high of 3.58 for collective feed-

back and 3.55 in communicating goals and standards.

From a theoretical perspective, the relative strength of communicating learning

goals and standards, collective feedback, flexible teaching, and monitoring student

learning all indicate the implicit but relatively substantial commitment of Singapore’s

teachers to a ‘visible’ model of teaching and learning (Hattie, 2009). Indeed, we think

this is a good news story, pedagogically speaking, although the weak score for per-

sonal feedback indicates a major gap in the instructional repertoire of Singapore’s

Table 9. Teaching for understanding, Secondary 3 mathematics and English

Mathematics English


N 1166 1027

Teaching for Understanding scale 3.38 .602 3.43 .564 .09

Collective feedback 3.59 .805 3.58 .766 .01

Communicating learning goals

and performance standards

3.57 .771 3.55 .681 .03

Flexible teaching 3.57 .873 3.47 .829 .12

Monitoring student learning 3.46 .801 3.48 .724 .03

Personal feedback 3.43 .829 3.47 .838 .05

Focus on learning

(understanding)

3.36 .710 3.43 .704 .10

Quality of questioning 3.34 .790 3.41 .733 .09

Curiosity and interest 3.25 .898 3.33 .894 .09

Whole class discussion 2.97 1.040 3.21 .929 .24

Collaborative group work 2.87 .962 3.28 .831 .46

Teacher scaffolding of group

work

2.79 1.023 3.28 .849 .52

78 D. Hogan et al.


Table

10.

Latentco

rrelationmatrix:teach

ingforunderstandingformathem

atics

andEnglish

FT

FOL

QTQ

SCF

MSL

PFB

CFB

CNI

CLGPS

CGW

WCD

Flexibleteach

ing(F

T)

.73

.73

.46

.70

.42

.47

.44

.73

.46

.44

Focu

sonlearning(F

OL)

.78

.79

.47

.74

.46

.52

.50

.80

.48

.43

Quality

ofquestioning(Q

TQ)

.78

.87

.53

.79

.47

.51

.52

.77

.57

.55

Teach

erscaffoldingofgroupwork

(SCF)

.64

.72

.66

.46

.32

.30

.34

.45

.80

.58

Monitoringstuden

tlearning(M

SL)

.78

.79

.81

.65

.44

.47

.46

.74

.48

.46

Personalfeed

back

(PFB)

.41

.37

.38

.33

.39

.81

.72

.47

.32

.31

Collectivefeed

back

(CFB)

.47

.41

.45

.38

.44

.78

.77

.53

.26

.23

Curiosity

andinterest(C

NI)

.49

.47

.47

.36

.46

.73

.78

.50

.34

.33

Communicatinglearninggoalsand

perform

ance

standards(C

LGPS)

.74

.84

.81

.63

.81

.38

.45

.45

.47

.47

Collaborativegroupwork

(CGW

).63

.66

.64

.82

.62

.35

.35

.38

.60

.77

Wholeclass

discu

ssion(W

CD)

.59

.66

.65

.62

.58

.33

.34

.38

.57

.69

Note:Allco

rrelationssignificantatp<.01.Correlationsformathem

atics

are

totheleftofthediagonalandEnglish

totheright.



teachers in both English and mathematics. More broadly, the relatively low scores for

focus on learning and quality of questioning are especially troubling while the particu-

larly low scores for collaborative group work, whole class discussion, scaffolding of

group work, curiosity and interest and personal feedback points to critical weak spots

from a TfU perspective, particularly with regard to the value of classroom talk as a

means of co-constructing meaning and developing conceptual understanding.

Correlations between the latent TfU measures are reported in Table 10. In gen-

eral, in both subjects, these are moderate to large. The strength of the correlations

between focus on learning and the remaining TfU variables, is particularly notable

and affirmative of the empirical, as well as theoretical, warrant for the TfU scale. We

consider the SEMmodels for TfU and CRLS jointly in light of their intimate concep-

tual (and, as it turns out, empirical) relationship (Figures 7 and 8).

As we have seen, our TfU scale is based on 11 separate (but relatively highly inter-

correlated) subscales. The co-regulated learning strategies scale (CRLS) scale is a

second order construct that builds on three multi-item first order scales for self-direc-

ted learning, self-assessment, and peer assessment and draws on recent theoretical lit-

erature (National Research Council, 2000, pp. 14–18; Paris & Paris, 2001; Nota et

al., 2004; Mok et al., 2006; James et al., 2007, pp. 3, 5; Darling-Hammond, 2008;

Hacker et al., 2009; Hattie, 2009; Zimmerman & Schunk, 2011). Meanwhile, a num-

ber of researchers have given considerable thought to how students might learn meta-

cognitive self-regulation. Dylan Wiliam, for example, argues that peer and self-

assessment is a particularly effective mechanism for developing the classroom as a co-

regulated learning environment (CRLE) and cultivating metacognitive self-regulation

and student management of their learning (Black et al., 2003, pp. 49–56; Wiliam,

2007, pp. 1076–1084).As an example, our specification of the CRLS and the CFA for the three compo-

nent sub-scales for English are reported below in Table 11. The models generated

Note: All values represent unstandardized estimates significant at p < .01. In brackets are standard errors. Double-headed curved arrows denote correlated latent disturbances.

Goodness-of-fit statistics: mathematics(N = 1166)Chi-square/df/p-value 75.248/49/.0094CFI/TLI .997/.996RMSEA (90% CI) .021 (.011–.03)SRMR .015

.14(.03)

.70(.04)

.43(.04)

.20(.04)

.23(.05)

.35(.05)

.36(.05)

.28(.06)

.28(.04) .43(.04)

.49(.06)

.37(.04)

.40(.04)

Monitor Student Learn

Collec ve Feedback

Focus on Learning

Comm Goals/stan

Teacher Scaffolding

Quality of Ques on

Flexible Teaching

Curiosity & Interest

Personal Feedback

.31(.04)

.24(.05)

.63(.04)

.57(.04)

.11(.03)

Whole Class Disc

Collabora ve GpWk

.55(.03)

.61(.04)

.12(.03)

.12(.03)

.25(.04)

CRLS .63(.04)

.19(.03)

.15(.04)

.13(.03)

Figure 7. SEMmodel for Teaching for Understanding and co-regulated learning strategies:

mathematics

80 D. Hogan et al.


strong goodness-of-fit statistics and factor loadings. All three scales are also highly—but not too highly—correlated. Factor loadings are all quite high, with one especially

high (personal assessment in English), a result that is not statistically troublesome but

that suggests that at least in English, personal assessment is an exceptionally proxy

for, and is indistinguishable from, the higher order latent construct (CRLS).

Table 12 reports the mean values, standard deviations and effect sizes of our mea-

sures for CRLS. What they indicate is that in 2010, teachers provided moderate

opportunities for self-directed learning, but far fewer opportunities for self-assess-

ment or peer assessment in both mathematics and English. The findings also indicate

that opportunities for CRLS are stronger in Secondary 3 English classes than in Sec-

ondary 3 mathematics classes.

Figures 7 and 8 report the TfU/CRLS SEM models for mathematics and English

respectively. (We also ran the TfU models separately with focus on learning rather

than CRLS as the key outcome variable, but since the results are almost identical to

the combined TfU/CRLS models, we have decided to report on the latter only here.)

Both models have exceptional good fit, rich, sensible and suggestive networks of path-

ways, strong coefficients, and theoretical gravitas. The selection of focus on learning

as the key outcome variable in the TfU models reflects our argument earlier that it

indexes the degree to which teachers focus on their instruction on meaning making

and developing student understanding at the heart of the TfUmodel generally. CRLS

as an outcome measure, on the other hand, identifies the extent to which teachers

seek to give students the opportunity to manage their own learning in line with the

substantial research on metacognition that underscores its importance in student

learning. In both subjects CRLS is positioned as an endogenous outcome measure

rather than a mediating variable that predicts variation in focus on learning. We also

attempted to see whether we could position CRLS as a predictor of focus on learning,

Note: All values represent unstandardized estimates significant at p < .01, *p < .05. Double-headed curved arrows denote correlated latent disturbances.

