Knowledge Construction in High School Physics: A Study of Student Teacher Interaction
By: Warren Wessel
SSTA Research Centre Report #99-04: 35 pages, $11
Table of Contents

Part I - Viewing Learning in Science as Knowledge Construction 
  Student Learning in Science 
    Student Alternative Conceptions: Knowledge Students Bring to Class 
    General Characteristics of Students’  Alternative Conceptions 
    Incorporating Alternative Conceptions in Teaching Science 
  Constructivism in Science Education  
     Social Construction of Knowledge  
Part II - Significant Findings of the Study  
  Student Views on Learning and Physics  
  Students’ Experiential and Conceptual Knowledge  
  Student Alternative Conceptions and Communication  
  Mathematical Representation of Concepts  
  Recognizing Direction as a Characteristic  
  Applying Vector Mathematics in Physics  
Part III - Considerations and Recommendations  
  Amount of Content in Secondary School Physics
  Increasing the Relevancy of Physics to Students  
  Implications and Recommendations for Instructional Strategies  
  Using Discussion as an Instructional Strategy  
  Questioning and Discussion Skills - Learned Processes  
  Implications of Students Learning  

Student learning in grade 12 physics is a complex process and causes frustration for teachers and students.  Learning to represent concepts using mathematics presents a considerable challenge for students to understand and for teachers to instruct.  Traditionally the model of teaching and learning in most physics classrooms can best be described as transmission of knowledge from teacher to students.  Science education has come as far as it is going to using this model of learning and instruction.  Advances in student performance will require a different approach. 

This study examined learning in Physics 30 during the time that the application of vector mathematics to physics concepts and problems was taught.  The results of the research provide a different picture of student learning and different strategies for teaching physics.  The recommendations are aimed at changes required for improvement in student performance in physics and science in general. 

Part I of this report provides a review of the literature related to learning in science as student knowledge construction.  Part II describes the major findings of the study related to student learning in physics.  Part II presents recommendations and suggestions for improvements in teaching physics and science.


    Science education is a complex process which in its simplest form involves at least teacher instruction, student learning and a science curriculum.  While this research was focused on a specific problem in teaching grade 12 physics, the outcomes have general relevance to science teaching at all grade levels.  The recently implemented Saskatchewan science curricula have at their foundation a view that student learning is an individual process and that concepts in science are constructed by learners through hands-on activities and personal experiences.  This research project sought to explore student learning in physics in an attempt to develop a more complete understanding of the process.  In particular, this study focussed on how students in grade 12 physics actively constructed their knowledge of the use of vector mathematics to represent certain complex physics concepts and solve associated problems.  The study also examined teacher interactions with those students as a means of assisting their learning during part of a five month semester in a regular physics classroom.
    During my twenty-three years of experience teaching high school physics, chemistry and science I have seen that most students correctly develop some ability to apply vector mathematics in  Physics 30, but at varying levels of competence.  This development varies considerably in a typical class of physics students.  Some students essentially master abstract concepts, while others are able to answer typical problems correctly, but cannot apply vector mathematics to new or atypical types of problems.  Normally, a few students never seem to develop any understanding of vector mathematics.
    Mathematics usage is required in most high school science courses in Saskatchewan.  Scientific formulae (mathematical models) which are common in most science courses require mathematics and consistently provide learning difficulties for a great many students.  These difficulties are a common reason for students not enrolling in science classes beyond those that are compulsory.  Although student learning difficulties in lower grades may seem less complex than those in Physics 30, they are of the same form.  For example, density in Science 8 and 9 and the mole concept in Chemistry 20 are closely related to the questions investigated in this research, and the outcomes have application to those courses.
    In this research project nine Physics 30 students volunteered to participate by describing their reasoning and problem solving strategies over a sixteen week period in a regular classroom setting.  The participants were taught the normal content of the Saskatchewan Physics 30 curriculum by the researcher who is an accredited, experienced physics and chemistry teacher.  Data were collected by video recording of classroom sessions, interviews, student assignments, and field notes maintained by the researcher.
    Part I of this report a presents summary of some literature related to the learning in science.  Part II discusses the most significant findings of the research into student learning in physics and science.  Part III discusses recommendations and considerations for changes in teaching physics and science.
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Part I - Viewing Learning in Science as Knowledge Construction
    Student learning in science is a very complex process partly because of the abstract nature of many scientific concepts and their representation by mathematics.  During the last two decades the model of learning in the science education literature has evolved beyond viewing students as passively receiving knowledge transmitted by teachers.  In this section a summary of some literature exploring learning in science is presented.

