Meaningful Learning Research Group Publications
The research in mathematics education has documented repeatedly that students perform poorly on non-routine problems, that students' error are reasoned and not capricious, that misconceptions on particular concepts are widely held, that students rely heavily on memorization and have weak strategies for approaching mathematical ideas. As a result, students hold conceptions of mathematics and mathematics learning which discourage conceptual development an the strengthening of mathematical processes. If such profound and convincing educational research is to become helpful and relevant to the classroom teacher, we must begin to develop some demonstration projects which are informed but these research findings and to seek to overcome the situation. The SummerMath program is a six-week program for young women in high school which is devoted to improving mathematical understanding for students for whom mathematics is a hurdle. In this presentation, I will suggest that a constructivist approach provides an appropriate theory through which to interpret these research findings, and I will discuss what I mean by constructivism. Finally, I will talk specifically about the implications of such a theory for curriculum writing and for the instruction of mathematics.
The discussion of "Misconceptions" is based on the hypothesis of a double "logic" in human behavior:
- the "right logic" is based on concepts in which the "Law if Matter" is fully presented (see for example the concept "Invariance of Volume" by Piaget),
-the "psycho-logic" works with analogies which, although understandable and plausible for human beings, partly of not at all correspond to the subject (e.g. animistic, finalistic and artificialistic explanations by Piaget; geocentric theory of the world in ancient times). For the child, this "psycho-logic" has a significant function in orientation (egocentrism according to Piaget), but it also remains important in later life. We all construct our own "theories" in many fields, especially the social- but not only here; we have our own logic, which often prevails over better knowledge. In this field misconceptions' have key-concept function.
One aim of education is to build up correct concepts, to rectify the inadequate and to secure an appropriate use of it. The quality of the presentation of the subject matter in school is, among other factors, decisive in whether this will happen.
A classic research in the field of "Misconceptions" dated form 1930 (E. Wohlfahrt) is presented as well as researches of the author and a co-author on the effect of model-instruction in biology and physics (12 to 14-year-old-students).
These models were constructed tin such a way that they correspond to the "Law of Matter" and to psychological basic structures.
Its positive effects on school learning were proved by posttests, which were given up to six months after the instruction.
In control groups there were found significantly more misconceptions, the number of which increased in proportion to the time elapsed since the instruction; they negatively influenced the quantity and quality of the results.
Much of the recent literature which has been directed at identifying and documenting student's common-sense knowledge (which I will try to characterize in terms of frameworks) in different subject areas us justified in terms of an assumption that this knowledge has significant instructional import. This paper will address this assumption form two vantage points: first, it will lay out some of the underlying theoretical and methodological issues which pertain to the possible interactions between student frameworks and classroom practice; and second, it will illustrate some of these issues using a series of empirical studies which have been recently carried out at the University of British Columbia.
Why do misconceptions persist? One reason is they feel comfortable, and we can act with them without the mistake costing us very much. To rid ourselves and our students of misconceptions requires us not only to think differently (change our concepts) but to feel, and then, to act differently. But this view is only to say that getting rid of misconceptions is an act of educating that integrated thinking, feeling, and acting. (Educating, 1981)
Metaphors are conceptual archetypes that subsume other concepts. A well-struck metaphor also makes us feel something and guides actions. The early stage of scientific inquiry are guided more often by generative metaphors than by acrid hypotheses. So, too, it may be the early stages of learning can be guided by subsumptive metaphors. Strangely enough, some metaphors that work out their meanings in helpful ways also appear initially as misconception. If I claim "A paintbrush is a pump," your first impression is likely a metaphor, you will begin to change your mind and see the channels between bristles transport paint like a pump.
The technique of multiple metaphors is described and explained as a way to improve science education.
Investigations carried out during lectures to first year college students of physics and of the humanities suggest that:
(a) physics students may have a poor grasp of the significance of certain familiar equations in elementary kinematics;
(b) given the right condition, it is possible even for students with no official interest in science to gain some idea of why and how such concepts as acceleration are invented and constructed.
If the above findings have some validity, there is cause for concern about the extent to which students acquire a sense of "what science is all about," and cause for cautious optimism about possible correction of the deficiency. It is suggested that there is room both for continued research into students' perceptions of aspects of scientific epistemology and for experimentation in the teaching and learning of these aspects.
A general model of conceptual change is presented, based on the previous work of Posner et al. (1982) and Hewson (1983). The potential applicability of the model is discussed. In particular, three application sites are analyzed. First, the applicability of the model to the study of student learning in various school subjects is explored. Am model of conceptual change will be most applicable for those subjects in which students' intuitive frameworks are well developed and inconsistent with accepted theory in the parent discipline.
Second, the appropriateness of the model for investigation of teachers' thinking will be discussed. In particular, teacher planning and teacher strategies will be analyzed as conceptual change problems. Third, educational change and, in particular, changes in science education, will be explained in terms of the conceptual change model.
Finally, limitations and new directions of conceptual change approaches will be discussed. In particular, extension of conceptual change models to include sociological and anthropological analysis will be suggested.
Recent research has described a widespread failure of science instruction to effect change in the native theories bring with them. This study examined changes in fifth grade students' (10-11 years) conceptions of plant growth and need for light during six weeks of instruction based conceptual change strategy. Pre-posttest responses, interviews, observation notes and transcripts of class discussions were analyzed to identify changes in student conceptions and develop grounded interpretations of features of instruction that might account for the results.