Goodness-of-fit statistics: English(N = 1027)Chi-square/df/p-value 74.146/52/.0235CFI/TLI .997/.996RMSEA (90% CI) .020 (.008–.030)SRMR 0.17

.26(.04)

.65(.04)

.52(.06)

.28(.06)

.16(.05).38(.05)

.32(.05)

.30(.05)

.40(.05) .26(.05)

.53(.05)

.29(.06)

.28(.06)

Monitor Student L

Collec ve Feedback

Focuson Learning

Comm Goals/stan

Teacher Scaffolding

Quality of Ques on

Flexible Teaching

Curiosity & Interest

Personal Feedback

.20(.05)

.40(.04)

.80(.04)

.65(.04)

Whole Class Disc

Collabora ve GpWk

.47(.07)

.43(.04)

.16(.03)

.43(.04)

.25(.07)

CRLS

.87(.05)

*.10(.05)

Figure 8. SEMmodel for Teaching for Understanding and co-regulated learning: English



Table 11. CFA co-regulated learning in Secondary 3 English

Variable

Standardized parameter estimates

Initial model Respecified model

11 items 10 items

Self-directed learning

The teacher encourages us to set

our own learning goals

.755 (.013) .758 (.013)

The teacher encourages us to

identify strategies to achieve our

learning goals

.823 (.011) .821 (.011)


check frequently that our work is

acceptable

.764 (.013) .764 (.013)

Personal assessment

The teacher asks us to grade our

own work

.729 (.013) .733 (.013)

The teacher explains how we can

grade our own work

.788 (.011) —

The teacher expects us to discuss

our own grading of our own work

.796 (.011) .813 (.011)


comment on our own work

.798 (.011) .810 (.011)

Peer assessment

The teacher asks students to grade

each other’s work

.815 (.010) .816 (.010)

The teacher explains how we can

grade each other’s work

.805 (.010) .800 (.010)

The teacher expects us to discuss

our grading of each other’s work

.825 (.010) .827 (.010)


comment on each other’s work

.810 (.010) .812 (.010)

Latent correlations:

Self-directed learning↔ personal

assessment

.851 (.012) .818 (.014)

Self-directed learning↔ peer

assessment

.666 (.018) .666 (.018)

Personal assessment↔ peer

assessment

.799 (.013) .783 (.014)

Higher order factor loading:

Self-directed learning .842 (.013) .834 (.014)

Personal assessment 1.01 (.010) .981 (.012)

Peer assessment .791 (.014) .798 (.014)



CFI/TLI .983/.977 .989/.985

RMSEA (90% C.I.) .052 (.045–.058) .044 (.037–.052)SRMR .021 .018

Note: The factor loadings were fixed to equality as the standardized estimates for personal assessment in initial

model was > 1.0.

82 D. Hogan et al.


on the grounds that teachers might use CRLS to enhance their focus on learning. But

the goodness-of-fit statistics with CRLS as a predictor variable is not as strong as the

excellent goodness-of-fit statistics with CRLS as the outcome variable in the two

models (in mathematics, a chi-square of 180.349/49/.000 versus 75.248/49/.094; in

English, 178.412/52/.000 versus 74.146/.52/.0235).

Before deciding on the final models, we tried a range of alternative models with dif-

ferent exogenous constructs, including flexible teaching and monitoring student

learning, but could not make the models work as well (as measured by the goodness-

of-fit statistics). Beyond this, a number of features of the two models stand out.

We begin with the two key outcome measures: co-regulated learning strategies

(CRLS) and focus on learning (FOL). But before we do, it’s important to recall that

in mathematics, the mean score for CRLS is a very low 3.01, in English, 3.28, indicat-

ing that teachers do not employ CRLS particularly often, especially in mathematics.

Nor does the use of CRLS, such as it is, alter the pattern and strength of the overall

structure of TfU practices in any obvious way in either of the two subjects if we com-

pare the two TfU SEMS with the CRLS SEMS. Instead, the internal structure of the

two models remains remarkably stable. In mathematics, CRLS is predicted multivari-

ately by teacher scaffolding of group work (.19), by whole class discussion (.13), by

focus on learning (.63) and by communication of learning goals and performance

standards (.15). All these are theoretically sensible. Of these, by far the strongest and

most interesting is focus on learning, for what this pathway suggests is that teachers

do not so much employ CRLS to increase their focus on learning but use a focus on

learning to scaffold a transition to CRLS. The one construct missing that we also

expected to predict CRLS is collaborative group work, although there is an indirect

pathway from it through teacher scaffolding of group work (.70*.13 = .09). In Eng-

lish, there are only two statistically significant pathways into CRLS: focus on learning

(.87) and flexible teaching (.10). Both of these are theoretically sensible. Indeed, all

told, the source of the strongest indirect effect on CRLS in both subjects is flexible

teaching.

We positioned focus on learning as the key endogenous outcome measure in the

two TfU models and as the penultimate outcome measure in the two CRLS models.

In both the TfU and CRLS models focus on learning (FOL) shares three predictors

in both subjects: communication of learning goals and standards (.36 and .32 respec-

Table 12. Co-regulated learning strategies, Secondary 3 English and mathematics

Mathematics English


Co-regulated learning

strategies (Alpha =.918, .920)

3.01 .770 3.28 .688 .37

Self-directed learning 3.41 .794 3.45 .747 .05

Self-assessment 2.92 .907 3.20 .782 .33

Peer assessment 2.80 .945 3.23 .802 .49



tively), quality of questioning (.35 and .38), and flexible teaching (.23 and .16). In

addition, in mathematics, for example, there are indirect pathways from flexible

teaching to focus on learning via quality of questioning (.20*.35 = .07) and commu-

nicating learning goals (.37*.36 = .133), while in English there are, for example, the

following indirect pathways: one via quality of questioning, whole class discussion,

collaborative group work and teacher scaffolding (.28*.47*.43*.65*.16 = .005), one

through whole class discussion, collaborative group work and teacher scaffolding

(.25*.43*.65*.16 = .011), and the third through collaborative group work, teacher

scaffolding of group work and focus on learning (.43*.65*.16 = .04). While the indi-

rect effects are small, they are theoretically sensible.

Flexible teaching (FT) functions as a critical lynchpin in all four TfU/CRLS mod-

els. We know from Table 9 that the mean scores for FT for both mathematics and

English are moderately high (3.57, 3.47 respectively), relatively speaking, although

against informal statistical protocols, these means are not especially high. Still,

although it has only one pathway leading into it (curiosity and interest with a respect-

able coefficient of .24), in mathematics, it has four pathways leading out of it: moni-

toring student learning (.63), communication of learning goals and standards (.37),

focus on learning (.23), quality of questioning (.20). In English, there are seven path-

ways emanating from FT: monitoring student learning (.80), communication of

learning goals and standards (.29), focus on learning (.16), quality of questioning

(.28), whole class discussion (.25), collaborative group work (.43) and self-directed

learning (.10). Not all of these are substantial coefficients, but one is very substantial

and the others moderate to strong. We interpret the striking generativity of FT, espe-

cially in English, to signify the pragmatic, non-sectarian instrumentalism of Singapo-

rean instruction.

For some researchers, feedback promises to be the Holy Grail of instructional prac-

tice. This might well prove to be the case but it’s clear from the mean scores reported

in Table 9 that teachers in both mathematics and English provide relatively substan-

tial levels of collective feedback to their students (3.59 and 3.58 for collective feed-

back respectively), but lower levels of personal feedback to their students (3.43 and

3.47 respectively). This suggests room for improvement, particularly in the provision

of personal feedback, given its demonstrable ability to enhance student understanding

and learning (Black & Wiliam, 1998; Hattie, 2009). This judgement is reinforced by

the fact that both forms of feedback generate only one pathway each—and both to

curiosity and interest (.49 and .28 respectively in mathematics, and .53 and .30

respectively in English). These are significant coefficients, nearly identical across sub-

jects, and theoretically sensible, since we can easily understand why teachers would

deliberately use feedback to students to build interest and curiosity among them. The

oddity is that the coefficients are stronger for collective feedback rather than personal

feedback, suggesting, given international research findings, that Singaporean teachers

do not fully exploit the ability of personal feedback to build student engagement as

much as they might. There are of course multiple indirect effects from the two forms

of feedback to focus on learning, both going through curiosity and interest, but once

these are multiplied out, the overall effect size is relatively small (.13 and .17 for

mathematics and English for collective feedback, and .08 and .10, respectively, for

personal feedback; Tables 13 and 14). This too reinforces the conclusion that the

84 D. Hogan et al.


overall generativity of the two modes of feedback is very low. This in itself does not

challenge the argument of Black and Wiliam and others who have argued for the

unique strength of the impact feedback on student learning given that we are measur-

ing instructional practices rather than student learning, but it reinforces the impres-

sion that Singaporean teachers do not employ feedback as often or as generatively as

they might.

