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Effects of a Problem-based Structureof Physics Contents on ConceptualLearning and the Ability to SolveProblemsCarlos Becerra-Labra a , Albert Gras-Martí b c & Joaquín MartínezTorregrosa da Instituto de Matemática y Física, Universidad de Talca , Talca ,Chileb Universidad de los Andes, CIFE-LIDIE and Departamento deFísica , Bogotá , Colombiac Universitat d'Alacant, Física Aplicada , Alacant , Spaind Universitat d'Alacant, Didàctica de les Ciències , Alacant , SpainPublished online: 29 Sep 2011.

To cite this article: Carlos Becerra-Labra , Albert Gras-Martí & Joaquín Martínez Torregrosa(2012) Effects of a Problem-based Structure of Physics Contents on Conceptual Learning andthe Ability to Solve Problems, International Journal of Science Education, 34:8, 1235-1253, DOI:10.1080/09500693.2011.619210

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Effects of a Problem-based Structure

of Physics Contents on Conceptual

Learning and the Ability to Solve

Problems

Carlos Becerra-Labraa∗, Albert Gras-Martıb,c andJoaquın Martınez Torregrosad

aInstituto de Matematica y Fısica, Universidad de Talca, Talca, Chile; bUniversidad de

los Andes, CIFE-LIDIE and Departamento de Fısica, Bogota, Colombia; cUniversitat

d’Alacant, Fısica Aplicada, Alacant, Spain; dUniversitat d’Alacant, Didactica de les

Ciencies, Alacant, Spain

A model of teaching/learning is proposed based on a ‘problem-based structure’ of the contents of the

course, in combination with a training in paper and pencil problem solving that emphasizes

discussion and quantitative analysis, rather than formulae plug-in. The aim is to reverse the high

failure and attrition rate among engineering undergraduates taking physics. A number of tests

and questionnaires were administered to a group of students following a traditional lecture-based

instruction, as well as to another group that was following an instruction scheme based on the

proposed approach and the teaching materials developed ad hoc. The results show that students

following the new method can develop scientific reasoning habits in problem-solving skills, and

show gains in conceptual learning, attitudes and interests, and that the effects of this approach on

learning are noticeable several months after the course is over.

Keywords: Physics teaching and learning; Problem-based content structure; Problem

solving; Recall effects; Student attitude; Interest

International Journal of Science Education

Vol. 34, No. 8, 15 May 2012, pp. 1235–1253

∗Corresponding author: Instituto de Matematica y Fısica, Universidad de Talca, Talca, Chile.

Email: cbecerra@utalca.cl

ISSN 0950-0693 (print)/ISSN 1464-5289 (online)/12/081235–19

# 2012 Taylor & Francis

http://dx.doi.org/10.1080/09500693.2011.619210

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1. Introduction

One of the roles we attribute to educational centres (schools, colleges and universities)

is that of training new generations for an effective integration into society. The history

of science education shows us how, just as there have been major changes in the scien-

tific, technological, economic and social orders, there has been a parallel promotion of

changes in education. And the current economic globalization and rapid scientific,

technological and organizational developments impose new challenges to both pre-

university educational institutions and universities, which have demanded substantial

changes in their educational processes and in the models used for training citizens and

professionals in the present century.

Given this newenvironment, educational institutionsmustdealwith this challenge and

encourage a process of cultural change and teaching innovations in the context of a cur-

riculum designed to develop skills (Gil & Carrascosa, 1985; Gonzalez, Wagenaar, &

Beneitone, 2004; Tirado et al., 2006), where student learning should be the focus of

the education system. From a teacher-centred model (traditional educational paradigm)

we should move to a student-centred model (new educational paradigm).

Teaching in this new educational paradigm should develop in students the ability to

solve problems, and teachers should try to learn how to best help students to acquire

the skills that will enable in them a systematic and continuous search of knowledge, as

well as developing a logical, critical and creative way of thinking. This involves review-

ing and implementing different pedagogical models, shifting the current emphasis on

knowledge transfer, to the process of knowledge generation and the development of

skills that are fundamental in our society today.

One of the goals of science education and, in particular, physics education research

(PER) worldwide is ‘teaching students to solve problems’ (Harskamp & Ding, 2006;

Sabella & Redish, 2007; UNESCO, 2004). In a previous paper (Becerra-Labra, Gras-

Martı, & Martınez-Torregrosa, 2005), a literature review shows that this activity is

usually, and almost exclusively, limited to solving end-of-chapter physics problems.

However, the widespread students’ failure in problem solving, especially in the first

year of their degrees, led us to question if, in reality, they are being taught to solve pro-

blems at all. The previous study concluded that students are not taught how to con-

front and solve real problems, but instead they are exposed to solving standard

excercises; this makes it very difficult for students to tackle new problems on their

own, due to deficiencies in the teacher’s methodology and the concommitant stu-

dents’ attitudinal deficits. In particular, in our universities (Becerra-Labra et al.,

2005) there is a widespread failure and attrition rate of students in introductory

physics courses for undergraduates.