The instruction was not very successful in bringing about the intended changes. Three implied assumptions of the conceptual change strategy appear to account for much of the failure; many students were often not attempting to make sense of the phenomena at the intended level of explanation, discussion and observations, were frequently not framed in such a way that the intended issues became the focus of attention, and communications and observations were often ambiguous in systematic ways. Theoretical and practical implications of these findings are discussed.
This paper sketches how misconceptions fit into a theory of conceptual change. Conceptual change can be characterized by contrasting it with empiricist views of learning. Empiricist theories of learning emphasize the predominant role of experience in learning. Conceptual change theory, while not neglecting experience, sees learning as the modification of current concepts and emphasizes the role of current concepts in learning. I will discuss three points about misconceptions form a conceptual change perspective.
1. Conceptual change theory can shed light on what it would make sense to mean by a misconception.
2. Conceptual change theory can shed light on how misconceptions can be changed.
3. Conceptual change theory can shed light on the origins of misconceptions.
The paper will give some emphasis to the role of culture (rather than experience) in generating and maintaining misconceptions.
TITLE: STUDENT PERCEPTIONS OF EVIDENCE AND INTERPRETATIONS
AUTHOR: ROBERT D. ALLEN, WALTER R. STATKIEWICZ, MICHAEL P. DONAVAN
WEST VIRGINIA UNIVERSITY
Practicing scientists are keenly aware of the relationship and differences between evidence (data, observations) and interpretations. Many students, however, fail to clearly distinguish between the two.
Specifically they fail to:
1) recognize that different assumptions can lead to different interpretations of the same observations.
2) recognize the facts they have learned as the products of interpretation.
3) modify accepted facts as new evidence is presented.
Instructional procedures used in the Introductory Biology {program at West Virginia University have been developed to detect the presence of these student difficulties and to assist students to overcome them. Progress is, however, often a slow frustrating process for both student and teacher. Moreover, these difficulties appear in a variety of contexts suggesting fundamental flaws in the reasoning process students use when dealing with science. Insight into m basis of these difficulties is provided by the theory of William Perry regarding students' views of the nature of knowledge and the role of authority. Perry's theory predicts difficulties such as those we have observed and offers some explanation for slow progress.
The best way to correct misconceptions is to avoid them in the first place. Concept mapping is a powerful technique to help avoid the formation of conceptual misconceptions. This paper will discuss the philosophy, preparation, and the use of concept maps. Examples will be taken form the author's experience teaching college chemistry will emphasize how teacher prepared concept maps have the potential to help teachers to:
a) make curricular decisions by locating potentially confusing conceptual areas in laboratory experiments, exam questions, lectures, etc.
b) clearly differentiate and integrate similar subject material that is isolated in different chapters of a text or areas of the course.
c) increase student problem solving success by helping to form important conceptual linkages.
d) ascertain what a student knows about a discipline.
As with any discipline, the teaching of genetics ideally involves exposing students to learning experiences through which they will meaningfully acquire and elaborate relevant concepts and integrate them into existing frameworks. That the desired outcome is often not achieved can be seen in reports of misconceptions and rote application of rules in problem solving (e.g. Stewart and Dale, 1981).
Through a comparison of students' conceptions of probability in "genetic" and "real life" contexts, this paper will present the view that some misconceptions are due to factors extrinsic to the learner and are engendered as a consequence of limitations and biases in e experiences and materials to which students of genetics are exposed. This paper will also describe a study in which computer simulations were used in a variety of modes to extend traditional learning experiences, e.g. in active data gathering and strategy generation and execution. Through these uses, student' misconceptions were successfully confronted and concepts refined.
Stewart, J. and Dale, M. Aust. Sci. Teach. J. 27 (1981): 59-64.
Communication in the mathematics classroom is of critical importance. It is through communication that teachers and students interact as a part of the learning process. Whether the communication be oral or written, it is of great importance that students and teachers receive information accurately and the interpret it correctly for application to the learning of mathematics.
As an example, in a teacher-student dialog there are four things which must occur: (1) the teacher says something; (2) the student hears it; (3) the teacher means something specific; and finally (4) the student understands it. Clearly, there are several possibilities here for something to go wrong. If this happens, the desired outcome will not be achieved.
This presentation will elaborate on this topic as well as presenting an informal look at common misconceptions in the elementary school mathematics classroom. Possible causes and remedies will be discussed.
Evidence for the existence of alternative frameworks is science has to be obtained form interviews with children and responses to specific tasks. The task of interpretation varies according to the amount of relevant instruction which the child has received and the quality of that instruction. Although the children need to be able to cope with the world of experience and interconnected explanatory concepts, unless, for some reason the phenomena involved are emotionally charged and recurrent and, hence, salient to the child. Other ways of dealing with, and talking about, phenomena are suggested. Where instruction has taken place, a lack of refined concepts may be attributed not only to the persistent ideas developed earlier in life but to the nature of the instruction itself and to the way in which the task of learning the concepts has been approached.
In the past decade, there has been a growing number of research studies showing that students of all ages show a wide spectrum of misconceptions regarding science or other areas of knowledge. Moreover, attempts to redesign curricula or "confrontation teaching strategies" with explicit efforts to make students and teachers aware of misconceptions have usually produced only limited positive results. It appears unlikely that a teacher or curriculum planner armed with a "compendium of typical students misconceptions" could organize a program where such student misconceptions would be markedly reduced. However, the latter alternative deserves to be, and is being, researched further.
Another alternative is to present students with strategies that help them to "learn how to learn" (metalearning) and to "learn ho w knowledge is constructed" (metaknowledge). We have employed concept mapping as a strategy to help students and teachers understand human learning, and which also contributes to and understanding of knowledge and knowledge production. Vee mapping is a strategy developed since 1977 that employs a heuristic device, the Epistemological Vee, to help students understand the nature of knowledge and the nature of knowledge production.