A further feature of feedback practices in both mathematics and English is that

both forms of feedback are predicted by the communication of learning goals and

standards (and with reasonably robust coefficients, especially in mathematics), and in

so-doing enhance the visibility of learning processes in the classroom. However, there

are no pathways from the monitoring of student learning to either of the feedback

constructs in both models. This is, to put it mildly, paradoxical, for we would nor-

mally expect teachers to provide feedback only after they have assessed the state of

student learning in their classroom, not without it. What the absence of these path-

ways suggests is that teachers do not follow up monitoring with feedback practices.

However, given the nature of the data we cannot draw firm conclusions on this mat-

ter—it merely indicates a suboptimal pattern of instructional behavior that we will test

further with qualitative data in a later publication. We will also use qualitative data to

follow up on the intriguing pathway from collaborative group work to personal feed-

back in mathematics. Although small (.12), it is statistically significant and intriguing,

suggesting teachers occasionally follow up group work with personal feedback to indi-

vidual students within the group.

We expected that curiosity and interest would exhibit a dense network of pathways

backwards and forwards, but we did not find this to be the case. In both mathematics

and English, personal and collective feedback predicted curiosity and interest,

although the coefficients for collective feedback are far higher (.49 and .53 respec-

tively) than they are for personal feedback (.28, .30 respectively). It is also the case

that in both subjects, teachers provide collective feedback more often than they do

personal feedback. In effect, teachers are far more likely to follow up collective feed-

back with activities that engage student interest and curiosity than they do following

personal feedback. Normatively, this is not optimal, given that research findings gen-

erally suggests that personal feedback, appropriately given, is far more likely to

enhance student learning than collective feedback (Hattie, 2009). At the same time,

however, the generativity of curiosity and interest is quite limited in both subjects. In

mathematics, there are two pathways from curiosity and interest, one to flexible

teaching (.24), one to quality of questioning (.11). Apparently, teachers respond to

student curiosity and interest by becoming more flexible and asking more demanding

questions. We expected to find that the pathways would go in the opposite direction,

but when tested, they were not statistically significant. In English there is only one

generative pathway—to flexible teaching (.40).

Whereas we included a measure of the frequency of questioning (FOQ) in the

Direct Instruction scale, we included a measure for quality of questioning (QTQ) in

the TfU scale designed to capture whether or not the questions teachers ask their stu-

dents develop their understanding of the topic or task (as in, for example, ‘the teacher

asks good questions to see if we really understand’). The news on the QTQ front is

mixed. The bad news is that the mean scores for the QTQ scale in both subjects are



relatively low (3.34 and 3.41 respectively; Table 9). The good news is that QTQ is

heavily enmeshed in a network of instructional practices. On the one hand, it is pre-

dicted by communication of learning goals and standards in both mathematics and

English (.28 and .40 respectively), flexible teaching (.20 and .28) and student moni-

toring (.28 and .40). Curiosity and interest also predicts QTQ but in mathematics

only (.11). On the other hand, QTQ predicts other instructional practices in turn:

focus on learning (.35 and .38), whole class discussion (.55 and .47), collaborative

group work (mathematics only, .25) and teacher scaffolding of group work (.14, .26).

In effect, the quality of teacher questioning matters, and matters a lot, especially

where it counts in generating whole class discussion and a focus on learning.

We suggested earlier, following John Hattie’s work, that communication of learning

goals and performance standards (CLGPS) is a key indicator of ‘visible learning’ that

he found to be highly predictive of successful teaching and learning. We also indi-

cated that relative to other instructional practices, Singaporean teachers do reasonably

well in this regard, with a mean score of 3.57 in mathematics and 3.55 in English.1.

CLGPS is predicted by monitoring of student learning (.43 and .52 respectively in

both mathematics and English), and by flexible teaching (.37 and .29 respectively).

These coefficients are both substantial and theoretically sensible: the first indicates

that teachers often respond to their monitoring of student learning with statements or

reiterations of their learning goals and performance standards, while the latter sug-

gests that teachers, as a part of their repertoire of effective teaching, state or reiterate

their learning goals and performance standards for the lesson. However, the SEM

model indicates that teacher communication of learning goals and performance stan-

dards is not especially generative in its own right, given that it generates only two

direct pathways in each subject: to focus on learning (.36 and .32 respectively) and to

quality of questioning (.28 and .40 respectively). However, there is an indirect path-

way from communication of learning goals and performance standards to focus on

learning via quality of questioning in both mathematics (.28*.35 = .10) and English

(.40*.38 = .152), along with, for example, indirect pathways in English via quality of

questioning, whole class discussion, collaborative group work and and teacher scaf-

folding of group work.

There is by now a substantial body of academic research that has focused on the

educational value of appropriately structured classroom dialogue—see, for example,

Barnes (1992, 2008), Alexander (2001, 2008, 2012), Mercer and his colleagues

(Mercer, 1992; Mercer & Littleton, 2007; Hodgkinson & Mercer, 2008), Cazden

(1988), Resnick (Resnick et al., 2010), Nystrand and colleagues (Nystrand et al.,

1999, 2001), Michaels and colleagues (Michaels et al., 2002, 2004, 2008) and Hogan

et al. (2012b). While our measure of whole class discussion does not specify key indi-

cators of ‘dialogue’ per se it does indicate in a very general way the frequency with

which teachers allow or support extended class discussions of various topics. The

mean scores reported in Table 9 indicate, however, that teachers do not permit

extended whole class discussions very often in either subject. In mathematics, the

mean score is a very low 2.97, and in English, a slightly better 3.21, but relative to

other TfU instructional practices in English, it is the instructional practice with the

lowest mean score in the larger TfU inventory. The SEM models also indicate that

whole class discussion is only weakly embedded in the network of TfU/CRLS

86 D. Hogan et al.


instructional practices in the two subjects. In mathematics, whole class discussion is

predicted by the quality of teacher questioning (.55) and nothing else. In English, it is

predicted by the quality of teacher questioning (.47) and by flexible teaching (.25),

suggesting that whole class discussion is a standard element of the flexible teaching

repertoire, at least in English, as well as a sensible follow-up activity that teachers

employed after asking high quality questions. Yet, surprisingly, whole class discussion

is not particularly generative in its own right in either subject, leading only to collabo-

rative group work (.61, .43 respectively, in mathematics and English).

The last two—and closely related—constructs we want to discuss focus on collabo-

rative group work and teacher scaffolding of group work. The former construct mea-

sures the frequency with which teachers ‘breaks the students up into small groups to

work together’. The latter focuses on the efforts teachers make to structure group

work in a way that builds an effective division of labor with a high level of interdepen-

dency by showing ‘us how to work together in groups’. While asking students to work

in groups collaboratively is all well and good, as Galton (2007) and others have

reminded us over many years, without careful teacher scaffolding of group work the

students are likely to end up working individually in pseudo groups rather than collec-

tively and collaboratively. But the theoretical promise is high; the mean scores for

both sets of constructs in both subjects are very low, especially in mathematics (2.87

and 2.79). In English, the mean scores are a little higher for both constructs (3.28

and 3.28). In short, mathematics and English teachers in Singapore, especially math-

ematics teachers, make little use of collaborative group work in their classes. In addi-

tion, there are only very limited pathways into and out of the two constructs. In

mathematics, collaborative group work is predicted by whole class discussion (.61)

and by the quality of questioning (.25). In English, whole class discussion also pre-

dicts collaborative group work (.43), but not quality of questioning. Instead, collabo-

rative group work is also predicted by that highly energetic TfU pivotal construct,

flexible teaching (.43). In effect, in both mathematics and English, teachers often

segue from whole class discussion into small group work, but in mathematics, teach-

ers often follow up demanding questions with collaborative group work, whereas in

English, collaborative group work appears to be a more basic staple of teachers’

instructional repertoire. In both mathematics and English, teacher scaffolding of

group work is predicted, reasonably enough, by collaborative group work itself (.70

and .65 respectively) and, perhaps less predictably, occasionally by the quality of

questioning (.14 and .26), suggesting that teachers occasionally—very occasionally—use high quality questions to set up the structure of the group work. There is also a

weak pathway from collaborative group work to personal feedback (.12) in mathe-

matics, indicating that teachers sometimes provide personal feedback on the basis of

their work in small groups, at least in mathematics. The generativity of teacher scaf-

folding though is very limited, with no pathways leading from it to other instructional

practices in mathematics and only one weak pathway, from teacher scaffolding to

focus on learning (.16), in English.