Student Learning in Science
    Before the last two decades most teachers accepted a transmission model as appropriate for teaching science because they viewed science in a traditional manner; that is, they believe that science provides right answers and that truths in science are discovered (Carr, et al., 1994).   The transmission model of teaching in science is deeply rooted in our culture, in both teachers and students (Roth, W-M. , 1993).
    Learning in science is typically a difficult task for students and this is unlikely to change because of the complex structure of science (Duit, 1991).  Instead of reading or discovering the book of nature, scientists impose constructs and concepts on observed natural phenomena to organize and to understand them better (Driver, Asoko, Leach, Mortimer and Scott, 1994).  Driver et al. argue the complexity in science lies in the study of the constructs advanced to explain natural phenomena rather than in the phenomena themselves.  Carr et al. (1994) state that exploration of the history and philosophy of science and inclusion of newer models of learning from cognitive psychology have prompted the science education community to focus on student learning in science and, as a result, have begun to change the view of teaching science from a transmission model to one of student construction of knowledge.
    Direct transmission models of student learning began to lose favor because of their inability to explain some important intellectual achievements, such as, creativity, decision making and problem solving ability (Gagné, 1985).  Our thinking about learning in science has gradually changed because of developments in learning psychology and epistemology.  Cognitive psychologists began to describe mental functions of students during learning; and, philosophers moved away from positivist and empiricist attempts to establish truths toward a constructivist view of knowledge building (Novak, 1988).
    Discovery and inquiry learning were among early attempts at curriculum development which were built on a view of students as active participants in their learning (Trowbridge & Bybee, 1996).  Discovery learning, pioneered by Bruner (1961), was used as the foundation for curriculum development and led to BSCS Biology, CHEM Study and PSSC Physics which were the standard courses from the 1960s to the 1980s in Canada and the United States.  In discovery learning classrooms students were expected to discover laws and concepts but never did discover them as expected.  Driver et al. (1994) have argued convincingly that students should not have been expected to discover laws of science because those laws are social conventions communicated through the social and cultural institutions of science.
    Ausubel (Ausubel, Novak & Hanesian, 1978) was among the first to describe the importance of the knowledge that students held before coming to science classrooms.  This experiential knowledge has a profound effect on how what students learn as a result of their science classroom experiences.  Edmondson and Novak (1993) included currently-held knowledge when they defined rote learning as “the acquisition of new information without specific association with existing elements in an individual’s conceptual structure (i.e., memorization)”; and, meaningful learning as occurring “when new information is linked with existing concepts, and integrated into what the learner already understands” (p. 548).  The goal of teaching science is meaningful learning because students are expected to make connections between what they learn in science classrooms and what they already know.
    Piaget (von Glasersfeld, 1984, 1995) argued that a person expects to understand each new experience in terms of what he/she already knows (assimilate the experience).  When a learner is unable to assimilate a particular experience to previous ones then some confusion occurs.  To reestablish mental balance a learner brings meaning to new experiences through accommodation.  This process requires a person to restructure currently-held knowledge or to construct entirely new knowledge (Von Glasersfeld, 1989a).  These two processes are important mechanisms in understanding learning in science.
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Student Alternative Conceptions:  Knowledge Students Bring to Class
    A variety of terms has been used to describe the knowledge which students bring to science classrooms.  For example, “alternative frameworks” (Driver & Easley, 1978), “preconceptions” (Ausubel, 1968), “misconceptions” (Driver, 1983), “personal models of reality” (Champagne, Gunstone & Klopfer, 1985b), “spontaneous knowledge” (Pines & West, 1986), and “intuitive theories” (McCloskey, 1983) have been used.  In this report alternative conception is used when referring to knowledge of physics concepts brought to class by the students because this term “conveys respect on the learner who holds those ideas” (Wandersee, Mintzes & Novak, 1994, p.178).
