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Mapping a Student's Causal Conceptions From a Problem-Solving Protocol
Abstract
INTRODUCTION The problem of how to describe t.he structure of B student's current concep tions in I!l given area is 8 fundamental one for researchers who Beek to develop 8 theoretical foundation for cognitively oriented instruction . Recent develop ments in the physics leaching community, for elample, have emphasized cogni lively oriented approaches to teaching and the need for understanding the cognitive processes tbat underlie one's ability to "do" physics. Ideally, we would Ilke to have 8 picture of the kinds of knowledge structures and reasoning processes that are present in beginning students and that ate present in experts. Detailed descriptions of experts' knowledge structures, including those tacit knowledge structures not represented explicitly in the curriculu.m, would pre· sumably belp to define more clearly what is to be learned by the student. Detailed descriptions of beginning students' preconceptions and misconceptions would have value not only 8S a sophisticated evaluation tool, but would also make it more possible to take ccmroon preconceptions and misconceptions into 8.ccounl during instruction. This paper attempts to show that it is possible to st.udy systematically certain types of beginning students' conceptions in physics; specifically, causal concep· tions in mechanics. The paper examines the conceptions 8 freshman student uses to understand a simple physicol system involving the horiz.ontal motion of 8 cart launched scross 8 table, The task given to the student does Dot ask him to find 8. long series of adions which will solve a problem. Rather he is Bsked for a prediction and explanation of the effects on the system resulting from a single action. Protocols of 8uch explanations are particularly interesting because they tend not to be limited to formal, deductive arguments, but to include informal arguments that reflect the structuring of the subject's physical intuitions. The methodology used in this study involves two phases: obtaining problem· solving protocols via taped interviews, and analyzing these protocols to produce a model of the conceptions that Wlderlie the student's responses in the in. krv.iew. Several considerations are important t.o the success of this U!chnique. An Import.ant consideration daring the interview process is the attempt to en.
... Many researchers f. e. Clement (1978), Watts, Gilbert (1983), Duit (1984Duit ( , 1981, Kesidou, Duit (1993), Trumper, Gorsky (1993), Trumper (1993, 1998), Legget (2003, Kuhnová, Held (2010), etc… have noted students´ lack of differentiation between energy and other physical term, especially the force and work. stated that the force is confused likes energy. ...
... -depository framework: some objects have energy and expend it. Clement (1978) named this model "source of force". Pupils see some objects as having energy, some as needing energy and yet others as neutral. ...
... The finding that students' naive conceptions are both pervasive and persistent is corroborated by the research of a number of investigators in various countries. Studies conducted by science educators and psychologists (including Brumby, 1982;Clement, 1979;Driver, 1973;Driver & Easley, 1978;Fleshner, 1963;Green, McCloskey & Caramazza, 1980;Gunstone & White, 1981;Leboutet-Barrell, 1976;Rowell & Dawson, 1977;Selman, Jaquette, Krupa & Stone, 1982;Viennot, 1980) demonstrate that, for several science content areas: ...
... The resistance of students' naive conceptions to change is particularly striking in the context of mechanics, where prior to formal instruction young people and adults have naive macroschemata for motion that are more Aristotelian than Newtonian (Champagne, Klopfer, Solomon & Cahn, 1980b;Clement, 1979;Driver, 1973;Leboutet-Barrell, 1976;Viennot, 1980). The persistence of remnants of the Aristotelian macroschemata in many 'successful' physics students-that is, students receiving high grades in introductory physics courses-has been shown in various studies (e.g. ...
... They are truly "explanatory," because they clarify why the world is as it is. In addition, these conceptions can be considered models because they usually consist of a set of concepts connected by causal links that help to interpret the phenomena concerned in terms of the underlying structure of these phenomena (Clement, 1979; Gentner & Stevens, 1983). This research was supported in part by a grant from the Faculty of Medicine of McGiil University to Henk G. Schmidt while he was a visiting professor at that institution and by Grant 27798 from the Josiah Macy Jr. Foundation to Vimla L. Patel. ...
... The question of interest with regard to the second issue was, In response to a problem, do subjects construct situation-specific explanatory models based on prior knowledge? An explanatory model was defined here as a set of concepts, connected by causal links, that provides an interpretation of observable phenomena in terms of their underlying structure (Clement, 1979; Gentner & Stevens, 1983). In order to find an answer to the question at hand, the analyses of the blood cell problem conducted by the various experimental groups were transcribed. ...