Tables 13 and 14 report the direct, indirect and total effects of the pathways

mapped in Figures 7 and 8 assuming focus on learning (FOL) as the endogenous out-

come variable. For both mathematics and English, flexible teaching has by far and

away the strongest total effects (.74 and .84). Communication of learning goals and



performance standards (.54) provides the second strongest effect size in mathematics

and English, while the monitoring student learning (MSL) (.37) and the quality of

questioning (QTQ) (.46) is the third strongest effect in mathematics and English

respectively. In broad terms then, the generativity of flexible teaching, followed by the

communication of learning goals and performance standards, in the Singapore con-

text is consistent with the theoretical arguments we endorsed earlier regarding the

importance of instructional alignment and visible learning. These findings do not of

course demonstrate that these instructional practices optimize student learning; they

are merely consistent with the broad theoretical claims made on their behalf by

researchers. We will report their impact on student learning in a latter report. For

now though, our modelling of TFU instructional practices indicates that instructional

practices in both mathematics and English are broadly in line with the normative

injunctions that researchers have identified, but that there are a number of practices

that are clearly suboptimal, normatively speaking, including, in particular, the

absence of pathways from monitoring student learning and feedback, and from whole

class discussion and collaborative group work to focus on learning.

Table 15, similarly, reports the direct, indirect and total effect sizes for the two

SEM models with co-regulated learning strategies (CRLS) as the key outcome vari-

able. Again, flexible teacher leads the way, followed by monitoring student learning.

Hybridity, assessment and the logic of instruction

In Table 16 we summarize the mean scores for the four instructional strategies

reported above. Clearly, the rank order differs in the two subjects and the spread is

unequal. In mathematics, TI leads over DI, followed by TfU a fair way back, and

CRLS in that order. The spread is quite substantial between TI/DI and TfU, and

even bigger between TfU and CRLS. In English, DI leads over TI, followed by TfU

and CRL in that order. The spread between the scales is not as wide in English as it is

in mathematics. Effect sizes are generally quite large. Moreover, at the scale level,

there are clear differences in mean scores between the two subjects, particularly with

respect to TI and CRLS, and these are reflected in the effect sizes. Although

the strength of TI in mathematics might lead one to conclude that mathematics

Table 13. Total indirect and direct effect sizes, SEM TfUmodel, mathematics

Pathway

Direct, indirect and total effects

Indirect Direct Total

FT to FOL .50(.04)* .24(.05) .74(.04)*

CLGPS to FOL .17(.02)* .37(.05) .54(.05)*

MSL to FOL .37(.04)* — .37(.04)*

QTQ to FOL — .34(.05) .34(.05)*

CNI to FOL .26(.04)* — .26(.04)*

CFB to FOL .13(.02)* — .13(.02)*

PFB to FOL .08(.02)* — .08(.02)*

Notes: *Significant at p < .01;— refers to paths not modelled.

88 D. Hogan et al.


instruction at least conforms to the East Asian stereotype, the relative strength of the

other instructional strategies should give pay to that suggestion.

A second look at Table 16 reveals a relatively narrow spread between the mean

scores in each subject, apart from CRLS. This hints at the possibility that the leading

three instructional strategies covary together. And indeed, this conclusion is sup-

ported by the correlations reported in Table 17: the correlations between DI, TI and

TfU are all high, whereas the correlations of each of these with CRLS are substan-

tially lower. This is an important finding, for it indicates some differentiation between

strategies that give the teacher an active instructional role in the classroom—TI, DI

and TfU—and the one strategy in our taxonomy (CRLS) that clearly shifts the centre

of instructional gravity away from teachers towards students and student agency. Just

as importantly, the strength of the correlations suggests that Singaporean teachers in

both English and mathematics appear to draw upon all three teacher-focused instruc-

tional strategies jointly rather than choose between them. We doubt very much that

they do so indiscriminately. Rather, our qualitative evidence, based on interviews

with 115 teachers, suggests that they do so because of their strikingly instrumentalist

Table 14. Total indirect and direct effect sizes, SEMTfUmodel, English

Pathway


Indirect Direct Total

FT to FOL .67(.05)* .17(.05)* .84(.04)*

CLGPS to FOL .25(.03)* .29(.05)* .54(.05)*

QTQ to FOL .06(.02)* .40(.06) .46(.06)*

MSL to FOL .42(.05)* — .42(.05)*

CNI to FOL .33(.04)* — .33(.04)*

CFB to FOL .17(.03)* — .17(.03)*

SCF to FOL — .16(.03)* .16(.03)*

PFB to FOL .10(.02)* — .10(.02)*

WCD to FOL .04(.01)* — .04(.01)*

CGW to FOL .11(.02)* — .11(.02)*

Notes: *Significant at p < .01;— refers to paths not modelled.

Table 15. Total indirect effect sizes, SEMTfU-CRLS model, mathematics and English

Pathway


Mathematics English

Indirect Direct Total Indirect Direct Total

FT to CRLS .70(.03)* — .70(.03)* .74(.05)* .10 (.05)^ .84(.04)

MSL to CRLS .41(.03)* — .41(.03)* .37(.05)* — .37(.05)*

CNI to CRLS .26(.04)* — .26(.04)* .33(.04)* — .33(.04)*

CFB to CRLS .13(.02)* — .13(.02)* .18(.03)* — .18(.03)*

PFB to CRLS .07(.02)* — .07(.02)* .10(.02)* — .10(.02)*

Notes: *Significant at p < .01; ^Significant at p < .05;— refers to paths not modelled.



and performative orientation to teaching and learning, prompting them to adopt a

pragmatic, fit-for-purpose hybridic instructional practice focused on exam perfor-

mance. At a system level, this suggests a well-integrated, coherent pedagogy that is

not at war with itself or riven by deep divisions on matters of pedagogical faith and

doctrine. Given the extraordinary success of Singaporean schools in international

assessments, such pedagogical hybridity appears to work.

Nonetheless, while the commitment of Singaporean teachers to traditional and

direct instruction, together with a milder commitment to elements of a teaching for

understanding instructional strategy, might suggest that teachers in Singapore lean

towards, to use John Hattie’s nomenclature, a model of ‘active teaching’, this would

be mildly misleading. This is not because teachers favour ‘constructivist’ or ‘facilita-

tive teaching’. They most definitely do not. While teachers are clearly active in Sin-

gaporean classrooms, they are not particularly active in the ways that matter, or at

least in the ways that John Hattie thinks matter. For Hattie, active teaching supports

‘visible learning’ and ‘is much more effective than unguided, facilitative instruction’

in promoting student achievement. ‘It is essential’, he writes:

… to have visible teaching and visible learning. This notion encapsulates directive, activat-

ing, and involved sets of actions and content, working with students so that their learning

is visible such that it can be monitored, feedback provided, and information given when

learning is successful. (Hattie, 2009, p. 37)

Elsewhere, we have argued that Hattie’s insistence on a combination of active

teaching and visible learning represents a sensible, evidence-based instructional

framework, but that his distinction between active teaching and constructivist teach-

ing is overdrawn and that his account of visible learning and teaching could be

enhanced by taking into account the importance of epistemic clarity—clarity about

the nature of the knowledge work that students engage in—in the design and imple-

mentation of instructional tasks during lessons (Putnam et al., 1990; Schoenfeld,

1992; Stein et al., 1996, 2009; Perkins, 1998; Rittle-Johnson & Alibali, 1999; Schraw,

2006; Hogan et al., 2011, 2012c, e; Rahim et al., 2012).