In order to try to change this situation significantly, we have developed a model for

teaching and learning (T&L) physics with a problem-based structure. The proposal is

based on an analysis of the evolution of physical science, which shows that scientists

discuss and attempt the solution of specific problems, usually guided by curiosity or

practical applications. In the process of solving specific experimental results or theor-

etical questions, scientists may come up with new concepts or new laws that may or

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may not apply to a range of problems wider that the one they have at hand. From this

point of view, one can simplify the overall evolution of science in terms of a few basic

and general problems that have been tackled and solved (at least temporarily). From

those basic ‘problems’, a large number of particular cases or applications may follow

that contribute to a deepening in understanding of the concept or the law that has

been developed. It is with this model of science evolution in mind, which we describe

as a problem-based structure of science, that we shall develop our proposal for the

process of T&L.

In the following section we shall describe the theoretical basis for the T&L model

proposed, and its application to improve students’ problem-solving skills. The

implementation of the model has been tested with the instruments described in

Section 3. In Section 4 we describe and analyse the results obtained. A conclusion

section closes the paper.

2. Theoretical Basis

In learning science, all students (not just a few) should learn to think effectively, to argue

and communicate scientificaly, to develop skills of analysis and synthesis, to solve pro-

blems (Bennett, 2008), and to operate with large amounts of data by selecting those rel-

evant for decision-making. This is not only important for a deeper understanding of the

conceptual content of the various scientific disciplines, but also (and simultaneously)

for the development of complex skills of logical thinking needed to function compe-

tently in these areas (Black, 2000; Pellegrino, Chudowsky, & Glaser, 2001). In particu-

lar, as stated by UNESCO (2004), science education should encourage and develop

both a scientific culture and the ability to solve problems. Furthermore, Garrett

(1987) points out that there is a long and widely held belief that solving problems is

a fundamental scientific activity, which differentiates it from other human activities.

Garrett (1987) argues that the process of solving problems goes beyond the scientific

field since it touches on other areas of life at individual and social levels, and can be con-

sidered as an expression of the development of creative thinking.

Consistently with these requirements, our proposed T&L model of physics

develops both cognitive skills (scientific knowledge), and procedural and trans-

verse skills (skills for life), like the development of logical, analytical and creative

thinking (Chang & Weng, 2002; Pushkinm, 2007). The simultaneous conceptual

and methodological development (Gil, 1993; Gil & Carrascosa, 1985; Martınez-

Aznar & Varela, 2009; Solbes, 2009) will be facilitated to the extent that the

process of T&L takes place in a context of (re)construction of knowledge (avoid-

ing, as much as possible, the transmission of knowledge in its final state) with

repeated and systematic opportunities to implement justification processes

typical of scientific research, and of problem-solving (as far as possible in each

educational level).

Furthermore, beyond teaching students problem-solving, physics courses also serve

as a pipeline for students to pursue careers in science. The fact is that there is a drop in

students’ interest towards studying science, in general, and chemistry and physics, in

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particular, since the mid-eighties in the past century (Matthews, 1994; Solbes & Traver,

2003; Yager & Penick, 1986). In an attempt to circumvent this problem, the proposals

in the nineties aimed at achieving not only conceptual and procedimental changes, but

also attitudinal changes (Aikenhead, 1985; Duschl & Gitomer, 1991; Martınez-Aznar

& Ibanez, 2006; Solbes & Vilches, 1997). Recent publications stress that this lack of stu-

dents’ interest towards science is not declining (Solbes, Montserrat, & Furio, 2007;

Vazquez & Manassero, 2008). Therefore, efforts are needed towards an attitudinal

change that increases students’ interest and motivation towards science learning.

There are many proposals in the literature, originating in PER that attempt to

address the variety of T&L problems mentioned above. To mention just a few,

there are the well-known books by Eric Mazur on Peer Instruction (1997) and by

Novak, Patterson, Gavrin, and Christian (1999) on Just in Time Teaching; both

books emphasize the importance of student discussions in the classroom under the

guidance of the instructor, as well as the need for student preparation of the lecture

materials before entering the class. Education research studies have also been the

basis for textbooks like those of Chabay and Sherwood (2010), or for detailed teach-

ing materials like those developed by Guisasola, Almudı, and Zubimendi (2004) and

Guisasola, Zubimendi, and Zuza (2010). In the recent T&L proposals, care has been

taken to include concept questions and problems that acknowledge research studies in

students’ misconceptions (Duit & Treagust, 2003) and students’ cognitive develop-

ment (Coll, France, & Taylor, 2005).

In the T&L proposal that orients the present investigation, and which is described in

the following section, we take inspiration from the approach of Guisasola’s group (Gui-

sasola et al., 2010), including in-class discussion under the guidance of the instructor. We

make use also of recent studies by our group in the area of problem solving (Becerra-

Labra et al., 2005). Most of these ingredients are new and untested within the University

culture of our region. Therefore, the main objective of the present research is to check

whether a new T&L model, based on new materials and methods that are inspired by

the PER literature, will be applicable in our institution, and whether instruments can

be developed that measure the effects of their implementation. This may open the way

for further innovation in our classrooms at the university level.

