The Skills of Asking Good Questions

8/11/2019 The Skills of Asking Good Questions

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vailable online at www.sciencedirect.com

18770428 2011 Published by Elsevier Ltd.

doi:10.1016/j.sbspro.2011.03.291

Procedia Social and Behavioral Sciences 15 (2011) 13541358

WCES-2011

The skill of asking good questions in mathematics teaching

Einav Aizikovitsh-Udi * Jon Star

Harvard University

Abstract

Those interested in mathematics education have recognized the value of asking good questions for centuries. Weassume that good teachers ask good (and lots of) questions of their students. Yet this general recommendation failsto consider important questions about howteachers implement question-asking. The purpose of this study is to think

more deeply about the implementation of this important practice. We explore question-asking in mathematics

classrooms by presenting two case studies, each of which involves a teacher teaching the same topic in differentclasses. We explore how these teachers implement question asking, both in the context of teachers' usual curriculum

that did not put a premium on question asking as well as curriculum supplements that focused explicitly on questionasking.

Keywords:Queshtion-asking, High order thinking, Mathamtics

1.Therotical Framewok

The changing and challenging world requires students, our future citizens, to go beyond the building of their

knowledge; they need to develop their higher-order thinking skills, such as critical thinking, decision making, and

problem solving (Barak & Dori 2005; Ben-Chaim, Ron & Zoller 2000; Ennis 1989; Facion 1990; Harpaz & Adam

2000).Todays education involves teaching how to think, and in particular, how to be a critical thinker. There

seems to be no clear consensus as to what exactly critical thinking is. Some see it as simply being 'everyday,

informal reasoning', whereas others feel differently. Regardless of how one defines critical thinking, it seems clear

that question-asking and question-answering play important roles in its development. By asking a question we

point at what is lacking: facts, causes, reasons that we lack in order to explain what is present and what is

experienced as absent. In order to ask to think about what is lacking we need what is present (Bingham, 2005;

Black, 2001; Ellis, 1993; Hufferd-Ackles, Fuson, & Sherin, 2004; Moberg, 2008; Pape, Bel, & Yetkin, 2003;Piccolo, Harbaugh, Carter, Capraro, & Capraro, 2008; Saint-Pierre, 2002; Sigel & Kelley, 1986). A central premise

of our work is that in order to develop critical thinkers, teachers need to ask students good (and lots of) questions.

Those interested in mathematics education have recognized the value of asking good questions for centuries. Yet

within this general recommendation about question asking are many interesting and important questions about how

teachers implement question-asking. The purpose of this study is to think more deeply about questions concerning

the implementation of this important practice. Many researchers (Bingham, 2005; Black, 2001; Boyer & Plwek,

* Einav Aizikovitsh-Udi Tel.: +972549718810

E-mail address: [email protected]


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2010; Hufferd-Ackles et al. 2004, Moberg , 2008; Sigel & Kelley, 1986; Zohar, Dgani & Vaaknin, 2001; Zohar &

Dori, 2003) examine the culture of asking questions in class. Although there is consensus on the importance of

question-asking, a variety of research has indicated that math teachers are not particularly good at asking questions

(and/or at asking good questions). For example, studies have shown that teachers report that they ask in an average

class between 12-20 questions, yet approximately half of the questions are procedural questions regarding

timetable, attendance, clarifying various technical issues, etc. Furthremore, most of the questions are closedquestions for testing knowledge (straight recall). Only a very small percentage of questions encourage higher-order

thinking. In addition, teachers tend not to allow students opportunities to think about questions; wait time has been

found to average 1.2 seconds. Finally, 70% of the students' answers consist of three words and their duration is

five seconds or less (Nystrand, 1997). The design and implementation of teaching strategies that enhance higher-

order thinking are not a simple endeavor; they challenge even the most expert teachers (Tobin, Tippins & Hook,

1994). Examples of such skills include question posing, decision making, and critical and systemic thinking (Zohar

& Dori, 2003; Zoller, Dori, & Lubezky, 2002). Curricula have been designed to help teachers improve their

question posing, but based on the existing research it is not clear how successful these question asking curricula

have been at improving teachers' ability to ask good questions. It is this relationship - between curricula that aim to

improve teachers' question asking and teachers' implementation of these curricula - that we are primarily interested

in for the present study. More specifically, under what conditions do teachers regularly and independently

incorporate advanced instructional strategies (such as the skill of asking good questions) into their teachingafter having tried these instructional approaches while using curricula explicitly focused on improving question

asking?