Two experiments assessed effects of activation of prior knowledge through small-group discussion. Subjects were given a description of natural phenomena and were asked to elaborate on possible explanations for them. In Experiment 1, small groups of subjects were presented with a problem describing the behavior of a blood cell in pure water and in a salt solution. No additional text was studied. The experimental subjects produced more than twice as many propositions about osmosis (i.e. the biological process explaining the blood cell's behavior) as a control group produced. Experiment 2 investigated effects of problem analysis on subsequent text processing for subjects with imprecise prior knowledge (novices) and subjects with precise knowledge (experts). Recall of the text showed considerable facilitative effects of problem analysis. Results are explained in terms of faster accessibility of prior knowledge and better integration of new information into explanatory models that may exist before, or are actively constructed during, problem analysis.
... The research we examine furnishes a context for describing the existing situation, the uninstructed student's cognitive state, and distinguishing it from the desired situation. Various empirical studies conducted by science educators (including Brumby, in press;Driver, 1973;Driver & Easley, 1978;Fleshner, 1963;Gunstone & White, 1981;Leboutet-Barrell, 1976;Rowell & Dawson, 1977;Singer & Benassi, 1981;Viennot, 1979) and psychologists (including Clement, 1979;Green, McCloskey & Caramazza, 1980;Selman, Jaquette, Krupa, & Stone, in press) demonstrate that, for several science content areas: ...
... Aristotelian' than Newtonian (Champagne, Klopfer, Solomon, & Cahn, 1980;Clement, 1979;Driver, 1973;Driver & Easley, 1978;Leboutet-Barrell, 1976;Singer & Benassi, 1981;Viennot, 1980). Other research findings show that remnants of the Aristotelian conception persist with many "successful" physics students, that is, with students receiving high grades in introductory physics courses (Champagne, Klopfer & Anderson, 1980;Gunstone & White, 1981). ...
The utilization of cognitive psychological theory and findings from research to inform the design of instruction is illustrated in this paper. Physics learning studies demonstrate that students' pre‐instructional world knowledge is often logically antagonistic to the principles of Newtonian mechanics taught in introductory physics. Under these conditions psychological theory predicts that learning will be inhibited, a prediction consistent with both the experiences of physics teachers and the results of empirical investigation. Informed by cognitive research on problem solving, semantic memory, and knowledge acquisition, instruction has been designed to encourage the reconciliation of world knowledge and physics content among beginning physics students.
... The finding that students' naive conceptions are both pervasive and persistent is corroborated by the research of a number of investigators in various countries. Studies conducted by science educators and psychologists (including Brumby, 1982;Clement, 1979;Driver, 1973;Driver & Easley, 1978;Fleshner, 1963;Green, McCloskey & Caramazza, 1980;Gunstone & White, 1981;Leboutet-Barrell, 1976;Rowell & Dawson, 1977;Selman, Jaquette, Krupa & Stone, 1982;Viennot, 1980) demonstrate that, for several science content areas: ...
... The resistance of students' naive conceptions to change is particularly striking in the context of mechanics, where prior to formal instruction young people and adults have naive macroschemata for motion that are more Aristotelian than Newtonian (Champagne, Klopfer, Solomon & Cahn, 1980b;Clement, 1979;Driver, 1973;Leboutet-Barrell, 1976;Viennot, 1980). The persistence of remnants of the Aristotelian macroschemata in many 'successful' physics students-that is, students receiving high grades in introductory physics courses-has been shown in various studies (e.g. ...
... They are truly "explanatory," because they clarify why the world is as it is. In addition, these conceptions can be considered models because they usually consist of a set of concepts connected by causal links that help to interpret the phenomena concerned in terms of the underlying structure of these phenomena (Clement, 1979; Gentner & Stevens, 1983). This research was supported in part by a grant from the Faculty of Medicine of McGiil University to Henk G. Schmidt while he was a visiting professor at that institution and by Grant 27798 from the Josiah Macy Jr. Foundation to Vimla L. Patel. ...
... The question of interest with regard to the second issue was, In response to a problem, do subjects construct situation-specific explanatory models based on prior knowledge? An explanatory model was defined here as a set of concepts, connected by causal links, that provides an interpretation of observable phenomena in terms of their underlying structure (Clement, 1979; Gentner & Stevens, 1983). In order to find an answer to the question at hand, the analyses of the blood cell problem conducted by the various experimental groups were transcribed. ...