Studies completed so far suggest that metalearning and metaknowledge ideas can be taught to students form six years old and up. Positive results in terms of complex problem solving have been demonstrated, and research is currently underway to ascertain the effects of these strategies on student misconceptions. As this time it appears possible that long-term use of meta learning and metaknowledge strategies (over a span of several years, preferably beginning early) could produce students who are qualitatively better learners and who acquire or retain significantly fewer misconceptions. Moreover, the se strategies have high promises as aids to design of improved instructional programs.
This paper discusses a study currently being completed to explore the role of the microcomputer in educational research. Two questions are being focused upon:
1. How does the microcomputer contribute to meaningful learning?
2. Can the microcomputer serve as a research tool in assessing cognitive development?
This research address the learner's reasoning, problem-solving methods, and level of thinking in Mendelian genetics. The microcomputer, interviews, and concept maps are being used to assess the extent of learning and cognitive development. Forty college students form and auto-tutorial biology course make up the sample.
The results of this study will be discussed with an Ausubel-Novak cognitive learning theory framework. Educational implications will be considered.
The common meanings of words such as "energy" are context-dependent, and even contradictory, but they are continually reinforced by daily usage and will not die. Even the most accomplished physicist will continue to speak of "cold coming in" and "the rising of the sun." This means that teaching new meanings for concept words will build up a second tier of knowledge coexistent with, but radically different form the first. If misconceptions are to be avoided, our students will need to be able to discriminate between these two worlds of knowledge.
The use of concepts involves the interpretation of everyday phenomena in terms of abstractions. This requires crossing over between two different domains, explaining the commonplace by means of the symbolic, which is the starting point for every piece of problem solving, and appears to be more demanding than the return to the concrete examples. Some recent research with grade 9 students learning about energy will be reported.
The word "constant" may evoke a range of meanings with the two following notions at each end: number, the essential being its numerical value; and a constant function of certain variables the important things now being the listing of these variables. In this way, constants appear as a particular aspect of functions of several variables. The results of an investigation among French and Belgian students at the beginning of their studies at University are reported and analyzed. These results show that the usual interpretation of the word "constant" is biased towards the numerical aspect of this notion, at the expense of its functional meaning. Lastly follows a plea for the use of exercises of "text criticism" as pedagogical tools in teaching.
In 1965, the Audio-Tutorial Elementary Science Project (A.-T.E.S.P.) was established first at Purdue and in 1967 at Cornell University. Its purpose was to investigate science concept development in children's minds as well as to test a new method of audio-tutorial instruction. The project adopted Ausubel's "advanced organizers" and "subsumption" ideas in analyzing concept acquisition.
Among others, Whitman (1975), Rowell (1975-76, 1978) and Gurley (1982) used "Cognitive Mapping" and clinical interviews in the A.-T.E.S.P. Ault (1980) improved the interview technique by introducing the Interview "v" Analysis (I.V.A.).
As of today, most of the 250 students that took part in the project have just completed high school, and were interviewed for the last time in the twelve-year study.
In this seminar, we will examine some examples of conceptual maps and misconceptions evolution over the last twelve years. The findings show wide diversity in concept acquisition in grade one and over the twelve-year span of schooling, with both "correct" and persistent misconceptions evident in some students.
Students enrolled in an elementary science methods course were asked to construct concept maps on a science topic before and after experiencing one or more of the following types of interventions:
1) The instructor graded the concept maps and returned the m to the students.
2) The methods students were shown the instructor's concept map containing the same concepts.
3) The instructor presented a lecture on the topic.
4) The instructor involved students in an inquiry activity to investigate the topic.
5) The instructor assigned a reading on the topic.
6) The methods students were required to wrote a lesson plan to teach the topic to children.
7) The methods students were provided the opportunity to teach the topic to the children.
This study examines the effectiveness of these different interventions in decreasing the number of misconceptions about the topic and in increasing the accuracy and complexity of the connections shown on the concept maps.
Many words used in science as names for concepts are also used in everyday language. Unfortunately, the scientific meaning and the everyday meaning of many of these words are quite different.
When introducing concepts, science teachers have to be aware that the concepts' names evoke a variety of ideas in the students' minds. Science instruction has to take this "variety" into consideration. When planning instruction, the differences of meaning in science and everyday language should be familiar to the teacher of to the curriculum developer.
The purpose of this paper is to deal with the following methods for investigating the meaning of concept names.
1) Association test (the student writes down what comes to his mind spontaneously when confronted with a concept name like energy or work)
2) Definitions (the student describes the meaning a concept has for him)
3) Examples (the student gives an example for a concept)
4) Description of a process (the student describes a simple process using the concept names, e.g. energy, work, force and power).
Theoretical considerations as well as experiences with the methods will be discussed.
By exploiting aberrant forms (mutants), geneticists have gained deep insights into normal cellular processes. Similarly, scientists exploit human aberrations (e.g., brain damage) and mental errors expressed in verbal, written, motor, or other behaviors to gain insights into the mechanisms of the mind. This paper reviews recent error research in the domain of mathematics and science learning. Findings are interpreted according to information processing theory. Relevant research on word associations is examined for its potential in reflecting conceptions in distinctive characteristics of the associative network. The aims are to: 1)provide a relatively complete reference to current error research, which is widely scattered in the literature; 20 identify points of convergence and divergence between studies; 3) examine the utility of information processing theory in interpreting errors and vice versa; and 4) to identify potentially fruitful directions for future research.