Despite our reservations about Hattie’s account of active teaching and visible learn-

ing, both conceptions contribute significantly to the scholarship on teaching and

learning. Unfortunately, we do not think the evidence from our broader research pro-

gram indicates that Singaporean teachers are committed to active teaching in ways

that matter. In particular, they rarely employ the kind of instructional strategies that

Hattie positions as central to the active teaching/visible learning nexus. Table 18, for

instance, reports our overall summative judgments from the three projects that make

up our broader Core 2 research program. (Panel 3, for example, is a classroom obser-

vation study of 624 lessons that we also conducted in 2010 using a subsample of clas-

ses and schools from the Panel 2 survey sample reported in this article, while Panel 5

uses the same sample to examine the intellectual quality of tasks and student work.)

It suggests a pretty bleak picture (Hogan et al., 2012d). In addition, evidence from

Panels 2, 3 and 5 reported in Table 19 and represented in Figure 9 indicate that

teachers in Secondary 3 mathematics and English rarely encourage strong forms of

student agency in the classroom, either in their support for self-directed learning, or,

even more fundamentally, in their design of instructional tasks that create substantial

90 D. Hogan et al.


opportunities for students to exercise epistemic, cognitive, metacognitive and discur-

sive agency that are pivotal to knowledge building pedagogies (Hogan et al., 2012d).

In sum, our evidence suggests an instructional framework that is both hybridic in

nature and performative in orientation and with very little commitment to active

teaching and visible learning. These findings again reinforce our conclusion that what

explains the comparative success of Singapore in international assessments is not the

commitment of its teachers to high leverage knowledge practices, active teaching or a

knowledge building pedagogy more broadly, but their single minded commitment

(for many complex reasons) to a highly instrumentalist and performative pedagogy.

Indeed, we can demonstrate this statistically with a SEM model that incorporates all

four instructional strategies—traditional, direct, TfU and CRLS—in a single model.

The SEM models represented in Figures 10 and 11 (and the relevant goodness-of

fit-statistics reported in Table 20) model the overall structure of all four instructional

strategies—traditional, direct, TfU and CRLS—jointly at the construct level in an

integrated model. Overall, keeping in mind that the models are very large and

Table 16. Summary of mean scores, by scale, Secondary 3 mathematics and English

Secondary 3

mathematics Secondary 3 English Effect size

Mean (1–5) SD Mean (1–5) SD d

TI 3.69 .642 3.45 .669 .37

DI 3.67 .670 3.61 .655 .09

TfU 3.38 .602 3.43 .564 .09

CRLS 3.01 .770 3.28 .688 .37

d d

TI vs DI .03 .24

TI vs TFU .50 .03

TI vs CRLS .96 .25

DI vs TfU .46 .30

DI vs CRLS .91 .49

TfU vs CRLS .54 .24

Table 17. Correlation matrix: instructional methods Secondary 3 mathematics and English

TI DI TfU CRLS

Mathematics

Traditional instruction 1

Direct instruction .72** 1

Teaching for understanding .58** .70** 1

Co-regulated learning strategies .28** .35** .73** 1

English

Traditional instruction 1

Direct instruction .75** 1

Teaching for understanding .63** .68** 1

Co-regulated learning strategies .41** .39** .77** 1



complex, the goodness-of-fit statistics are exceptionally good. Notably, the chi-square

statistic for English is substantially lower than it is for mathematics (353.981/194/

.0000 versus 404.786/191/.000). Both models are fully recursive: above all, there are

no feedback loops from TfU back to TI or DI practices. In addition, the internal

structure of each of the broader instructional categories (as indicated by the pattern

of pathways between practices within each category) remained remarkably stable.

Task SetUp and Enactment, Student Agency and Knowledge Building

Epistemic Agency

Discursive Agency

Cognitive Agency

Metacognitive Agency

Task Set Up andEnactment: DistributingOpportunities to Learn

(Opportunities toGenerate,

Communicate,Deliberate and Justify

Knowledge Claims)

(Opportunities todevelop Conceptual

Understanding)

(Opportunities toacquire Metacognitive

Knowledge andExercise MC Self-

Regulation)

(Opportunitiesfor Extended

UnderstandingTalk)

Figure 9. Task set-up and enactment, student agency and knowledge building

Note: All values represent unstandardized es mates significant at p<.01. In brackets are standard errors. Double-headed curved arrows denote correlatedlatent disturbances.

Note. EXPR=Exam prepara on; TXBF=Textbook Focus; WKSF=Worksheet Focus; DRILL=Drill; MEM=Memoriza on; SNC=Structure & Clarity; MLT=Maximumlearning me; REV=Revision; FOP=Frequency of prac ce; FOQ=Frequency of ques oning; CFB=Collec ve feedback; PFB=Personal feedback; CNI=Curiosity &

interests; FLT=Flexible teaching; MSL=Monitoring student learning; CLGPS=Communica ng learning goals and performance standards; QTQ=Quality ofques oning; WCD=Whole class discussion; CGW=Collabora ve group work; SCF=Teacher scaffolding; FOL = Focus on learning; CRLS=Co-regulated Learning

MSL

CFB

FOLCLGPS

SCFQTQFLT

CNI

PFB

WCD CGW

CRLS

EXPR REV

SNC

MLT

FOQ

FOPTXBF

DRILL

WKSF

MEM

.33(.06)

.19(.04).34(.04)

.24(.05).14(.04)

.46(.06)

.48(.04)

.17(.04).46(.05)

.17(.05).33(.05)

.13(.05)

.17(.05)

.19(.06)

.25(.06).27(.05).14(.05)

.57(.04)

.43(.04)

.33(.05)

.22(.04)

.27(.04)

.29(.04)

.47(.04)

.12(.04)

.31(.06)

.15(.05)

.43(.05)

.17(.05)

.37(.06)

.59(.04).14(.04)

.15(.04) .39(.04)

.34(.04)

.22(.03)

.20(.04)

.28(.04).40(.04)

.12(.03)

.24(.05)

.36(.05)

.35(.05)

.14(.03)

.70(.04)

.61(.04)

.25(.04).56(.03)

.64(.04)

.19(.03)

.15(.04)

.13(.03)

.27(.05)

.13(.03)

.33(.05)

.25(.04)

.34(.05)

.29(.05)

.25(.04)

.14(.02)

Figure 10. Integrated SEMmodel for instructional strategies: mathematics

92 D. Hogan et al.


Both of these findings, especially the former, were a surprise to us in that we expected

to find a re-assembling of the networks of pathways and number of feedback loops

from ‘higher order’ (TfU) instructional practices to ‘lower order’ (TI/DI) ones. How-

ever, in both subjects there is a linear, fully recursive sequence to instructional prac-

tice that underscores the coherent and hybridic nature of the instructional regime in

Singaporean classrooms, at least in mathematics and English, and that confirms our

arguments earlier on the basis of our CFA modelling of the four general instructional

strategies.

Table 18. Extended inventory of ‘active teaching’/‘visible learning’ indicators

Criteria

Measured standard

Core 2 data source

Secondary 3

mathematics

Secondary 3

English

Checking for prior knowledge Moderate Moderate Panel 3

Communicating learning goals Low Low Panels 2, 3.

Communicating performance standards Low Low Panels 2, 3, 5

Exemplars of successful performance Low Low Panel 3

Monitoring student learning Low Low Panels 2, 3

Feedback Low Low Panels 2, 3

Learning support/scaffolding Low Low Panel 3

Knowledge representation Low Low Panels 2, 3

Focus on metacognitive knowledge Low Low Panels 2, 3, 5

Epistemic clarity of knowledge work Low Low Panels 2, 3, 5

Open questions/extended responses Low Low Panels 2, 3

Understanding talk Low Low Panels 2, 3

Explicit instruction in norms regulating

whole class discussion and group work

Low Low Panel 3

Note: All values represent unstandardized es mates significant at p<.01, *p<.05. In brackets are standard errors.Double-headed curved arrows denotecorrelated latent disturbances.