Two experiments assessed effects of activation of prior knowledge through small-group discussion. Subjects were given a description of natural phenomena and were asked to elaborate on possible explanations for them. In Experiment 1, small groups of subjects were presented with a problem describing the behavior of a blood cell in pure water and in a salt solution. No additional text was studied. The experimental subjects produced more than twice as many propositions about osmosis (i.e., the biological process explaining the blood cell's behavior) as a control group produced. Experiment 2 investigated effects of problem analysis on subsequent text processing for subjects with imprecise prior knowledge (novices) and subjects with precise knowledge (experts). Recall of the text showed considerable facilitative effects of problem analysis. Results are explained in terms of faster accessibility of prior knowledge and better integration of new information into explanatory models that may exist before, or are actively constructed during, problem analysis. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
... The majority of studies investigating students' beliefs of force and motion have occurred along the nomothetic strand. Researchers operating from this perspective are Champagne, Rlopfer, and Anderson (1979), Clement (1981, 1977), diSessa (1981, Fleshner (1970), Gunstone and White (1981), Helm (1978), Leith (1982), McCloskey (1983), McCloskey, Carmozza, and Green (1980), Minstrel1 (1981, Saltiel and Malgrange (1980), Sjoberg and Lie (1981), Trowbridge and McDermott (1980a, b), and Viennot (1979). These researchers have attempted to assess student beliefs relative to accepted scientific concepts within the following contexts: classical mechanics Anderson, 1979, Sjoberg andLie, 1981), computer-simulated motion in two dimensions (diSessa, 1981), force (Fleshner, 1970), gravitational force (Gunstone and White, 1981), dynamics (Helm, 1978), curvilinear and projectile motion (McCloskey, 1983 andMcCloskey, Carmozza, andGreen, 1980), the 'at rest' condition of an object (Minstrell, 1981), motion and velocity in varying frames of reference (Saltiel and Malgrange, 1980), velocity and acceleration (Trowbridge and McDermott, 1980a, b), and energy and motion (Viennot, 1970). ...
... In order to contrast student beliefs with scientific concepts the majority of researchers have employed paper and pencil tests with definable 'right' answers. Exceptions to this methodological format are found in the investigations of Clement (1977( ), diSessa (1981, Fleshner (1970), McCloskey (1983), Minstrel 1 (1981 , and Trowbridge and McDermott (1980a, b where the researcher is the teacher, and thus, he has opted for a whole class discussion/interview format. ...
Vita. Thesis (M.A.)--University of British Columbia, 1988. Includes bibliographical references (leaves 124-126).
... En otras palabras, ignoran el efecto del rozamiento, o lo entienden de modo incorrecto (Piaget, 1972;Seré, 1982) -creyendo, al modo aristotélico, que esas fuerzas pueden actuar a favor del movimiento-o son incapaces de componer el efecto de dos fuerzas invisibles (Selman et al., 1982). Incluso los adultos suelen creer equivocadamente que el rozamiento no constituye una fuerza sino una simple resistencia (Clement, 1979;1983b). En una investigación realizada por nosotros (Pozo, 1985;1987a) y a la que haremos alusión extensamente más adelante, pudimos comprobar que, tras realizar una amplia serie de problemas mecánicos, sólo un 30 por 100 de los sujetos adolescentes y adultos universitarios habían recurrido a la existencia de fuerzas no observables (rozamientos, etc.) para explicar los fenómenos que habían percibido. ...
... Sin embargo, la mayor parte de los sujetos, incluidos los adultos universitarios, se niegan a aceptar la existencia de movimiento en ausencia de fuerzas, por lo que atribuyen ese movimiento a una fuerza que el objeto ha recibido de su motor (FM4). Clement (1982Clement ( , 1983a pidió a alumnos de primero de universidad que acababan de completar un curso de mecánica que le dijeran qué fuerzas estaban actuando sobre una moneda lanzada al aire. ...
Newtonian mechanics is frequently used to study students� spontaneous conceptions. The paper reviews in detail adolescent and university students� spontaneous conceptions with respect to some of the most relevant concepts in this domain: force, movement and gravity. In particular, it analyses the surprising parallelism between these spontaneous conceptions and the historical evolution of pre- Newtonian scientific ideas. Finally, the internal consistency of identified spontaneous conceptions is briefly discussed together with the mechanisms for conceptual change Una de las áreas en las que se han estudiado más abundantemente las concepciones científicas espontáneas de los alumnos es la mecánica newtoniana. El presente artículo revisa detenidamente las concepciones espontáneas de adolescentes y adultos universitarios con respecto a algunas de las nociones más relevantes en ese dominio: fuerza movimiento, y gravedad. Se analiza especialmente el paralelismo sorprendente existente entre dichas concepciones espontáneas y la propia evolución histórica de las ideas científicas prenewtonianas. Por último, se estudia brevemente la consistencia interna de las concepciones espontáneas identificadas y la forma en que pueden ser modificadas
... Essays were first divided into topic and comment units (Clement, 1979). This was accomplished by identifying each clause, then segmenting it into topics and comments on topics. ...