Standard psychometric methods are inappropriate to asses the reliability and validity of misconceptions test. Several principles are proposed for the enhancement of the reliability and validity of an interview in which the student is asked (1) to explain a certain situation, (2) to recall and evaluate partial conflicting alternative explanations, (3) to compare them to her/his own, and (4) to refer to prespecified elements of the alternative explanations. Among the design means are (a) using one misconception in different contexts and different misconceptions in the same context, and ((b using similar but structurally different problems in different arrangements. Among the factors used to enhance the reliability of misconceptions assessment are (1) considering the amount and nature of recall, (2) considering the effects of intervening easier problems, (3) characterizing the ways in which elements of the alternative explanations are treated, and (4) observing their susceptibility to change by presenting easier or more difficult problems.
The clinical interview is characterized as a three-stage methodology for formulating and testing hypotheses regarding alternative conceptions. In Stage One, the interviewer formulates hypotheses of a particular student's reasoning and tests these in the form o probes during the interview. In Stage Two, several individuals independently analyze the recorded interviews and then, through a cyclical process of negotiation and review of the tapes, arrive at agreed-upon hypotheses regarding the nature of alternative conceptions. These hypotheses are then subjected to further test in Stage Three by recycling through another stage of data collection and analysis. These various stages are illustrated with examples form research that explores alternative conceptions of statistics and probability. In one study that will be reviewed, a model o probabilistic reasoning was inferred form a set of clinical interviews. Then, specific predictions were made of how subjects, reasoning in accord with this conception, would respond to a different set of problems. These predictions were verified in a second set of interviews with the same subjects.
The ultimate goal of education research is to improve educational practice. TO this end, a great deal of research in science education focuses on the cognitive mechanisms which students use to process scientific information and concepts. This paper suggests that a purely cognitive approach to scientific research, while useful, is not the only way to understand the educational process. In particular, the fact that science education involves social interactions, both between student and teacher and between professionals scientist and classroom teacher, has significant consequences for the understanding of "purely cognitive" information processing mechanisms, and therefore for educational practice. Examples and suggestions for future work will be offered.
Geometric problems involving two or three dimensional objects were administered to over 300 high school or college students. Various misconceptions were revealed through analysis of responses and reactions to hints. Some subjects made incorrect assumptions about the mathematical knowledge needed to solve the problem or about their abilities to do so. But misconceptions also arose form the stimulus side and, in particular, form the way the problems were represented. Descriptions of a geometric object which ran counter to the object's structure tended to foster more misconceptions than descriptions of the same object which were in line with its structure. The latter descriptions tended to facilitate solutions and to reduce sex differences as well as differences in responses between mathematics and non-mathematics majors. Suggestions are made for further studies of misconceptions stemming form the stimulus rather than the reactive side.
Research studies have investigated a number of ways of trying to probe and understand the misconceptions of student. On area of biology in which students have learning difficulties is genetics. Students are generally able to mechanically manipulate certain types of genetic problems; however, the more abstract ideas and the interrelationships between those ideas often escape understanding.
In Victoria, Australia, year 12 students undertake an external examination . In 1982, a "new type" of question was included in the Biology examination paper. After being given an example, students were asked to make a diagrammatic representation (concept map) of their understanding of genotype and phenotype and the relationships between them.
This paper reports on the results of the "new type" of question. Sample answers will be discussed. In addition, student and teacher reaction to the question will be presented. The implications for the teaching of genetics and biology will also be considered.
In this paper, an attempt is made to analyze the process-product dichotomy in Physics and Mathematics education. The analysis is made form two perspectives:
(a) The Feuerstein approach to cognitive development as it relates to disadvantaged students.
(b) Gowin's Vee heuristic as a means of gaining perspective of the relation between conceptual and procedural knowledge.
Results of the research are presented indicating the strong influence that these approaches can have on our understanding of how pervasive and deep-rooted misconceptions are.
Investigators use various methods., including individual interviews and written questions, to probe students' conceptions in science. The methods can involve several difficulties, assumptions and pitfalls. Unless these are recognized, the validity of the findings may be uncertain. The methodology and precautions of research in the social sciences need to be considered in research on student conceptions.
Among the difficulties involved in investigations of conceptions are the following:
-Presence of confounding variables
-Lack of controls
effect of the theory base, expectations, and subjectivity of investigator
-Unrecognized complexities underlying apparently simple physics problems
-Semantic problems, including multiple and variable meanings, meanings which vary with context and different meanings to subject and investigator
-Premature conclusions and categorizations, especially form written texts
-Insufficient depth of probing, and need for mapping of schemata
-Concept modification during interviews
-Demand characteristics of the investigation situation
-Effect of mode of presentation
-Cues, prompting, and suggestibility in interviews
-Need to check inferences and conclusions with subjects
These difficulties complicate cognitive studies of students' conceptions, and suggest the need for care in the design of investigation procedures, and caution in the
interpretation of response data.
Results of the research are presented indicating the strong influence that these approaches can have on our understanding of how persuasive and seep-rooted misconceptions are.
This paper points out the main tendencies of experts in analyzing students' mistakes and illustrated these tendencies on two instances in the field of mechanics. It is shown that common interpretations of students' comments built in the very terms of the accepted theory may erase some important aspects of spontaneous reasoning which are illustrated in this paper with results obtained at college level.