2. Methods

We explore the question above through two case studies, each of which involves a teacher teaching the same

content in a junior high school Algebra I class. The two teachers, Robert and Naomi (fictional names) were

experienced algebra instructors (20 and 15 years of math teaching experience, respectively) who participated in a

larger year-long project from which the present data is drawn. We have analyzed two types of lessons taught bythese two teachers. The first type was a regular lesson according to the curriculum adopted at the teachers' school,

while the second type was a lesson provided to the teachers by the researchers, which was designed to promote the

skill of question-asking. Both teachers participated in a one-week professional development institute in the

summer prior to the data collection year. The institute focused on the implementation of the supplemental

question-asking curriculum materials, which we expected to facilitate the teachers' implementation of the new

questioning strategies.

3. Results

The findings presented here examine the practices and the character of interactions in class in which the teacherand the students take part. We use these two teachers' cases to help illuminate important and unexplored issues in

the implementation of question asking: the teachers role in asking questions, the character of questions directed at

students, and the way the questions are asked.


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The Role of the Teacher: There are differences in the attitude of teachers to their function as questioners. Naomi

defines her teaching style as "direct teaching." She conveys a topic stage by stage, being responsible for every

stage (e.g. choosing every step in solving a problem). She gives many instructions during the process of solution:

how to solve equations, perform calculations, work with models, when to contract, etc. Her teaching is very

detailed and precise and is accompanied with oral and written explanations. Naomi solves each equation until the

final result and does not skip stages in problem simplification, including detailed substitutions and making all thenecessary calculations. Such teaching as Naomis is extensively described in literature documenting traditional

teaching (Metz, 1978; Chazan, 2000). In contrast to Naomi, who sees herself as responsible for giving the suitable

formula with explanations to the students, Robert prefers to allow the students to find the solutions while only

helping them to do so. Robert consistently applies methods that appear in recent educational literature as

innovative. For instance, he encourages reliance on intuition and gives a minimum of laws and rules. Also he

does not function as an authority for deciding whether an answer is correct (Cazden, 1988). We find it helpful to

label these cases as exemplifying two types of teachers: the conserving teacher vs. the leveraging teacher (i) The

Conserving Teacher: Naomi teaches her class according to traditional patterns of teaching (Bauersfeld, 1988;

Voigt, 1989). The place of the teacher in the teaching process is central. She gives ample explanations and

instructions frontally to the students while solving problems. The teacher serves as a source of knowledge and

therefore is responsible for establishing correctness or incorrectness of answers. The teacher dominates the

discourse in class, presenting multiple questions but answering most of them herself. She does not encouragediscussion. Most of the questions are focused on mathematical content and purport to obtain information and

evaluate answers rather than attempting to understand the individual students way of thinking. The students'

answers to the teachers questions are very brief, and their own questions aim at clarifying points they did not

understand rather than further investigation (ii) The Leveraging Teacher: Robert teaches his class in a method that

is characterized by features of the contemporary approach (Darling-Hammond, 1996; NCTM, 2000). While

Naomis place in teaching is central, Roberts place is central as well, but with different emphases: he guides the

students, gives few rules and laws and allows the students to choose different ways for solving a particular

problem. Robert does not answer his own questions, but waits for students to respond. In cases when the answer is

slow to arrive, he repeats the question in different ways. He encourages discussion in class, which can be seen

from the encouragement he gives to students who reply, from asking repeated questions of students who cannot

reply, or from the fact that students ask investigative questions themselves. The purpose of the teachers questionsis not only to evaluate knowledge of mathematical content but also to understand how the students think. Davis

(1997) calls this mode of listening to answers interpretive listening. The teacher does not function as the

authority for establishing the correctness or incorrectness of the solution or for correcting the solution, but directs

students by means of questions to correct their mistakes. Such pattern is termed by Wood (1994) the focused

pattern.