2.1 A Physics Teaching Model with a Problem-based Structure

In order to organize the course structure and the contents of the various modules of a

physics course one starts by identifying some of the problems that lie at the root of the

scientific theories that the students should learn. One needs to discuss the relevance of

these problems and, more importantly, contextualize them. Then one has to design a

strategy that will allow students to advance towards a solution to the problems raised,

in a hypothetical/deductive process, and to provide opportunities for the appropria-

tion of the related scientific epistemology.

This requires performing a historical, epistemological and didactic analysis on the

subject to be taught, and to present it in a way that its study can be useful, interesting

and feasible for students. As a result we designed a course structure that allows

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students, under the guidance of the teacher, to face problems of interest, putting into

play much of the production and validation processes of scientific knowledge (Millar,

Leach, & Osborne, 2000; Monereo & Pozo Municio, 2003). More specifically, the

proposed T&L model requires that:

1. We must design the sequencing of course topics with a problem-based structure

as a possible strategy for advancing towards the solution of the fundamental initial

questions (structuring problems). This will provide a common thread of analysis

where every issue becomes a specific problem whose solution can help in addressing

the initial set of problems. And, at the same time, new problems will appear, thus

increasing the relations between the different topics and creating a more complex

structure of the subject matter.

2. We should explain, at the beginning of the course and of each section, what are

the structuring problems that serve as a starting point for the student’s work. Of

course, care should be taken that students properly appropriate themselves of these

structuring problems.

3. We have to organize the discussion of each of the issues raised by the set of pro-

blems so that they respond to a possible strategy for its solution; although active stu-

dents’ work is the main methodology used, the programme or guide of activities may

include appropriate activities to be developed by the teacher. The structure and

sequence of each part of the course must be logically linked to the initial problematiza-

tion. The structure of the contents is, therefore, not guided, as it usually happens, by the

fundamental concepts of that part of the discipline, but by the fundamental questions,

in an attempt to raise and advance key issues within the subject matter. In an attempt to

solve these problems, concepts are introduced functionally, as part of the process of

addressing the issues raised and trying to unify initially unrelated fields. In effect, if

scientific knowledge is the result of an attempt to answer questions, why should we

pretend that students learn answers without knowing what questions to answer?

4. We should consider problem solving in this sense of addressing some fundamen-

tal questions in a specific branch of physics. In this problem-solving context, concepts

and models are introduced, by the students and the teacher, on a tentative or hypothe-

tical basis which has to be tested; testing may involve both its predictive ability in lab-

oratory practices and also addressing specific problematic situations, which can be

modelled on the basis of the same concepts that have been introduced (context of

problem solving, including decision-making in situations of social interest). The res-

olution of ‘pen and paper’ problems and hands-on lab work can be integrated within

this problem-based structure and with the introduction of concepts and their relation-

ships (Gil et al., 1999; Monereo & Pozo Municio, 2003).

5. We have to carry out periodic summaries (problematized summaries) of what has

been achieved in the solution to the initial structural problems, what obstacles have

been overcome and what still remains to be done. This is an essential part of the

T&L process.

The T&L model which has been outlined above is carried out within a context of

classroom work that encourages explaining one’s own ideas and comparing them

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with the fellow students’ (Heller, Keith, & Anderson, 1992), in a hypothetical-

deductive environment which is rich in reasoning and justification episodes, since

these are important factors for learning scientific knowledge (Driver, Newton, &

Osborne, 2000; Leach & Scott, 2003). The aim is to ultimately create an environment

that simultaneously promotes the emotional involvement and scientific rationality of

all actors implicated (teachers and students) in the resolution of problems. Of course,

this requires careful planning by the teacher of properly intertwined guides with activi-

ties that incorprate the necessary time for students to think, analyse, argue, refute and

interpret.

We have applied this methodological strategy to an introductory course in Newto-

nian mechanics for first year undergraduate students. The first problem we start with,

which is at the origin of mechanical theory, and which serves as a starting point for

student’s work, is ‘to find a unitary explanation, common to the movement of all

things (celestial and terrestrial bodies)’. The details of the contents developed have

been published elsewhere (Becerra-Labra et al., 2005). This T&L model has been

complemented with a revised approach to how students solve ‘pen and paper’ pro-

blems that we describe below.

2.2 Regarding Problems and Their Resolution

In a previous paper (Becerra-Labra et al., 2005) we addressed the question: ‘What do

we mean by a problem?’ The consensus in the literature is to consider a problem as a

situation that poses difficulties for which solutions are not apparent (Gil & Martinez

Torregrosa, 1983; Krulik & Rudnik, 1980; Perales, 2000). The definition of Krulik

and Rudnik (1980) summarizes this consensus: ‘A problem is a situation, quantitative

or otherwise, which calls for a solution, for which the individuals involved know no

apparent means or ways to solve it’. Thus, ‘solving a problem’ means ‘to find a sol-

ution to a problematic situation that is relatively new to the person trying to solve

it’. This requires, to some degree, having previously developed certain skills and abil-

ities; for example, the ability to analyse, understand and set limits to the problem, the

skill to apply and synthesize prior knowledge about the problem to be solved,

the ability to make decisions about how to proceed, the knowledge of how to assess

the measures taken in the resolution process and being able to analyse the result

(Becerra-Labra et al., 2005; Gil, Dumas, & Martinez-Torregrosa, 1990; Harskamp

& Ding, 2006; Maloney, 1994; Martınez Torregrosa, Gil, Becerra Labra, & Guisa-

sola, 2005; Perales, 2000; Polya, 1957).