The problem I want to explore in this paper is one I take to be very closely linked to the central concerns of those engaged in the type of research being discussed in this seminar. More specifically, it has to do with using some of the insights deriving form recent work in the history and philosophy of science as a way of gaining a better understanding of the problems and pitfalls encountered by children and adolescents during their initial encounters with scientific concepts and theories. These youngsters are in a rather different position form those, slightly older and more experienced perhaps, who have already gotten on the inside of, and have achieved some level of understanding and proficiency in, on of the conceptual schemes in the sciences. In the case of the initiated, we at least have some understanding of what they know when they have caught on to the kinetic molecular view of heat, the rudiments of evolutionary theory, or Newtonian mechanics. We know something of the content of their views because we understand the theory. Of course, we know more than this. We know something about where these views have come form. And we're learning more about how they have developed, the circumstances under which one theory may replace another, the standard used in judging the adequacy of competing theories, and so on. Now all of this, especially the latter-concerning the nature and development of concepts and theories within the unfolding tradition of science -stemming' in part form recent work in the history and philosophy of science, seems to hold great promise for illuminating the problems students experience in learning science. Nevertheless, at present, it shows most promise as one way of illuminating the problems of those on the inside ø well understood concepts or theories within the scientific community. This, for example, the influential works of Popper (1959). Kuhn (1970), Lakatos (1970) and Toulmin (1972), are primarily concerned with the domestic affairs of science and to very much lesser extent with its "foreign relations." Of course, none of this is meant to deny that this same body of research also holds out considerable promise as one way of getting to grips with the obstacles confronting the unitiated. But there are special problems here too. The primary one is the simple fact that we possess little in the way of an explicit an systematic appreciation of the content of the concepts, beliefs, and so on, that hey bring with them to their formal encounters with science education. Indeed, I take it that the great virtue of the recent work done on the views of children and adolescents is that it has gradually begun to dispel some of the ignorance and prejudice that has too long beclouded our understanding of these matters. However, in the absence of more comprehensive and systematic knowledge of this kind, we must be on guard against the tendency to adopt the framework of conceptual change and theory development in an "all out" or unqualified way. That is, by simply taking it for granted that pupils are immature scientists, that they are animated primarily by a concern with scientific truth, consistency and explanatory power, and, in consequence, that their views are properly assessed in term of their adequacy form a scientific point of view. (And if caution is to be urged so as to avoid premature and ill conceived attempts to solve it.) Prior to the wholesale adoption of any such high-level explanatory framework, we require studies providing us with more detailed portraits of the kinds of concepts , beliefs and views that pupils command , along with better pictures of the ways in which and the circumstances under which providing us with more detailed portraits of the kinds of concepts , beliefs and views that pupils command , along with better pictures of the ways in which and the circumstances under which yield of previous research is highly suggestive, it is nevertheless fragmentary. This makes it difficult to know hat to make of the views pupils espouse. Do they represent a position in which they have some continuing stake? Or are they transient artifacts of the research design, including the tasks employed, the questions asked, and so on? In short, what is essential if talk about conceptual change and theory development and so on to gain a proper purchase on the perspectives of those who are not yet on the inside of some part of the scientific framework, is some basis for thinking that the beliefs they espouse form a more or less coherent view on the topic in question, that the view has scientific purport and, there fore, that it is appropriate to science. Unless such a beachhead is established, any talk about preconceptions, misconceptions and the like is bound to be wide of the mark.
The label "Aristotelian" was first introduced as an adjective for the pre-instructional knowledge of children with a great deal of caution. Now, four short years later, the label is used quite freely, though still with some degree of caution by some researchers, to describe whatever it is in the minds of children which is non-Newtonian. Further, a pattern of nomenclature has been accepted, a convention for labeling pre-instructional knowledge in the minds of students by historical referent.
Clearly, the facilitation of communication between researchers is one good reason for widespread acceptance of such labels; but it is not a sufficiently good reason. These labels are very meaningful; they are not consciously non-meaningful as is quark form particle physics. If the labels are to be accepted then their meaningfulness should be accepted also.
Maybe now is the time to ask some questions about the validity of the label "Aristotelian" before the convention has such inertia that questioning basic assumptions will seem inappropriate. One question is: In what sense are children who are labeled as Aristotelian, Aristotelian?
The content area usually used in this important work on children's conceptions of motion is free fall, the motion of objects under gravity. The proposition called Aristotelian is not Aristotle's, however, since for him no force at all was involved in such motion.
One possible approach then would be to seek detailed evidence of a content-proposition match between children's conceptions and Aristotle's, in many content areas.
Another question is: Is this to-be-proven match between propositions merely a curious and interesting phenomenon, but without any causal relationship? If so, its establishment would seem to be a waste of time. If, however, causality is to be established, as perhaps in vestigial language remnants, or in some learning theory which assumes that the growth of knowledge in an individual parallels the growth of scientific knowledge in history, it would seem that precise evidence of the existence of such a parallel is a prerequisite.
The persistence of myths and misconceptions masquerading as scientific facts in the teaching and learning of science is die to several factors. Inherent in the process of the scientific enterprise is the inevitability of myths and misconceptions. These errors may have originated as heuristic or speculative tolls quite legitimate to the scientific method. Such intellectual tools, however, long outlive their utility and persist as intractable myths.
Another factor is our reliance on writers of textbooks who with patience and perseverance package an immense mass of information which often advertently includes such errors. Authors of textbooks are retailers of information using materials that have been produced by innumerable research scientist, past and present. Often these scientists, too, may be victims of erroneous preconceptions.
Among such myths and misconceptions, some are esoteric whereas others are widespread and commonplace. Examples of those that are esoteric include sophisticated concepts such as gene, mutation, species, et cetera, concepts which are inculcated by teachers and textbooks. Ideas relating to such concepts as race, intelligence, evolution, et cetera are examples of widespread myths acquired form parents and society at large which, of course, includes educators.