Pre-service teachers' conceptions of effective and ineffective instruction stand to inform their personal views of what constitutes effective and ineffective instruction, yet few qualitative studies have examined both conceptions of effective and ineffective instruction. The purpose of this study was to determine whether pre-service teachers described what happens in university courses primarily in terms of teacher characteristics, teaching practices, or instructional context. There were two research questions guiding the study. First, how are the dimensions of effective and ineffective instruction alike and different? Second, how do results correspond to similar qualitative studies? Nine distinct themes were inductively derived through open coding of 34 pre-service teachers' essays: (a) motivation, (b) student autonomy, (c) meaningful learning, (d) comfortable learning environment, (e) classroom management, (f) student-teacher relationship, (g) teacher's personal characteristics and manner, (h) lesson organization, and (i) teacher impact/student development. The results of this study support previous findings and add to the small number of studies that have examined pre-service teachers' descriptions of effective and ineffective instruction. Findings have also contributed a new category that has not appeared in previous literature: teacher impact/student development. Pre-service teachers' descriptions in this study confirm that the theoretical conception of what happens in classrooms must include the teacher's characteristics, teaching, and the context of instruction. Les conceptions qu'ont les enseignants en formation de l'enseignement efficace et inefficace informent naturellement leurs points de vue personnels de ce qui constitue l'enseignement efficace et inefficace; pourtant, peu d'études qualitatives se sont penchées sur les conceptions de l'enseignement efficace ainsi que sur celles de l'enseignement inefficace. L'objectif de cette étude était de déterminer dans quelle mesure les enseignants en formation décrivent ce qui se passe dans les cours à l'université, notamment en fonction des caractéristiques des enseignants, des pratiques d'enseignement ou du contexte pédagogique. Deux questions ont guidé la recherche. D'abord, qu'est-ce que l'enseignement efficace et l'enseignement inefficace ont en commun et qu'est-ce qui les distingue? Deuxièmement, comment les résultats correspondent-ils à ceux d'études qualitatives similaires? Un codage ouvert de 34 dissertations écrites par des enseignants en formation a permis de recueillir, par induction, neuf thèmes distincts: (a) motivation, (b) autonomie des étudiants, (c) apprentissage significatif, (d) milieu d'apprentissage confortable, (e) gestion de la classe, (f) rapport étudiant-enseignant, (g) caractéristiques et manières
... La confusione tra i concetti di energia e forza è ben conosciuta ed è stata messa in rilievo da parecchi ricercatori [4,17,20,8]. L'indagine svolta in classe dimostra che i ragazzi avevano grande difficoltà a separare il termine "forza" da quello di "energia". ...