PER in problem solving shows that in spite of the fact that many students may have

sufficient prior knowledge about the problem to be solved, they fail in its resolution

(Harskamp & Ding, 2006; Sfard, Nesher, Streefland, Cobb, & Mason, 1998). The

main difficulties that students face in solving problems relate to a low degree of devel-

opment of certain skills that are essential in any process of problem solving, for

example, linking their prior knowledge to the new problem situation, conducting a

qualitative analysis of the situation, developing a solution strategy or carrying out

appropriate calculations. Based on an analysis of physics problem-solving research,

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Maloney (1994) described the conditions for students success in problem solving,

namely that they develop a solution strategy, do a qualitative analysis of the

problem (doing a sketch of the problem and rebuilding it in his/her own words),

Table 1. A flexible guiding structure for problem solving

‘Resolution indicators’ for problem solving

There are five indicators that show in students an adequate approach towards solving a problem:

1. Analyse qualitatively and understand the problematic situation

Read the problem situation and start its solution with a description of what is going on, analysing

and imagining the physical situation. Make a schematic-drawing

To understand the problematic situation or problem, ask oneself ‘framing questions’. To answer the

questions, think, reflect and look for information. For example, ask the following guiding questions:

What is the problem? What are we seeking? and, What conditions should we assume to solve the

problem?

In this preliminary stage, we express the conditions that will lead us to narrow down and define the

problem, formulating in physical–mathematical terms what is to be determined (operativization). In

other words, we express explicitly what is to be determined and under what conditions will it be

solved

Once the conditions and what needs to be determined are identified explicitly in the problem, one

should analyse, reflect and discuss them

2. Hypothesis formulation

Ask the following guiding question (and discuss it, if one is working in a team): On which factors do

the physics quantities that are sought depend upon? One needs to activate relevant prior knowledge

and formulate hypothesis about the factors upon which the physical quantity that is sought may

depend. Next, ask: How does it depend on the magnitude of the proposed factors?

3. Strategy elaboration

Elaborate, with a temptative character, a possible strategy for solving the problem before attempting

to do it, in order to facilitate a rigorous confrontation of the assumptions, and show its coherence

with the body of knowledge that is available. Do not present the strategy as something evident or

certain

4. Problem solving

Solve the problem by implementing the proposed strategy, verbalizing what is done and avoiding

operational manipulation lacking any physical significance

5. Analysis of results

Analyse the results obtained in the light of the scenario which has been developed, and their

consistency with the available body of knowledge, always questioning the results

6. Prospects opened up

Finally, it may be useful in many cases to consider the prospects opened up after the solution. Take

into account, for example, the possibility of addressing the problem to a higher level of complexity or

to address new situations of practical or theoretical interest. Reflection on new perspectives should

include a brief summary of the difficulties encountered and how they have been overcome; this helps

improve the ability to cope with new problems

(Note: if one works as part of a team, the entire solution process should be done by using the

approach of ‘discussing proposals and ideas’ with the team in order to reach an ‘informed

agreement’)

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and have the ability to connect the problem with the equations and laws that conform

to its solution.

In the following, we propose a ‘problem-solving’ model that helps develop the

ability to solve ‘pen and paper’ problems. The different stages of the model are

shown in Table 1. It should be emphasized that this set of steps (resolution indicators)

should not be applied as a closed and linear loop (step by step and including all stages)

(Harskamp & Ding, 2006; Schoenfeld, 1992, 1994). Instead, we are proposing a

structure of ‘relevant guidance’ only and of ‘flexible’ implementation, which is only

intended to help students develop their own strategies for resolution. The stages of

a problem-solving strategy will depend on the type of problem to be solved and the

students’ mental models with which they study science (Redish, 1994). It is essential

to promote and encourage students to develop their own strategy for resolution.

We have applied this approach toproblemsolving in conjunctionwith teaching materials

based on the T&L model described in Section 2.1. The results will be shown below.

3. Working Hypotheses and Experimental Designs

Three sets of assumptions will guide the application of the T&L model with a

problem-based structure, which we shall test with the experimental designs that are

described in each case.

Assumption 1: It will provide adequate opportunities in the classroom for students to

learn scientific concepts with understanding, and the significance of this learning will

remain long after the instruction is over.

To verify this assumption, we have designed:

(a) A ‘proof of concept’ with 10 questions. By way of example, Table 2 shows one of

the questions. This assessment tool will be solved by all students (in a test setting)

in the penultimate week of the course term.