The present paper will examine a number of these myths and misconceptions, both esoteric and commonplace, that bedevil the teaching and learning of biology.
The proposed analogy between the history of science and the conceptual development of the individual has become widely accepted by researchers who investigate students' "misconceptions" or "alternative frameworks." They believe that this analogy may provide us with better insight in to the psychological processes which take place in science learning. However, the history of science is not a field which is governed by one monolithic approach. Historical accounts may vary, depending on the philosophical commitment of the researcher. This, one who assumes that such an analogy is valid and potentially helpful for educational research should be more specific in indicating the specific approach in history of science that he adopts. He should examine this approach fro all the potential implications it bears fro education.
In this paper, the argument will be made that the reference made by many science researchers to Kuhn's revolutionary account of the development of science ideas may not e suitable. This may be so if we accept the rival evolutionary account, given by people like Toulmin and Lakatos.
The author's studies of children will be reviewed as supporting the evolutionary approach. Some of the practical implications which evolve from adopting an analogy with the evolutionary approach, in the history of science, will be considered.
Scientific knowledge is characterized as tentative, as having the capacity to be changed under appropriate conditions. Because the methods of inquiry in science are inextricably linked to their product, knowledge tentative. The controversy-rich philosophy of science literature provided theoretical background for this study of issues in epistemology of science.
Twenty-nine college biology student were asked to comment on statements about scientific knowledge which reflected one of two views of science. Student's' accounts of the growth of knowledge and of the nature of objectivity in science revealed alternative conceptions of some of the bases of the tentativeness of scientific knowledge. Three general themes about scientific knowledge emerged from the comments: (1) it is an unchanging accumulation of empirically discovered facts; (2) it is tentative because of new evidence arising by new equipment and techniques; and (3) it is theoretical, a human construction based in part on theory-guided and theory-limited observations.
A series of studies was conducted to determine the development of children's intuitive understandings of the concepts of heat and temperature for the purpose of devising a curriculum unit that engages these intuitions.
Among other things, the first study mapped out how 180 children ages 3-14 understood the intensive physical aspect of temperature. It was found that very young children solved the tasks correctly, older children solved the same tasks incorrectly,. while still older children solved them correctly.
In the second study, we exploited a conflict between children's correct intuitive understandings of intensive physical quantity (cold water when mixed with more cold water yields water at the same temperature) and their incorrect understanding of the same concept when presented numerically (water at 10 C when mixed with water at 10 C yields water at 20 C). Three age-related ways of dealing with this conflict were found.
A curriculum unit was revised by incorporating the above into the unit. A third study tested the effectiveness of the unit and it was found to be as effective as individual instruction and more effective than a control group.
The distinction between student' intuitive understanding of their world (students' science), and the conceptual understanding of science held by the science teacher (scientists' science) is illustrated using the concept of energy in elementary science. Aspects which characterize students' science (e.g. animistic thinking), often considered incompatible with traditional scientific "objectivity" are interpreted from a Kellyian perspective. Implications fro science teaching using a "consecutive alternativist" philosophy are explored in this paper.
Data from written tests and video-taped problem-solving interviews show that many students have a stable, alternative view of the relationship between force and acceleration. This "conceptual primitive" is misunderstood at the qualitative level in addition to any difficulties that might occur with mathematical formulation. The misconceptions is highly resistant to change and is remarkably similar to one discussed by Galileo, as shown by comparison of his writings with transcripts form student interviews. The source of this qualitative misunderstanding can apparently be traced to a deep seated preconception which makes a full understanding of Newton's first and second laws very difficult. In such cases learning becomes a process in which new concepts must displace or be remolded fro stable concepts that he student has constructed over many years.
Energy education has become an area of major interest within school learning. Science instruction, especially physics instruction, is expected to take care of the basics, the physical concept of energy. Empirical studies on learning the energy concept in physics instruction reveal severe difficulties on the part of the students to grasp this concept. The results of these studies point out that it seems to be unlikely that many students- during physics instruction- gain a concept of energy which is indeed useful fro understanding the energy problems of society.
I would like to outline some studies which have been carried out at the IPN (Institute for Science Education) on learning the energy concept: 1) a study on the form -ation of energy ideas during cognitive development (done in the Piagetian manner); 2) studies on learning the energy concept through an instruction unit and in the course of four years of physics instruction (using interviews and questionnaires); 3) a small study on applying the energy concept outside of physics classrooms (the students were asked to write an essay on energy in the German class). Some consequences fro science instruction as well as some general considerations on learning science knowledge will be discussed.
Students can pass through introductory physics courses without acquiring a sufficient conceptual knowledge of physics. It is often assumed that this will be provided by more advanced courses. CON-PHY-TEST has been developed to evaluate at what level basic concepts of mechanics and electricity and magnetism are grasped by students. It has been administered to sophomore and senior engineering physics students, whose performance in standard, quantitative physics exams is better than that of non-physics majors. The results of the test have revealed a low qualitative understanding of physics, with only a slight difference in favor of senior students. Though some researchers have pointed out that even physics majors may have conceptual problems, the situation may be more profound. Implications for introductory physics instruction are suggested.
This paper will give examples of student interviews on matters related to simple electrical circuits and will describe various types of preconceptions encountered. Among these are preconceptions based on: previous experience with similar physical phenomena, analogy with different physical phenomena, animistic conceptions, and moral determinant. It appears that the presence of the last two types of preconceptions plays a role in the inability of some students to carry out simple predictive tasks. Excerpts from our interviews will be used to illustrate the relationship between these subjective preconceptions and the students' difficulties in making correct predictions.