4. Discussion

We have found that although both teachers are considered good teachers and the structure of the lesson was

the same in both classes, the practice and culture of question asking of the two teachers are different and areshaped and applied differently. This has to do with the differences in the patterns of the teachers discourse. For

instance, the pattern of Naomis discourse is described in literature as the funnel pattern (where the teacher

directs the students by means of questions toward the expected answer), while the pattern of Roberts discourse is

similar to the focused pattern (the teachers leaves the responsibility for arriving at the solution to the students,

while helping them to focus on the important aspects of the problem), as described by Wood (1998). Also the

ways of listening of the two teachers are different, where Naomi predominantly exercises evaluative listening,

while Robert was applied both evaluative and "interpretive" listening (Davis, 1997). While most questions by both

teachers were concerned with mathematical content, Naomi's questions were not directed personally at the


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students, that is, the purpose of the question was to receive a mathematical answer and not emphasize the

individual student (we will term this type of question "technical"). By contrast, most of the questions in Roberts

classes required more explanation and argumentation than those in Naomis classes (we will term this type of

question "investigative").We have observed that both Naomi and Robert essentially preserved their teaching styles

both in the supplemental question-asking portions of their classes and in the regular classes that adhered to their

regular curriculum. Thus, in order to foster and encourage question-asking in class, it is not enough to provide thequestions to the teachers. The way in which the questions are asked, the timing and the number of times each

question is asked have a central role in the culture of question-asking. In other words, even investigative questions

can be asked in a technical way and not to give rise to any significant process of investigation. The results show

that in order to change traditional teaching styles, it is not enough to give the teacher a small, narrowly focused

exemplary learning unit, even if the teacher has previously taken a course in implementing new teaching methods,

as Robert and Naomi did. The initial evidence shows that leveraging teachers are more likely to incorporate

advanced instructional strategies than conserving teachers. However, the exposure of both teachers to the

question-asking teaching methodology was very brief, and it remains to be seen whether a more extensive

exposure might or might not change a conserving teacher's questioning strategies.

5. Closing Remarks

In the context of higher order thinking, many in-service programs aim at enhancing teachers' teaching

capabilities and expanding their repository of instructional strategies by emphasizing the connections between

theory and practice. Indeed, making the connections between educational theories and practice in the classroom is

doubtlessly essential (Zohar, 2004; Zoller, Ben-Chaim, Ron, Pentimalli, & Borsese, 2000; Osborne, Erduran, &

Simon, 2004). In summary, it is essential that the teacher understand the importance of Good Question-asking

Skills in mathematics lessons. The teachers need to create a variety of situations in which their own questions

relate to the proposed questions, as well as recognizing situations that call for fostering the skill of question-asking

and addressing them immediately and in the long run. To achieve this, it is necessary to plan the teaching by

choosing question items that suit the student population, the teaching goals, the different needs and the teacher'sown teaching style. We also suggest encouraging teachers to apply a variety of instructional strategies, as presented

in this and other studies (Aizikovitsh & Amit, 2010).

References

Aizikovitsh, E., & Amit, M. (2010). Evaluating an infusion approach to the teaching of critical thinking skills through mathematics. Procedia -

Social and Behavioral Sciences, 2(2), 3818-3822. doi: DOI: 10.1016/j.sbspro.2010.03.596

Barak, M., & Dori, Y. J. (2005). Enhancing undergraduate students chemistry understanding through project- based learning in an IT

environment. Science Education, 89(1), 117139.

Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In T. Cooney & D. A.

Grouws (Eds.), Effective mathematics teaching (pp. 27-46), Reston, VA: National Council of Teachers of Mathematics and Erlbaum

Associates.Ben-Chaim, D., Ron, S., & Zoller, U. (2000). The disposition of eleventh-grade science students toward critical thinking. Journal of Science

Education and Technology, 9(2), 149159.

Bingham, C. (2005). The Hermeneutics of Educational Questioning. Educational Philosophy and Theory, 37(4), 553-565.

Black, S. (2001). Ask Me a Question: How Teachers Use Inquiry in a Classroom. American School Board Journal, 188(5), 43-45.

Boyer, K. E., & Piwek, P. (Eds.). (2010). QG2010: The third workshop on question generation. International Conference on Intelligent Tutoring

Systems. Pittsburgh, PA: Carnegie Mellon University.

Cazden, C. (1988). Classroom Discourse: The language of teaching and learning. Portmouth, NH: Heinemann.

Chazan, D. (2000). Beyond formulas in mathematics and teaching: Dynamics of the high school algebra classroom. New York: Teachers College

Press.