(b) Three conceptual tests will be used to assess to what extent the significance of this

type of learning remains after the instruction period is over. With questions

similar to the question shown in Table 2, we aim at measuring the level of concep-

tual ‘memory’ in three different moments once the course is over. These instru-

ments will be applied, to students who have passed the introductory physics

course, 3, 6 and 12 months after completion of the course.

Table 2. Sample conceptual test question (answered in an exam setting)

One person claims it is possible to get a collision between two identical billiard balls on a smooth

horizontal table (one ball moving with a speed V1 towards a resting ball), so that after the collision

the resting ball moves with a speed 2V1 and the other ball bounces back at a speed (2V1) (in a

direction opposite to the motion of the initial ball), as this process would comply with the principle

of conservation of momentum. Analyse the extent to which this statement may be correct or not;

explain and justify your answer

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Assumption 2: It will positively alter the students’ attitudes and interest towards

physics. In order to verify this we designed two questionnaires. Part of the question-

naires is shown in Section 4, in Tables 7 and 8.

Assumption 3: Faced with a problem, students will not immediately start manipulat-

ing formulas, data and unknowns, a typical attitude of ‘blind operationalism’. On the

contrary, it is expected that:

(a) They start to address the problem with a qualitative approach, i.e. with a descrip-

tion of what the problem is, specifying under which conditions they will solve the

problem, and formulating in physical and mathematical terms what they are

looking for. This will show a correct operationalism.

(b) Explain a possible strategy for solution before attempting it.

(c) Reach the solution as the implementation of the proposed strategy, always

explaining and verbalizing what they do.

(d) Discuss the results.

In order to check whether there has been a significant increase in the ability to solve

problems, we have developed a ‘problems proof’; in Table 3 we show an example of

test problem. This assessment tool will be solved by all students in an exam setting in

the last week of the course term. In order to assess to what extent students show a sig-

nificant increase in the ability to solve problems, we have designed three tests ‘pro-

blems’ similar to the one above. These will be applied, to students who have passed

the introductory physics course, 3, 6 and 12 months after completion of the course.

In order to prove that a T&L approach to physics with a problematized structure leads

to significant improvement in all aspects mentioned in previous sections, we have pro-

ceeded as follows: students (aged 17–18) of the first year physics course in the Agronomy

Engineering degree were randomly divided into two groups of about 60 students:

1. The experimental group (EG) was taught by a teacher using the problematized

physics T&L approach.

2. The control group (CG) was taught by a teacher using the traditional teaching

approach.

All evaluation instruments (conceptual tests and problema sets) are the same for

both students groups; the correction matrices and the corresponding indicators

were built and agreed by the teachers of both groups. Therefore, before the start of

Table 3. An example of a model problem, posed in an exam setting

1. A plane that flies horizontally at height H0 and with a constant velocity u, drops a bomb. In the

direction of the plane’s flight, and at ground level, there is a weapon depot. At which horizontal

distance must the plane be from the depot at the instant the bomb is dropped, to impact on it?

2. A boy of mass m is at rest at the highest point of a hemispherical mound of radius R. When he

slides down the mound, at which height does the boy stop touching the hemispherical track? (Ignore

friction)

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the course the teachers of the EG and CG knew the kinds of questions and problems

that would be used to assess student achievements. Furthermore, the correction

matrices were also made available to all students at course start. By way of

example, Table 9 shows the indicators (Becerra-Labra et al., 2005) of the problems

administered to both student groups.

3.1 Quality of the Experimental Instruments

A few words are in order concerning the quality of the instruments that have been

used in this study. Table 4 shows these instruments.

The detailed validation process of each test is described in Becerra-Labra (2011). In

brief, the procedure suggested by Beichner (1994) was followed for each test and

included a formulation of the objectives, a construction of the test items, a content vali-

dation among colleagues in the department and a reliability check of the final form of

the test. The tables of specifications for for the cognitive levels that were addressed in

each test item were based on Bloom’s taxonomy (1956). In writing down the items

or the set of problems for a test we took into account both suggestions for writing

good items and questions (Linn & Gronlund, 2000) and the ample collection of stu-

dents’ misconceptions that have been reported in the PER literature (Duit & Treagust,

2003). Field testing was performed among colleagues in our university and in the uni-

versities of Alacant and Valencia. With this exercise we evaluated test reliability and val-

idity and item analysis (Crocker & Algina, 1986). Of course, a slow editing process of

test items took place during the 12 months of test preparation and validation.

As an example of the kind of data obtained in these procedures for test validation let

us note that the p-value (measuring the difficulty of a given item) was always in the

acceptable range 0.4–0.65 (Doran, 1980), and the Ferguson’s delta (Ding, Chabay,

& Sherwood, 2006) which is used to determine the discrimination power of a test as

a whole, was larger than 0.85 for all the tests in Table 4. Along the investigation we

were also able to check the reliability of the tests, i.e. ‘the consistency of the scores

obtained by the same persons when reexamined...’ (Anastasi, 1988). We obtained a dif-

ficulty value around 43–56%, which is close to the optimum difficulty level of 50%.

Other measures of classical test theory were also employed (Becerra-Labra, 2011).