When confronted with a task that involves manipulation of a physical apparatus or a judgment or prediction about a physical phenomenon, students often respond incorrectly. Furthermore, the ideas expressed are often in conflict with the principles of physics. We believe that these incorrect ideas should be considered misconceptions only if a student makes use of them
consistently to explanations or responses to several different but related tasks. Using this criterion, we will describe some misconceptions that students have about images in mirrors and lenses. Our discussion will be based on the results of over 100 individual demonstration interviews that we have conducted this year with students enrolled in college level introductory physics courses. We will describe several interview tasks, illustrate typical incorrect responses with excerpts, and discuss methodological difficulties concerning the interpretation of the data.
High school students were found to have the following misconceptions regarding the speed and time concepts: Speed is an extensive rather than an intensive quantity; tine is not a necessary mediator in situations that involve speed; replacement of the nonexistent three-concept relationship S=vt by two-concept direct and inverse (not strictly proportional) relationships; and nonrecognition of the distinction between local and global features of concepts and their relationships. These misconceptions resulted in ten incorrect solution strategies that were employed in the solution of algebra speed problems involving uniform motion of two cars, each with two speed and direction changes. These forward strategies were schema driven, had a bottom-up nature, employed time-independent quantities, capitalized heavily on chance numerical relationships rather than three-concept formulas, and did not distinguish local from global considerations.
The existence of some misconceptions in physics amongst secondary school students in Nigeria has been studied and compared with a similar study elsewhere. A test on multiple choice items in physics concepts was administered to a group of students in selected school believed to have adequate facilities in both human and materials to enable physics to be taught effectively. Teachers of physics in these schools were interviewed and also required to respond to the test. Two major causes of misconceptions in physics amongst students have been identified as teaching as teaching and available textbooks. Some suggestions towards improvement have been made.
The history of ideas shows that it has taken mankind 2000 years to formulate the key ideas of optics, that is, that light is a physical object that propagates in space, apart from sources and effects. We ask to what extent Swedish school pupils, 12-15 years of age, use the key idea of optics, what they imagine the link between object and eye to be, and how they explain a phenomenon of refraction and the effect of colored filter of light. Our questions are answered by allowing about 600 pupils to write down their solutions to four optical problems and in doing so explain how they think, A qualitative analysis is made of the explanations, and this shows that for each problem given, about 30% of the pupils apply the key ideas of optics after attending lessons.
The nature and extent of preconceptions pertaining to Newton's First and Second Laws of Motion held by beginning grade ten physics students prior to formal instruction in the topic was explored and related to end-of-course marks and criterion test achievement.
Forty students randomly selected form classes in four high schools were each presented with four tasks in an individual interview setting: horizontal motion along a groove, inertia of a ball in a cart, inertia in space, and acceleration produced by a constant force.
Protocol analysis revealed that only approximately one-third of the student expressed conservation of motion or perception of motion relative to an external frame of reference, many of the other preconceptions reflecting Aristotelian views. Gravity was used to explain the inertia of a stationary or a moving body in nearly half the instances. The vertical force of gravity was also thought to retard horizontal motion.
While girls performed significantly lower level than boys on each task, they scored significantly better in end-of-term marks (p < 0.05) but not on the concept-related criterion test.
Recent research suggests that "Current is the primary concept used by students, whereas potential difference is regarded as a consequence of current flow, and is not its cause." This major conceptual difficulty appears to be largely independent of prior instruction in static electricity. As a remedy, I propose exploring electrostatic phenomena in circuit contexts through hands-on experimentation employing miniature light bulbs as current detectors and large-value capacitors as sources of variable potential difference. A lecture-demonstration will illustrate some of the possibilities fro fostering an effective conception of electrical potential. Ways of dealing with such misconceptions as light bulb = electric sink, resistor = current catcher, and wire = propertyless conduit will also be considered.
This author's recent article in the American Journal of Physics reported an analysis of college students' responses to six questions on trajectory motion. Examples of "incorrect" reasons for "correct" answers were provided in the discussion, but these were not studies in detail. This paper will extend the analysis of this aspect of study.
This study was aimed at uncovering the valid concepts and alternative interpretations which students in grades 4, 5, 8, 10, and 13 hold about the human circulatory system. The research progressed in two phases: a constructive phase followed by a validation phase. The constructive phase employed interviews and concept maps to construct a conceptual inventory of beliefs from 50 students. The validation phase involved the administration of a written instrument (n=195). The instrument was developed from the interview protocol and the resulting conceptual interpretations. The relative frequency of responses for each belief category fro each grade level revealed that the alternative interpretations offered by elementary students persist in the higher grade levels. Students' statements of certainty in the validity of their alternative interpretations indicated that many of these beliefs about circulation may increase teachers' awareness of students' alternative interpretations and their influence on the development of accurate science concepts.
Tests and interviews over ten years reveal a persistent error among genetics and biology students: 45% to 75% are unable to identify a specific product of protein synthesis (activating enzyme) in a list of four items. Most who answer incorrectly chose "amino acids" (a reactant). Student confusion has the following characteristics. Students apparently have difficulty: 1) translating between general classes (proteins) and specific instances activating enzymes), even when they can recite the litany "Enzymes are proteins"; 2) imagining that a product of protein synthesis (enzyme) is involved in the process in protein synthesis (this seems to violate a preconception of the students that the class which is acting cannot be the class that is acted upon); 3) recognizing where amino acids do come from (ingestion and biosynthesis), a topic only briefly mentioned ion texts; 4) making connections between a compartmentalized bits of knowledge; and 5) thinking through a logical thought chain in a new knowledge area.