This paper examines cognitive processes involved in physics learning, using the concept of schema as a knowledge representation model. Its purpose is to study the relations among acquired concepts and especially to analyse how prescientific common sense conceptions are replaced or integrated by scientific conceptions taught in classroom. In order to understand how schemata are constructed, two approaches were pursued: the first (bottom-up) started from the teaching aspect, by testing in classroom a physics teaching project in Italian middle school ("progetto ORA"). From classroom observations some primitive schemata were derived, concerning physics concepts of energy and force. In the second (top-down) approach, previously outlined schemata were revised considering answers to questions about relevant concepts given by physics teachers and students. Results show a considerable difficulty in modifying already learnt conceptions, in particular when following notions are abstract. The most effective modifications that replaced primitive conceptions were suggested by concrete activity and even experts always represented such concepts concretely. 1. Introduzione A partire dagli anni Sessanta l'insoddisfazione per la qualità dei risultati di un insegnamento scientifico impostato sui principi comportamentistici ha portato allo studio, alla stesura, alla sperimentazione di progetti di insegnamento contenenti elementi estremamente innovativi sia sul piano curricolare che su quello metodologico. Infatti, il superamento delle teorie comportamentiste e del modello lineare stimolo-risposta nella definizione del processo di apprendimento ha spostato l'attenzione dal monomio insegnamento al binomio insegnamento-apprendimento. Il contributo della psicologia cognitiva e delle ricerche didattiche ad essa collegate è consistito appunto nell'evidenziare come gran parte degli insuccessi in campo educativo siano dovuti proprio alla resistenza che la mente esercita contro ogni cambiamento non sentito come necessario e al condizionamento che le vecchie conoscenze esercitano sulle nuove acquisizioni, tanto da far percorrere nell'apprendimento strade e direzioni totalmente diverse da quelle che erano nelle intenzioni del docente e negli obiettivi dell'istituzione scolastica. Il cognitivismo sfugge al rigido determinismo della connessione automatica tra stimoli e risposte, creando l'immagine di un individuo che non subisce la sollecitazione degli stimoli ambientali, bensì interagisce attivamente con il contesto. Per questa ragione oggi all'espressione "insegnamento scientifico" si preferisce educazione scientifica, per accentuare l'importanza dei processi costruttivi del soggetto in relazione all'apprendimento di specifici contenuti di conoscenza. Con tale espressione si intende quel complesso di attività volte alla costruzione di un sempre più ampio sistema di interazione cognitiva del soggetto con il mondo che lo circonda, nella direzione di una conoscenza e di un dominio dei fenomeni naturali a partire da quelli di cui egli ha esperienza quotidiana (1). In questo quadro hanno trovato giusta collocazione le ricerche tese a riconoscere l'esistenza e a valutare il significato delle rappresentazioni mentali. E' necessario tuttavia rilevare come, nella gran parte dei casi, simili ricerche assumano valenza prevalentemente descrittiva, tendente a definire le
... Several research groups have investigated the difficulties that students have with basic principles of mechanics (e.g., Champagne, Klopfer, Solomon & Cahn, 1980;Clement, 1979Clement, , 1982diSessa, 1979;Mmstrell, 1982). have reported that on problems involving free fall, many college students indicate that objects fall at a constant speed. ...
... Appendix B contains the entire set of 92 beliefs. We did not try to construct causal networks like those proposed by Clement (1979) on the basis of these beliefs. The beliefs themselves are the units of analysis used in answering our research questions. ...
Conceptual change in mechanics can neither be understood nor facilitated without knowledge of the content and structure of the common sense beliefs with which it starts. However, empirical investigations of common sense beliefs about physical motion have not yet produced a consensus about the correct characterization of such beliefs. Different researchers have proposed different hypothesis about the content of common sense beliefs, about their relations to historical theories in physics, and about the reasoning processes available to scientifically naive persons. The empirical validity of the alternative claims are difficult to appraise because many published reports give little information about how well the various hypotheses account for the data on which they are said to be based. In this paper we apply a four-step method to the analysis of a single interview protocol in order to answer three questions: a) What, exactly, does the subject believe about physical motion? b) What is the relation between the subject's common sense beliefs and the impetus theory of physical motion formulated by the philosopher Jean Buridan in the fourteenth century? and c) What theoretical reasoning processes, if any, does the subject have at her disposal for reasoning about physical motion? (kt)
The concept of electric current is fundamental in the study of electrical engineering (EE). Students are often exposed to this concept in their daily lives and early in middle school education. Lower-division university courses are usually limited to the study of passive electronic devices and simple electric circuits. Semiconductor physics is an upper-division course that presents the physics behind semiconductor devices in depth and exposes the students to microscale explanations of different types of current, such as drift and diffusion currents. This paper investigates how third-year college students majoring in EE link microscale and macroscale concepts of current, and what misconceptions they reveal after one quarter of advanced instruction in semiconductor physics. The interviewees were posed a problem, based on a distracting device structure that exposed student difficulties in defining current, charges and doping, and the plotting of current-voltage (I-V) characteristics. For example, some students had the naïve idea that current is the flow of a particular type of charge (i.e., only electrons or only holes) or that there is a "spectrum of doping." Almost all students drew a one-quadrant coordinate system for the I-V curves, which might imply that students think only about positive voltages. These findings can inform further studies to identify and address misconceptions in the important area of semiconductor device physics.
Résumé
La plupart des élèves possèdent déjà des représentations premières de la réalité qui vont souvent leur nuire plutôt que les aider dans leurs apprentissages en sciences et persisteront fréquemment malgré l’enseignement de représentations radicalement différentes. Ce texte esquisse l’état de la question des représentations premières de la réalité et donne un aperçu des connaissances actuelles sur les représentations de quelques concepts en sciences physiques chez les jeunes.