Note. EXPR=Exam prepara on; TXBF=Textbook Focus; WKSF=Worksheet Focus; DRILL=Drill; MEM=Memoriza on; SNC=Structure & Clarity; MLT=Maximumlearning me; REV=Revision; FOP=Frequency of prac ce; FOQ=Frequency of ques oning; CFB=Collec ve feedback; PFB=Personal feedback; CNI=Curiosity &

interests; FLT=Flexible teaching; MSL=Monitoring student learning; CLGPS=Communica ng learning goals and performance standards; QTQ=Quality ofques oning; WCD=Whole class discussion; CGW=Collabora ve group work; SCF=Teacher scaffolding; FOL=Focus on Learning; CRLS=Co-regulated Learning

MSL

CFB

FOLCLGPS

SCFQTQFLT

CNI

PFB

WCD CGW

CRLS

EXPR REV

SNC

MLT

FOQ

FOPTXBF

DRILL

WKSF

MEM

.18(.04).54(.04)

.42(.04).14(.04)

.20(.05)

.37(.04).24(.04)

.19(.06).26(.05)

.14(.04)

.26(.08)

.24(.08).12(.03)*.14(.06

.69(.05)

.48(.04)

.25(.04)

.21(.03)

.31(.04)

.52(.04)

.26(.06)

.17(.04) .38(.06)

.31(.06)

.30(.06)

.77(.04)

*.10(.04) .51(.06)

.27(.06)

.11(.03)

.28(.06)

.40(.05).29(.06)

.32(.05)

.36(.05)

.26(.04)

.65(.04)

.43(.04)

.43(.04)

.47(.07)

.96(.02)

.49(.06).36(.06)

.13(.04)

.38(.07)

.30(.07)

.22(.05)

.12(.02)

.30(.06)

.34(.04)

.25(.05)

.15(.05)

.15(.04)

.20(.03)

.16(.03)

.19(.05)

.25(.07)

Figure 11. Integrated SEMmodel for instructional strategies: English



In broad terms, the structure goes something like this: traditional instruction

provides the foundation of the instructional order, direct instruction builds on TI

practices and extends and refines the instructional repertoire, while TfU/CRLS prac-

tices build on TI and DI practices and extend the instructional repertoire even further

in ways that focus on developing student understanding and student directed learn-

ing. Instructional practices in Singaporean classrooms then, on this data, cannot be

considered either Eastern or Western, but a coherent combination of both. However,

they combine in a particular way, as ensembles of practices grouped by broad instruc-

tional categories, rather than as new or reassembled configurations of instructional

practices that more or less ignore the instructional categories that we had imposed on

them for theoretical reasons.

What then ties or links the four instructional groupings together in an orderly chain

of instructional practice? A close review of Figures 10 and 11 indicates that four

instructional practices play pivotal roles in chaining the instructional groupings

together: two TI practice (exam preparation and textbook focus) and two DI prac-

tices (structure and clarity, and revision).

Of the four, exam preparation is the most important. In both subjects, exam prepa-

ration is highly generative both directly and indirectly, reaching well beyond its own

close family of TI practices into direct instruction and TfU practices. In mathematics,

there are nine separate direct pathways leading from exam preparation to DI and TfU

practices, and numerous indirect paths that link exam preparation, on the one hand,

to all of the remaining instructional practices, on the other. In English, exam prepara-

tion generates eight pathways to other instructional practices spread across both DI

and TfU. The aggregate indirect effect of exam preparation on focus on learning in

mathematics is .38(.02) (p < .01), and in English, .35(.02) (p < .01). The aggregate

indirect effect of exam preparation on CRLS in mathematics is .38(.02) (p < .01)

and in English, .34(.02) (p < .01).These are substantial effects, attesting to the strik-

ing institutional authority of the assessment system over instructional methods gener-

ally, not just traditional and direct instruction, and helping to account for the

remarkably isomorphic structure of instructional practice in mathematics and English

when we might well have expected quite distinctive subject-specific instructional

regimes to be generated by fundamental differences in the disciplinarity of the two

subjects.

Of course, as we have indicated elsewhere, there are other factors in play as well

that account for this instructional isomorphism, particularly the pervasive cultural

influence of a vernacular ‘folk pedagogy’ on teacher conceptions of teaching and

learning (Hogan et al., 2011, 2012d; Hogan, 2012). But there is little doubt that the

institutional and cultural authority of the assessment system, operating via exam

preparation, is exceptionally important, and that the very considerable alignment of

instruction, the curriculum and the assessment system in Singapore is in large part a

direct function of the pivotal role of exam preparation in shaping the overall structure

of the instructional system as a whole. As we indicated at the beginning of the article,

this is hardly new news to Singaporean teachers, parents, students—or researchers.

Indeed, as we saw earlier, Kramer-Dahl (2008) and others have long emphasized the

limits the assessment regime imposes on instructional practice, even when there

is a strongly reformist English syllabus in place nationally to support instructional

94 D. Hogan et al.


innovation. Similarly, teachers we interviewed in 2010 as part of our larger research

program express remarkably similar constructions of the challenges they face in trying

to reconcile the demands of the TLLM initiative and the imperatives of high stakes

assessment. The following quotations come from two different Secondary 3 teachers:

T2: I find that for mathematics, using TLLM is a bit…How do I say, a bit tough? Because

I guess at the end of the day, what students want to see, what parents want to see, what the

school wants to see is the O level grades. So how does doing like, things like the portfolio

even, how does it value-add to what the student will gain upon their graduation. Yes, so

I’m a bit apprehensive about this TLLM, actually. (Secondary 3 mathematics teacher)

T3: I think it’s actually very difficult. Something has to give. And if the focus is so much

on the… [Sigh]. So if indeed we really want to go full steam ahead with TLLM, exams

unfortunately, have to take a backseat. But unfortunately the problem is that, the way Sin-

gaporean boys are, you know, when it’s through discovery learning, when it’s through

character development, what happens is, they may enjoy the process but enjoying the pro-

cess may not actually translate to learning the skills or motivating yourselves to do the very

best that you can. It’s like what happened years ago we had the whole concept of language

learning with the communicative approach? And it fell flat on the face. (Secondary 3

English teacher)

These teacher accounts, along with Kramer-Dahl’s account (mentioned earlier) of

the constraints imposed by the assessment system on the willingness of teachers to

implement national reform initiatives in English, is supported by evidence from a sur-

vey of over 2000 teachers we conducted in 2010. We asked teachers to identify the

impact that 21 influences had had on their teaching in Singapore—what we termed

the subjective logic of instruction.On a five-point Likert scale, ‘the ability of students’

came in first with a mean score of 4.02, followed by ‘your skills as a teacher’ (4.00),

‘coverage of the curriculum/department’s scheme of work’ (3.90) and ‘the national

high stakes assessment system’ (.3.86). We also asked teachers what influence they

thought the national high stakes assessment system had on the instructional practices

of teachers in general. We report the results in Table 21. Clearly teachers think it has

a very substantial influence, and that, in addition, it strongly influences the willing-

ness and opportunity of teachers to engage in instructional innovation.

In short, for teachers, institutional context matters—and matters a great deal. Our

strong suspicion then is that in order to explain the stability—indeed, intractability—of instructional practice in Singapore we need to recognize the persistent institutional

Table 19. Task design, student agency and knowledge building pedagogy

Criteria

Measured standard

Core 2 data sourceSecondary 3 mathematics Secondary 3 English

Epistemic agency Low Low Panels 2, 3, 5

Cognitive agency Low Very low Panels 2, 3, 5

Metacognitive agency Low Low Panels 2, 3, 5

Discursive agency Very low Very low Panels 2, 3



grip that the national assessment system in Singapore has over classroom practice.

While TLLM invited teachers to change their instructional practices and classroom

culture, it did not alter the national high stakes assessment system in a way that might

have increased the willingness of teachers to be more adventurous and innovative in

their classroom practices in the way TLLM hoped for. To be sure TLLM gave schools

and teachers permission to devote up to 20% of curriculum time to their own curricu-

lum preferences or interests (the so called ‘White Space’ initiative). But the anecdotal

evidence we have is that the ‘White Space’ curriculum time was quickly colonized by

more of the same and exam preparation. It’s clearly a good thing for classroom

instruction to be aligned to the assessment system, and its clearly appropriate and

sensible of teachers to align their classroom practices to it, but there are opportunity

costs as well when the degree of alignment constrains the opportunity or willingness

of teachers to alter their classroom practices in ways sought by policy-makers in

response to urgent national priorities.