Table 4. Instruments developed to test the research questions

Objectives to measure Tests developed

Understanding and long-term recall Proof of concepts

Conceptual tests

Students’ attitudes and interest Questionnaire 1

Questionnaire 2

Problem-solving strategies Problems proof in final exam

3–6–12 months problem-solving test

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4. Results and Analysis

The model of T&L physics with a problem-based structure that we have described has

been tested in three successive terms. In this article we just show the results of the first

application of the model, since (and this is a very important fact in support of the pro-

posed model) the results of the other two applications were virtually identical.

The percentage of correct answers to the ‘conceptual test’ is shown in Table 5.

A total of 50 CG students and 57 EG students took the exam, and the differences

in favour of EG are large and statistically significant in all the questions. Furthermore,

and as an example of qualitative differences between both groups, we discuss the

results of question six (shown in Table 2): the correct answer requires knowing that

changes that can occur in an isolated system are constrained by the conservation of

momentum and energy; and to verify that, under the circumstances of the problem,

although the result suggested in the formulation of the problem complies with the

principle of conservation of linear momentum, the total kinetic energy after the col-

lision is four times the total kinetic energy before the collision; therefore, that event

is not possible. In total, 61.4% of the EG gave a correct answer compared with

28.0% of CG and, also, when the number of meaningful sentences is accounted for

(an indicator of qualitative and argumentative thinking), the average is much higher

(almost a factor two) in the EG than in the CG.

Table 6 shows the percentage of correct answers to the three tests designed to

measure the level of conceptual ‘memory’ of students from EG and CG. The test

was administered, 3, 6 and 12 months after the course was over, only to those students

who passed the physics course; since student participation was voluntary and not all of

them took the tests. Consistently with the results of the conceptual test, students from

EG obtained a notable percentage of correct results, and significantly higher than CG

Table 5. Results from the conceptual test (in exam situation)

Correct answers (%)

Question

1 2 3 4 5 6 7 8 9 10

CG (N ¼ 50) 32.0 40.0 30.0 28.0 34.0 28.0 28.0 26.0 32.0 20.0

EG (N ¼ 57) 54.4 61.4 50.9 52.6 57.9 61.4 61.4 70.2 56.1 49.1

Table 6. Results from tests to measure the degree of conceptual ‘memory’ recall

Total percentage of students with correct answers (%)

Three months later (First test) Six months later (Second test)

Twelve months later

(Third test)

EG (N ¼ 25) CG (N ¼ 15) EG (N ¼ 26) CG (N ¼ 14) EG (N ¼ 20) CG (N ¼ 15)

61.7 29.5 53.2 27.5 50.7 24.7

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students. This monitoring clearly shows that the level of conceptual ‘memory’ of EG

students is significantly higher than students from CG. Therefore, according to the

results shown in Tables 5 and 6, we can say that a problem-based education in

physics provides appropriate opportunities in the classroom for students to learn

scientific concepts, with proper understanding, and that significant learning lasts at

least several months after the instruction period is over. On the other hand, the fact

that typically a third or more of the answers to the tests in the EG are still incorrect

indicates that there is still room for improvement in the T&L method proposed.

As mentioned in Section 4, we expect that the proposed T&L method positively

alters the attitude and interest of students towards physics. In other words, it is

expected that the proposed method is valued more positively than the traditional

method in the corresponding items in the questionnaire I of Table 7. The question-

naire has been answered by the students from the EG, anonymously and individually,

on completion of the course. The result of the comparative assessment of both T&L

methods is shown in Table 7, and it clearly proves the point. One finds profound

differences in the ‘perceptions’ that the students have among the proposed method

and the ones used in past physics courses.

The questionnaire II of Table 8 has been answered, voluntarily and anonymously,

by students from the EG and CG 12 months after the teaching period was completed.

Table 8 (part 1) shows the answer to the question: ‘Which subject(s) (maximum two)

from past semesters gave you a greater feeling of learning?’ In total, 65.5% of EG stu-

dents mentioned physics as one of the two subjects providing a greater feeling of learn-

ing. However, no CG student stated physics within this category, while 33.3%

mentioned it among the subjects providing the least feeling of learning. The results

of the evaluation of the two different T&L methods, 12 months after the teaching con-

cluded (see Table 8, part 2), clearly shows that the proposed method is still perceived,

Table 7. Questionnaire I, designed to measure students’ perceptions regarding the T&L method

Please rate from 0 to 10 the degree of conformity with the following

statements in reference to the T&L method of the current physics

course and of previous T&L methods in physics that you have

experienced (10: totally agree; 5: indifferent; 0: totally disagree).

Comparative rating.

EG (N ¼ 57)

Present

method

Previous

methods

Average

(Sd)

Average

(Sd)

1 It increases the ability to solve all sorts of problems and physics

situations.

8.0 (0.9) 3.7 (1.2)

2 It trains you on how to solve problems and situations that have

not been dealt with before.

8.1 (0.7) 3.5 (0.7)

3 It promotes deep understanding of the concepts. 8.5 (0.6) 3.7 (0.9)

4 It leads to the acquisition of habits of discussion, argumentation,

strategic planning, and analysis of results.