Three research paradigms, those of Ausubel, Gagné and Piaget, have received a great deal of attention in the literature of science education. In this article a fourth paradigm is presented—an information processing psychology paradigm. The article is composed of two sections. The first section describes a model of memory developed by information processing psychologists. The second section describes how such a model could be used to guide science education research on learning and problem solving.
Diagnosis of the problem-solving state of a novice student in science, by an accomplished teacher, is studied in order to build a computer system that will simulate the process. Although such “expert” systems have been successfully developed in medicine (MYCIN, INTERNIST/CADUCEUS), very little has been accomplished in science education, even though there is a reasonably close parallel between expert medical diagnosis of patients with physiological problems and expert instructional diagnosis of students with learning problems. The system described in this paper, DIPS: Diagnosis for Instruction in Problem Solving, involves a new line of research for science educators interested in interdisciplinary efforts and ways in which computer technology might be used to better understand how to improve science learning. The basic architecture of the DIPS system is outlined and explained in terms of instruction and research implications, and the role of such “intelligent” computer systems in science education of the future is considered.
Piaget's theory has profoundly influenced science education research. Following Piaget, researchers have focused on content-free strategies, developmentally based mechanisms, and structural models of each stage of reasoning. In practice, factors besides those considered in Piaget's theory influence whether or not a theoretically available strategy is used. Piaget's focus has minimized the research attention placed on what could be called “practical” factors in reasoning. Practical factors are factors that influence application of a theoretically available strategy, for example, previous experience with the task content, familiarity with task instructions, or personality style of the student. Piagetian theory has minimized the importance of practical factors and discouraged investigation of (1) the role of factual knowledge in reasoning, (2) the diagnosis of specific, task-based errors in reasoning, (3) the influence of individual aptitudes on reasoning (e.g., field dependence-independence), and (4) the effect of educational interventions designed to change reasoning. This article calls for new emphasis on practical factors in reasoning and suggests why research on practical factors in reasoning will enhance our understanding of how scientific reasoning is acquired and of how science education programs can foster it.
A father is now 20 years older than his son. In 8 years, the father's age will be 5 years more than twice the son's age. Find their present age.
Word problems, such as this one, are a perennial source of difficulty for students of school mathematics. Unfortunately, very little is known about why they are problematic, mainly because so little is known about how students understand such problems or the strategies they use in their efforts to solve them. Traditional research into word problems has shed precious little light on this question owing, in no small part, to its almost singular preoccupation with results of pupils' activities—as expressed in some sort of test score, and to its tendency to all but ignore what students actually do when confronted with problems of this kind.
This study was carried out as one facet of a larger research project designed to gain more insight into some of the ways in which students understand school mathematics. It focuses on the efforts of one pupil, a twelve-year-old girl in grade seven, to come to terms with solving word problems using an algebraic approach. Strategies associated with both the structured and the unstructured clinical interview were used in order to reveal what was involved in her attempts to make sense of the word problems in her grade seven mathematics textbook.
Based on the information gained in the interview, a rational reconstruction of the student's problem-solving strategy is proposed, and compared with the strategies normally prescribed in contemporary school mathematics textbooks. What emerges from this comparison is the finding that, while there appear to be systematic and fundamental differences between the procedures prescribed by the text and those actually used by the pupil in working through certain problems, these differences are undetectable in the finished product; either in the answer itself or in the “rough” or “finished work”. What this suggests, among other things, is that if, as educators and/or researchers, we limit our attempts to understand how students go about learning to solve word problems (or how they approach any other part of the school mathematics curriculum, for that matter) to examining what they commit to paper, we are apt to be seriously misled concerning what they genuinely understand and what they fail to understand. In short, if we are to learn more about why pupils experience difficulties with word problems we must begin to pay serious attention to what they say and do as they work their way through them.
How can we use Watts’ frameworks for talking about energy to design education on the subject of energy ? We showed 6 pictures also used by Watts and gave a writing assignment to 17 fifteen year olds prior to any physics education on energy. We refined the definitions of Watts’ frameworks in order to solve our problems with assigning student-statements to frameworks and found the frameworks not to be mutually exclusive. Results found include the frequency of the 7 frameworks in the studied group of students, and the overlap between these frameworks. We also found that certain frameworks are involved positively and / or negatively in reaching the desired goal of secondary school learning about energy. Finally we will present some ideas on how to use the results in the design of educational materials which we hope to develop in the near future.
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