Beyond exam preparation, a second traditional instructional practice is notably

generative, and generative well beyond the somewhat artificial ‘boundaries’ of

Table 20. Goodness-of-fit statistics: integrated instructional strategies SEMmodels (Secondary 3

mathematics and English)

Goodness-of-fit Mathematics English

N 1166 1027


CFI/TLI .986/.982 .989/.986

RMSEA (90% CI) .031 (.027–.035) .028 (.024–.033)SRMR .028 .031

Table 21. Teacher beliefs about the influence of national high stakes assessment on teaching

practices

Mean (1–5) SD Factor loading

Pedagogical effect of national high

stakes assessment system (alpha =.836)3.64 0.86

The national high stakes assessment system……has a very large influence on how teachers teach. 4.11 0.72 .670

…limits the willingness of teachers to try new instructional

or assessment practices.

3.64 0.92 .846

…limits the opportunity for teachers to try new instructional

or assessment practices.

3.63 0.90 .880

…pushes teachers to teach in ways contrary to their

professional beliefs.

3.46 0.90 .760

…compromises the quality of teaching. 3.36 0.88 .717

Not included in scale:

…maintains high standards of teaching and

learning

2.58 0.85

Source: Panel 2 Teacher Survey.

96 D. Hogan et al.


traditional instruction, especially in mathematics—a focus on textbooks. In mathe-

matics, for example, there are three strong pathways from textbook focus to other TI

practices and one relatively weak one: worksheets and workbooks (.46), memoriza-

tion (.46), drill (.33) and structure and clarity (.12). But, in addition, there are three

pathways, generally weaker but still statistically significant, from textbook focus to DI

practices: frequency of practice (.27), frequency of questions (.13) and maximum

learning time (.27). These pathways all make theoretical sense, especially in mathe-

matics, where teachers tend to rely on textbooks more than they do in other subjects.

In English, textbook focus is less generative, with no pathways to drill, structure and

clarity or maximum learning time, but modest pathways to worksheets and work-

books (.24), frequency of questions (.14) and frequency of practice (.12). The aggre-

gate indirect effect of textbook focus on focus on learning in mathematics is .14(.02)

(p < .01) and in English, .03(.01) (p < .01). The aggregate indirect effect of textbook

focus on CRLS in mathematics is .14(.02) (p < .01), and in English, .02(.01)

(p < .01). Yet a third of TI practice, focus on worksheets and workbooks, had much

smaller indirect effects on the two outcome measures. The aggregate indirect effect of

worksheet focus on learning in mathematics is .02(.01) (p < .01) and in English, .04

(.01) (p < .01). The aggregate indirect effect of worksheet focus on CRLS in mathe-

matics is .02(.01) (p < .01) and in English, .04(.01) (p < .01).

The two remaining gateway instructional practices—structure and clarity and revi-

sion—belong to the DI family of instructional practices. The practice that John Hattie

closely identifies with visible learning, structure and clarity, has multiple pathways

into other DI practices and, in mathematics, into four TfU practices: collective feed-

back (.27), personal feedback (.34), curiosity and interest (.43) and communication

of learning goals and performance standards (.22). In English, it generates pathways

into four TfU practices: collective feedback (.49), personal feedback (.38), curiosity

and interest (.38) and communication of learning goals and performance standards

(.11). The aggregate indirect effect of structure and clarity on focus on learning in

mathematics is .37(.02) (p < .01), and in English, .37(.03) (p < .01). The aggregate

indirect effect of structure and clarity on CRLS in mathematics is .37(.02) (p < .01)

and in English, .35(.03) (p < .01). Revision is somewhat less generative than struc-

ture and clarity, but it has pathways into two other DI practices—frequency of prac-

tice (.16 and .26) and frequency of questions (.17 and .19)—and into three TfU

practices in both mathematics and English: flexible teaching (.37 and .30), collective

feedback (.33, .36) and personal feedback (.29, .30). The aggregate indirect effect of

revision on focus on learning in mathematics is .28(.03) (p < .01), and in English, .30

(.05) (p < .01). The aggregate indirect effect of revision on CRLS in mathematics is

.26(.03) (p < .01) and in English, .28(.04) (p < .01).

One further comment. The two proto-cognitive practices, focus on memorization

and focus on learning, occupy very different positions in Singapore’s overall instruc-

tional scheme. Focus on memorization, although it continues to be strongly net-

worked backwards to all other TI practices in the integrated model, either directly or

indirectly, remains determinedly non-generative in its own right (in mathematics)

with no pathways leading from it towards either DI or TfU practices. In effect, focus

on memorization in mathematics is as much an instructional cul de sac in the inte-

grated model as it is in the DI or the TI/DI models we discussed earlier, although in



English, focus on memorization generates two small to modest pathways, one to revi-

sion (.21) and one to focus on practice (.15). From these practices there are slight

indirect pathways to focus on learning, but nothing strong enough to suggest that Sin-

gaporean teachers are committed to a putative East Asian nexus between memoriza-

tion and learning, at least in mathematics and English. TfU’s focus on learning, on

the other hand, remains strongly networked to other TfU practices (with three path-

ways leading into it from other TfU practices), remains an important instructional

practice in its own right as well as generating a pathway to CRLS in both subjects.

Conclusion

In the course of this article we reported the relative importance and interrelationships

between four theoretically specified arrays of instructional strategies: traditional

instruction, direct instruction, teaching for understanding, and co-regulated learning

strategies. Specifically, we reported that traditional and direct instruction are the two

most common modalities of instructional strategy in Secondary 3 English and mathe-

matics, followed by teaching for understanding and co-regulated learning strategies.

Second, we argued that the relative weighting and overall structure of instructional

practice suggests a pervasive performative orientation to pedagogy generally in Singa-

pore. Third, we argued that instructional practice in Singapore is characterized by

hybridity rather than loyalty to an ‘East Asian’ or ‘Western’ model of pedagogy.

Finally, we used SEM modelling to establish that the hybridic nature of instructional

practice in Singapore is not institutionally innocent, but instead reflects the over-

whelming institutional authority of the assessment system over the pattern of instruc-

tional practice in Singaporean classrooms and that the alignment of instructional

practice and assessment underscores the overall performative orientation of Singa-

pore’s pedagogical framework. This arrangement, as comparative education research

suggests, is typical of systems characterized by high stakes assessment systems, and in

turn suggests that what matters most in shaping the pattern of instructional practice,

is not so much regional identities (East Asian, Western), but the broader institutional

and cultural ordering of the instructional regime.

At this point we want to note three further sets of findings that our larger research

program has generated that bear on our overall judgment of Singapore’s pedagogical

regime. The first is that using multilevel structural equation models we found that

instructional practices in Singapore that focus on procedural skills and functional

forms of cognitive activity are far better able to predict student achievement outcomes

than instructional practices that research suggest are likely to generate conceptual

understanding and related outcomes (Hogan et al., 2012d, e). Critically, we found

this pattern of relationships across a broad range of instructional practices, including

instructional tasks, classroom talk, classroom organization and instructional strate-

gies. Importantly, these findings are contrary to the Ministry of Education (MOE)

policy priorities. Our research does not indicate that teachers do not employ or value

instructional practices that focus on conceptual development or metacognitive self-

regulation or knowledge building, although their mean scores are substantially lower.

Rather, our results indicate that these more conceptually orientated instructional

practices do not have a strong impact on student achievement, given the nature of the

98 D. Hogan et al.


current assessment system. A different assessment regime—one including different kinds

of assessment tasks, for example—would in all likelihood generate a different pattern

of relationships and do so in line with current policy priorities. So while the current

assessment system has improved teaching and learning standards over the years, it

now appears that the current assessment regime inhibits or constrains the willingness

and opportunity of teachers to change their instructional practices in line with current

policy priorities that favours what Singaporeans loosely (and misleadingly) view as

‘learner-centered’ pedagogy. In effect, the current assessment regime incentivizes and

rewards teachers to teach (and students to learn) in ways that maximize assessment perfor-

mance rather than the kinds of teaching and learning called for in national policy documents

and generally associated with teaching for understanding frameworks. This suggests that

current policy settings are not internally consistent, as we indicated above.