8.7 (0.7) 3.7 (0.7)

5 It makes it attractive and interesting to solve problems and

physics situations.

8.2 (0.8) 3.3 (0.9)

6 It contributes to making physics more interesting. 8.0 (0.9) 3.3 (1.0)

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by students of EG, in a much more positive way than any other methods used in other

undergraduate courses. In contrast, CG students did not perceive in the same way the

method used in their own physics course.

Results from both questionnaires clearly show that students perceive the proposed

method in a much more positive way than any other methods to which they were

exposed, and this produced a positive change in their attitudes and interests in

physics.

In Table 9 we compare the answers given by the EG students to two problems in

physics with those given by CG students. The comparison is performed for the

Table 8. Questionnaire II, to test students’ recall of various T&L methods

Part 1 We are conducting an analysis to

improve the quality of teaching at our

university. With this in mind, please answer

the following questions:

Result obtained 12 months after completion

of the course.

EG (N ¼ 29) CG (N ¼ 15)

Subject n % Subject n %

1. Which subject(s) (maximum two) from

past semesters gave you a greater feeling of

learning?

Physics 19 65.5 (Physics is

not

included)

0 0.0

Biochemistry 15 51.7

2. Which subject(s) (maximum two) from

past semesters gave you the least feeling of

learning?

(Physics is not

included)

0 0.0 Physics 5 33.3

Calculus I 6 40.0

Part 2 Please Dear student, please rank

from 0 to 10 the following statements about

the Physics course that concluded a few

months ago (10: totally agree; 5: indifferent;

0: totally disagree).

EG (N ¼ 29) Average (Sd) CG N ¼ 15)

Average (Sd)

1. It helped improve my attitudes towards

physics.

8.5 (0.8) 3.2 (0.9)

2. It was really important to understand,

not memorise formulae.

9.0 (0.5) 6.5 (1.3)

3. The way the class was developed helped

towards ‘real’ learning.

8.7 (0.7) 3.5 (0.8)

4. It helped to improve my thinking skills, in

order to tackle new problematic situations.

8.6 (0.6) 4.1 (1.1)

5. I found it complicated: there was no

connection between what was done in class

and what was requested in the exam.

0.0 (-) 8.2 (1.0)

6. If I had to take another physics course I

would like it to be taught in a similar way.

8.4 (1.2) 2.5 (1.2)

7. I was guided during the course: I knew

why and what for we did everything (as

opposed to doing things without knowing

the aim or their relevance).

8.3 (1.1) 3.5 (1.3)

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characteristics listed in Table 9. Features such as ‘the formulation of hypotheses’,

‘questioning the results’ and ‘consideration of the perspectives opened up after the

problem is solved’ (mentioned in Table 1) have not been considered as indicators

in the answers of CG students, because these students have not been trained accord-

ingly. However, these three features are present in the answers by EG students: ‘for-

mulating hypotheses’ is present in 64% of EG students, ‘questioning the results’ is

present in 49% of the answers and ‘consideration of the perspectives opened up

after the resolution’ is present in 44% of EG students.

The results shown in Table 9 on the presence of the characteristic #1, namely, ‘are

there data or numeric values and formulae at the beginning of the solution?’, reveal

that at least for 77% of the students of CG this is true. In contrast, the presence of

data and formulae right at the start of the resolution does not exceed 10% of the

responses of EG students.

In line with this, no more than 48% of the students of CG ‘expressed the qualitative

aspects of a physics situation’, in other words, they provided an interpretative descrip-

tion of what happens. In contrast, the presence of this exceeds 75% of EG students.

The results show that the characteristic #4, namely, ‘a strategy for solution is devel-

oped before proceeding with it’, is present in no more than 42% of CG students. The

presence of a possible strategy for solution is present, in contrast, in more than 72% of

EG students. As above, the difference is quite significant in favour of EG students.

About 33% of CG students ‘address the solution of the problem as the implemen-

tation of the proposed strategy’. In the EG the presence of this feature exceeds 70% of

the students. In characteristics #6, ‘makes the decision based on the planned route

and verbalizing what is done’ and #7, ‘begin with a literal resolution before introdu-

cing numerical values’, the difference between the two groups (CG and EG) is even

larger in favour of EG students.

Table 9. Analysis of solutions to physics problems

All 60 students participated in each group.

Problem

1 (%)

Problem

2 (%)

CG EG CG EG

1 There are data and numerical values at the beginning of the solution 80 10 77 3

2 Expresses qualitatively the physics situation: functionality and

description of what happens

45 75 48 80

3 Expresses the conditions that will be assumed to address and define the

situation, formulating in physics-mathematical terms what the aim is

15 72 17 78

4 Develops a strategy for resolution before proceeding with it 38 72 42 75

5 Solves the problema as the implementation of the proposed strategy 33 70 35 75

6 Makes the decision based on the planned route and verbalizing what is

done

30 62 32 67

7 Begins with a literal resolution before introducing numerical values 32 67 33 73

8 Interprets in some way the results 17 52 15 62

9 Correct solution or answer 28 52 32 58

10 Gives up without solving the problem 43 13 43 8

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Characteristic #8, ‘interprets in some way the results’, is present in only a small per-

centage of CG students: no more than 17% (versus 52% of EG students) accompanies

the result with a comment about the quantities obtained or their physical meaning.