This paper will discuss the nature of the data which have been collected in our laboratory, according to the different types of investigation we used.
Our investigations have been of two kinds:
1) Studies of children's conceptions at a given moment (fro example, at the age when we plan to introduce a given field of physics);
2) Studies of the evolution of children's ideas with a teaching.
To do this, we used different techniques: individual interviews, case studies of the conceptual changes of some children working within a standard class or within a small experimental group, large scale studies involving about 600 pupils in several classes of the same grade.
These different methods bring information of different nature, which we will illustrate with examples taken from researches conducted with children aged 11-14.
The understanding of osmosis presents a significant challenge to many students. Expert conceptions of this physical phenomenon often entail subordinate concepts of concentration, semipermiability, and pressure. Misconceptions of any or all of these subordinate concepts may result in erroneous solutions to osmotic problems.
A detailed study of student responses to a wide variety of osmotic problems has allowed us to characterize a number of misconceptions of concentration, semipermability and pressure. Concepts of concentration and pressure appear to have roots in intuitive experience. Conceptions of membrane permeability are most likely acquired through instruction in science.
Comparative studies, conducted on students prior to and following instruction, indicate which of these misconceptions are most stable and thus require particular instructional attention. some novel demonstrations and experiments are suggested as a means for modifying persistent conceptual misunderstanding. Finally, two osmotic problems are presented as a challenge to expert conceptions of osmosis.
This presentation will report the findings of a study designed to investigate students' understanding of photosynthesis. A paper-and-pencil instrument (Photosynthesis Concept Test) was administered in 49 schools to a total of 1405 students in grades 5, 8, 11, and 14. The kinds of cognitive difficulties certain aspects of the photosynthesis concept present will be interpreted within an Ausubelian framework.
Students in a college chemistry class were instructed on the importance of concepts in understanding chemistry and in e technique of concept mapping. Students were assigned to concept map chapters of their textbook and given other mapping assignments. Students were also interviewed three times during the semester and after the course ended. The data showed that key misconceptions could be identified and that in general, concept maps were good representations of the students' knowledge of chemistry, as confirmed in part by later interviews with the students. Students found that concept mapping was difficult but that it helped them to gain understanding, and to identify some of their areas of confusion.
TITLE: ARE MISCONCEPTIONS MISCONCEIVED? SOME MATHEMATICAL, EPISTEMOLOGICAL, PSYCHOLOGICAL AND PEDAGOGIC RESERVATIONS
AUTHOR: WILLIAM HIGGINSON
QUEEN'S UNIVERSITY AT KINGSTON
In some ways the "misconceptions" perspective is a recent and promising jumping-off point fro research in science and mathematics education. It is possible, however, to argue that the approach has a number of major weaknesses, particularly at the implementation stage. In this paper, a case will be made for "misconceptions" as more a part of the problem than par of the solution. Reference will be made to the theoretical work of, inter alia, Papert, Piaget, Polanyi, Polya, and Popper and to research on children's conceptions of mathematics.
What cognitive and metacognitive resources does the child use to make school mathematics meaningful? The procedures employed to answer this question were a combination of classroom observations of a series of elementary mathematics lessons and interviews with the children and the teacher following the lessons.
The interview questions were espoused to the children as they worked on math problems and were designed to reveal each child's (1) definition o the task; (2) evaluation of the type and difficulty level of the problem (3) selection of an algorithm; (4) choice of aids; (5) recording intermediate values; and (6) mode of checking the results.
The results indicated significant differences between the teacher's and the children's values, concepts, guiding theories and problem-solving strategies in doing math. These differences will be discussed in detail.
Misconceptions are misunderstandings which are based upon incorrect meanings. Since mental representations, or images, precede meaning, then to work on misconceptions necessarily leads one to work on images. A source of misconceptions for learners of mathematics can be their lack of insight in or the insufficiency of their images of the mathematics with which they are dealing. Without adequate images, it is unlikely that misconceptions, where they exist, can be correctly re-conceived or that very deep understanding of the mathematics can be gained. This presentation will explore hoe imagination and imagery can be used in generating mathematical knowledge and avoiding misconceptions. Participants will be invited to explore the use of their own imaging powers in learning mathematics, to reflect on that experience, to formulate researchable hypotheses with regard to imagery and mathematics education.
Epistemological issues are inherent in the mathematical tasks of making hypotheses and checking them out, searching for negative evidence and seeking inconvenient facts or posing questions without knowing if answers exist or new methods that will lead to solutions. The contextual nature of mathematical statements is made explicit by the ever-present caution, "Holds true under the following conditions...".. The mathematician realizes, at least cognitively, the contextual nature of mathematics and has come to some personal resolution of these issues. Not so with many students who see mathematics as a-contextual and apart form relationships. This session will describe two approaches to mathematics problem solving. One reflects an assumption of an every-day reality of connection while the other assumes an approach of laws and structure.
Our research has focused on the difficulties students have in translating the context of a problem into mathematical symbol systems. The crux of such difficulties apparently lies in misconceptions of mathematical symbol systems, i.e., in the failure to appreciate that mathematical symbol systems differ in crucial ways from "natural" representational system, viz., language and imagery. We started with a problem that requires solvers to write an algebraic equation fro a proportional relationship. Fewer than 50% of college students are able to solve such problems. We first explored the source of such errors by manipulating problem content in ways that affect problem difficulty. We found two strong and consistent error patterns. One error type appears to reflect direct translation from a linguistic to a pseudoalgebraic equation, while the other is associated with an imaging strategy. In our subsequent research, we explored the generality of these results in terms of other word problems and related cognitive abilities.
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