5/5

1358 Einav Aizikovitsh-Udi and Jon Star / Procedia Social and Behavioral Sciences 15 (2011) 13541358

Darling-Hammond, L. (1996). The right to learn and the advancement of teaching: Research, policy, and practice foe democratic education.

Educational Researcher,25(6), 5-17.

Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education,

28, 355-376.

Ellis, K. (1993). Teacher Questioning Behavior and Student Learning: What Research Says to Teachers. Retrieved from ERIC database.

(ED359572)

Ennis, R. R. (1989). Critical thinking and subject specificity: Clarification and needed research. Educational Researcher, 18, 410.Facione, P. A. (1990). The California Critical Thinking Skills Test (CCTST): Forms A and B; and the CCTST test manual. Millbrae, CA:

California Academic.

Galton, M. J., & Simon, B. (1980). Progress and performance in the primary classroom. London, Boston and Henley: Routledge & Kegan Paul.

Harpaz, Y., & Adam L. (2000). Communities of thinking. Educational Leadership , 58(3), 54-57.

Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing Levels and Components of a Math-Talk Learning Community. Journal for

Research in Mathematics Education, 35(2), 81-116.

Metz, M. H. (1978). Classrooms and corridors: The crisis of Authority in desegregated secondary schools. Berkeley: University of California

Press.

Moberg, E. M. (2008). Socrates Lives: Dialogue as a Means of Teaching and Learning. Retrieved from ERIC database. (ED507870)

NCTM (2000). Principles and standards for school mathematics. Reston, VA: Author.

Nystrand, M. (1997). Opening dialogue : understanding the dynamics of language and learning in the English classroom. New York: Teachers

College Press.

Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science. Journal of Research in Science Teaching,

41, 9941020.Pape, S. J., Bel, C. V., & Yetkin, I. E. (2003). Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a

Seventh-Grade Mathematics Classroom. Educational Studies in Mathematics, 53(3), 179.

Piccolo, D. L., Harbaugh, A. P., Carter, T. A., Capraro, M. M., & Capraro, R. M. (2008). Quality of Instruction: Examining Discourse in Middle

School Mathematics Instruction. Journal of Advanced Academics, 19(3), 376-410.

Saint-Pierre, Y. (2002). Canadian Statistics in the Classroom. School Libraries in Canada, 22(1), 2-44.

Sigel, I. E., & Kelley, T. D. (1986). A Cognitive Developmental Approach to Question Asking: A Learning Cycle-Distancing Model. Retrieved

from ERIC database. (ED269424)

Tobin, K., Tippins, D. J., & Hook, K. S. (1994). Referents for changing a science curriculum: A case study of one teachers change in beliefs.

Science Education, 3, 245264.

Voigt, J. (1989). Social functions of routines and consequences for subject matter learning, International Journal of Educational Research, 13(6),

647-656.

Wood, T. (1994). Patterns of interaction and the culture of mathematics classrooms. In S. Lerman (Ed.), The culture of the mathematics

classroom (pp. 149-68). Dordrecht, Netherlands: Kluwer Academics Publisher.

Wood, T. (1998). Alternative patterns of communication in mathematics classes: funneling or focusing? In H. Steinbring, M. Bussi, & A.Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167-78). Reston, VA: NCTM.

Zohar, A., Degani, A., and Vaaknin, E. (2001). Teachers beliefs about low achieving students and higher order thinking. Teaching and Teacher

Education, 17, 469-485.

Zohar, A. (2004). Higher order thinking in science classrooms: Students learning and teacher professional development. Dordrecht, The

Netherlands: Kluwer.. Zohar, A., & Dori, Y. J. (2003). Higher order thinking skills and low achieving students: Are they mutually

exclusive? Journal of the Learning Sciences, 12(2), 145183.

Zoller, U., Ben-Chaim, D., Ron, S., Pentimalli, R., & Borsese, A. (2000). The disposition toward critical thinking of high school and university

science students; An inter-intra IsraeliItalian study. International Journal of Science Education, 22(6), 571582.

Zoller, U., Dori, Y., & Lubezky, A. (2002). Algorithmic, LOCS and HOCS (chemistry) exam questions: Performance and attitudes of college

students. International Journal of Science Education, 24(2), 185203.

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