Table 9 shows also that the characteristic #9 ‘Produces a correct solution or answer’

is provided by 32% of CG students in problem 2, whereas in the EG, 58% of students

have the right solution on the same problem.

Given the attrition rates and wrong answers (#10 and #9, respectively) provided by

students in the CG, we can say that they are not taught properly to confront and solve

problems, but instead solutions are just presented to them during the lectures. No

wonder, then, the tendency of the students to try to recognize whether the problem

presented to them is similar to one that has been done before; if that is not the

case, they just give up on the solution of the problem. As in all characteristics, the

difference is significant in favour of EG students with respect to CG students.

The three tests of ‘memory’ recall mentioned in Section 3 have been applied only to

those EG and CG students who have passed their respective physics course, and the

student participation is voluntary. In the light of the results shown in Table 10 for tests

of ‘memory’ recall applied 3, 6 and 12 months after the teaching period of the subject

concluded, the results clearly show that EG students give a good percentage of correct

results and the figures are significantly higher than for the CG students. Accordingly,

Table 10. Analysis on the persistence of problem-solving abilities, 3, 6 and 12 months after the

instruction period is over

Problem 1

EG CG EG CG EG CG

After 12

months

After 6

months

After 3

months

%

1 There are data and numerical values at the beginning of the

solution

15 80 4 71 8 67

2 Expresses qualitatively the aspects of the physics situation:

functionality and description of what happens

60 33 62 36 76 53

3 Expresses the conditions that will be assumed to address

and define the situation, formulating in physical and

mathematical terms what the aim is

55 13 58 14 60 27

4 Develops a strategy for resolution before proceeding with it 50 27 58 29 68 33

5 Solves the problem via implementation of the proposed

strategy

50 27 58 29 64 33

6 Takes decisions verbalizing what is done 35 20 50 21 56 20

7 Begins with a literal resolution before introducing

numerical values

50 27 54 29 60 27

8 Interprets in some way the results 40 7 42 7 56 20

9 Correct solution or answer 50 20 54 21 52 27

10 Gives up solving the problem 15 53 12 50 16 40

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we can say that the ability to solve ‘pencil and paper’ problems is maintained even

several months after the instruction is received.

In conclusion, the results expressed in Tables 9 and 10 show that the problem-solving

model incorporated in out T&L proposal produces a significant increase in the ability to

solve ‘pencil and paper’ problems and this ability is maintained long after the instruc-

tion is over; they also show that significant improvements in student learning of EG stu-

dents are obtained. In spite of the fact that the results expressed in Tables 5–10 show

clearly these gains and the efficiency of the model, we performed a ‘statistical hypothesis

test’ (Welkowitz, Ewen, & Cohen, 1971) to decide whether the percentage difference

for ‘the presence of the characteristics being studied’ is statistically significant in

favour of EG students. For this type of data it is appropriate to apply the z-test statistics.

With a significance level of 5%, if the absolute value of z is larger than the critical value

(1.96) then there is a significant statistical difference in favour of EG students. This is

the case for all characteristics and data shown in Tables 5–10.

5. Conclusions

Let us remind ourselves that the main objective of this study was to develop a T&L

model of physics with a problematized structure with the aim of yielding significant

student learning and reverse the high failure and attrition rates, which traditionally

varied in the 20–35% range. In the study we split first year physics students in two

groups (CG and EG) of about 60 students each. We obtained the following final

pass rate (including an extra optional test for those who failed in the first chance,

and which was equivalent to the problems test): about 38% of the CG students

passed, and about 60% of the EG students passed. These pass/failure results for

the two groups were similar in the three different semesters that the model was

implemented.

In the instruments that were applied (tests and questionnaries), we find that in all

the indicators and characteristics the difference is quite significant in favour of the EG

group. Furthermore, an improvement in the academs results of the EG group was

obtained. Since the previous results were reproduced in various semesters, we feel

that the implementation of the T&L strategy described in this paper would yield

similar results in other higher education institutions. However, this point has yet to

be tested.

In the light of the results obtained in this study, we can say that a problem-based

structure of T&L physics produces a significant improvement in learning and aca-

demic achievement of most students. It has been proven that a physics education orga-

nized around a problem-solving approach produces a significant improvement

in conceptual learning, a significant increase in the ability to solve ‘pencil and

paper’ problems and in the attitudes and interests of students towards physics.

However, one question which we have not addressed in this research project is the

application of our T&L model to laboratory sessions; this was due to the fact that the

particular introductory physics course that we studied does not include them. This

task remains for the future.

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This research opens up new and fruitful ways of teaching in our region for the first

semesters of undergraduate studies, via the implication of both students and teachers

in a collective task, in line with the usual methods of scientific work. The results of this

study may help change the situation in the classrooms in our region, by paving the way

for the necessary and urgent updating in physics teachers, both for improving physics

learning and to increase the scientific knowledge that society demands.

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