The second additional finding we want to report now is that we found that prior

achievement was consistently the single strongest predictor of student achievement.

However, we also identified the existence of very large direct and indirect social class

effects on prior achievement (PSLE) and student allocation to curriculum streams

and on Secondary 3 student achievement at the classroom level. Social class effects at

the individual (L1) level were much smaller, although larger in the case of English

than mathematics, a result that we think underscores the importance of linguistic,

social and cultural capital at the family level. But although social class effects at the

individual level within classes were relatively small, there can be no mistaking the sig-

nificance of the impact of social class on Secondary 3 student achievement at the

aggregate classroom level. In Singapore, as in other systems committed to homoge-

neous grouping, it appears to matter less what particular family students come from

then who they go to class (and school) with. To put it in technical terms: institutional

and composition effects matter, and matter a great deal. This is consistent with inter-

national research, but the relationship between social class and educational inequality

in Singapore is exaggerated by institutional rules and organizational arrangements

(above all, the streaming system) by virtue of the very tight relationship with social

class and streaming in Singapore that we (and others) have quantified. In effect, in

Singapore, streaming compounds and inflates the influence of social class on student

achievement at the classroom and school level. (By contrast, systems with lower levels

of aggregation are typically characterized by higher social class effects at the individ-

ual student level).

These particular findings have very substantial policy implications for the improve-

ment of teaching and learning across the system and the design of interventions

intended to ameliorate the effects of social inequality in education. In particular, they

suggest that the improvement of teaching and learning will depend substantially on a

different assessment regime, including, in particular, alteration in the nature of the

assessment tasks in the high stakes assessment system, and a different kind of curricu-

lum framework to give appropriate guidance to the enacted as well as the prescribed

curriculum. In addition, our evidence suggests that if the system wishes to reduce

social class differences in student performance, it will need to address sources

(including impacts on student motivation and identity formation and access to

human, social and cultural capital at the classroom level) of inequality that are a func-



tion of organizational arrangements and policy settings as well as those that arise at

the family and individual level.

Finally, again using structural equation procedures, we found that teacher effects,

independent of instructional or teaching effects, are minimal. Our measures of

teacher effects included pre-service education, participation in professional develop-

ment activities, participation in in situ professional learning communities (profes-

sional collaboration and reflective dialogue), teaching experience, learning priorities

(‘problem-solving efficiency’ versus ‘learning to learn’), conceptions of teaching and

learning (‘conventional’, ‘constructivist’), self-efficacy beliefs (with respect to class-

room management, student motivation and instruction), and ability and effort attri-

butions regarding student achievement. Indeed, in both mathematics and English,

the only statistically significant pathway we could identify was from one of the learn-

ing priorities measures (‘problem-solving efficiency’) to our student achievement

measures. We interpret this finding to reflect (and reinforce) the performative orien-

tation of Singapore’s pedagogy. In addition, we found that the pattern of relationships

between participation in professional development and professional learning commu-

nity activities, on the one hand, and instructional beliefs and student outcomes, on

the other, suggest that professional development and professional learning commu-

nities reinforce rather than challenges the dominant performative orientation of peda-

gogical practice in Singapore. This in turn suggests some tension between MOE

policy priorities (in this case, a commitment to learning to learn) and the overall struc-

turing of teacher beliefs and participation in professional development and profes-

sional learning communities.

Of course, these limitations of Singapore’s instructional regime need to be placed

in the broader context of a highly successful system that by any measure has gener-

ated an extraordinary record of achievement over the past two or three decades so

that it is now widely recognized as one of the leading educational systems in the

world. But notwithstanding this record of achievement, our judgment now is that

while the performative and hybridic character of the system has served Singapore

well, it is far from clear that the current framework can support successful, substantial

and sustainable innovation in classroom practice. From a normative perspective, the

current system is suboptimal in a number of respects—the small mean scores for TfU

practices as a whole, particularly whole class discussion, collaborative group work

and focus on learning and the absence of key pathways, including pathways from

monitoring student learning to student feedback (collective and personal). Finally—and perhaps the most concerning of all—is the apparent constraint that the assess-

ment system places on the willingness and opportunity of teachers to alter instruc-

tional practice, even when urged to do so by relevant national syllabi or by national

reform initiatives. This might suggest that the sensible thing to do would be to elimi-

nate the national high stakes assessment system. We don’t agree. Rather, the chal-

lenge for the Ministry of Education, teachers and researchers is to figure out how to

transform and use the institutional authority of the assessment system as a lever for

change rather than a constraint on improvement. Our sense is that this might be

accomplished in four ways: (1) by improving the quality of the assessment tasks in the

national high stakes assessment system, and doing so in a way that prioritizes

extended, elaborated, authentic, multidimensional twenty-first century knowledge

100 D. Hogan et al.


building tasks (including tasks that are both collaborative and ICT-mediated) that

will drive instructional improvement, given the strong proclivity of teachers to teach

to the test; (2) by introducing a school-based, professionally moderated, standards-

driven component (say initially, accounting for up to 30% of the final grade) into the

national high stakes assessment system; (3) by enhancing the professional capability,

authority and pedagogical autonomy of teachers in ways that allows them to moderate

or buffer the demands that emanate from exogenous pressures outside the classroom;

and (4) by a modest additional deregulation of the assessment market in Singapore

(some, but not all, Singaporean schools are permitted to offer the International

Baccalaureate (IB) rather than participate in the Cambridge assessment system)

granting all schools permission to choose which national assessment regime to join in

a semi-deregulated assessment market—Cambridge, IB, or a hybrid that combines

national plus school-based components—depending on what pedagogical priorities

schools establish for themselves in the spirit of devolved pedagogical authority that

TLLM supported in 2004/2005.

For purists, the proposal to use the assessment system to support instructional

improvement might well appear misconceived, or at least paradoxical, given the well

documented negative effects national high stakes assessment systems can have. And

there is some evidence that the one experiment in school based assessment in Singa-

pore we are familiar with, an experiment using ‘science practical assessments’ as a form

of school based assessment lacked the capacity to drive significant pedagogical change

(in this case, inquiry science) without a considerable investment in teacher preparation

and professional development and other collateral changes. Rather, it cornered teach-

ers into assessing that which could bemost easily observed in laboratories and exposed

fears from a range of actors about a lack of content knowledge and assessment literacy

(Towndrow & Tan, 2006; Towndrow, 2008; Towndrow et al., 2010). Consequently,

we conclude that school-based assessment by itself will not achieve instructional

improvement. Rather, instructional improvement is primarily likely to depend on

transforming the nature of high stakes assessment tasks, backed up by school-based

high stakes assessments and significant investments in building teacher capacity.With-

out these changes in the assessment system, we can see no other solution in sight that

has the capacity to be as effective, sustainable, scaleable and, critically, politically man-

ageable in the Singaporean context. In Singapore (as elsewhere), instructional legiti-

macy depends on formal inclusion in the assessed curriculum. More broadly,

instructional systems, like organizational systems generally, are prone to isomorphism

with their institutional environments (Powell & DiMaggio, 1991; Scott, 1995; Hogan

et al., 2008b). Unless assessment tasks that focus on complex knowledge work are

properly integrated into the assessed curriculum, students, parents or teachers will not

take complex knowledge instruction and related assessment tasks seriously. If this were

accomplished, the tight coupling (or alignment) of instruction and summative assess-

ment (‘teaching to the test’) in Singapore becomes a pedagogical strength rather than a

constraint on sustainable pedagogical innovation. In effect, appropriately constructed

high stakes assessments might, other things being equal, leverage desirable instruc-

tional innovation and pedagogical realignments in classrooms across the system in a

sustainable way at scale and at verymodest financial (and, importantly, political) cost.



NOTE

1 However, a very large classroom observation data set from a related project we are conducting suggests a farbleaker picture on this front. See Hogan et al. (2012d).

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