    As the importance of students’ prior or existing knowledge became recognized, Driver and Easley (1978) were among the first to recommend more extensive research to examine and describe student conceptions.  They argued for research studies using interviews and classroom interactions, because these methods were better suited to exploring individual student knowledge construction.  Driver and Easley felt teachers needed to know something about the range of student alternative conceptions because of their effect on classroom instruction.
    A wide range of studies exploring student alternative conceptions has been made over the past two decades.  A sample is reviewed in the following.  For a more extensive list of the studies that have been done see Pfundt and Duit (1994 as cited in Dykstra, 1996).
    Osborne and Gilbert (1980), using a technique called interviews-about-instances (IAI), explored understanding of force in forty students aged seven to nineteen.  Students were shown cards depicting familiar situations and asked questions about the scientific concepts represented.  Their results showed one group of students confused common meanings of words with their physics meaning; a second group did not think of force unless motion was occurring; and a third group viewed force as a physical quantity possessed by objects in motion which ran out as they stopped.  In a similar study Gunstone and Watts (1985) examined concepts of force and motion in students nine to nineteen years old.  These authors found that students thought constant motion required a constant force perpendicular to the direction of motion, the amount of motion was proportional to the applied force and stationary bodies had no forces acting on them.
    Watts (1982) used the IAI technique to investigate conceptions of gravity held by forty secondary school students.  He found many students viewed gravity as being caused by air, and that they believed without air there was no gravity.  Some thought gravity increased with height above ground and others thought gravity acted on falling objects but not on stationary ones.  In a related study Watts (1983)  investigated student views on energy.  Some students thought of energy as a human attribute, while others viewed it as something stored in objects that caused events to happen.  Other views were that energy is associated with activity and movement, and energy was a kind of fuel capable of doing things.  Students did not think of energy as conserved; rather, they saw it as a product that was released like smoke.  Boyes and Stanisstreet (1990) assessed 1130 boys and girls aged eleven to sixteen about their understanding of the law of conservation of energy.  They found that students understood law most frequently as a legal term rather than as a description of objects in nature.  Conservation was most frequently interpreted in the environmental sense of using sparingly or wisely.
    Jacobs (1989) worked with first year physics students to explore their understanding of vocabulary used in physics.  She examined students’ understanding of words which were part of their everyday vocabulary but have special meanings in physics, such as, speed, velocity, mass and weight.  She found that student comprehension of the physics meanings was weak and argued this lack of understanding had important implications for teaching physics because confusion occurs when teachers use the physics meaning and students apply their everyday meaning.
    Aguirre and Erickson (1984) interviewed twenty grade 10 boys and girls about their conceptions of vector quantities.  Their goal was to create a data base of alternative conceptions held by students.  Students were given tasks involving position, displacement and velocity of boats in a river.  They were asked to solve various problems, such as, how a location on a lake is described, and how fast a boat travels in a moving stream.  The authors concluded students intuitively use some vector characteristics in their solutions; for example, students knew the location of a fishing spot on a lake had to be specified by distance and direction, and river currents changed the velocities of boats.  Aguirre (1988) interviewed thirty grade 10 students about their conceptions of vector kinematics using laboratory apparatus.  He presented three situations during interviews - a power boat crossing a river, a frictionless cart moving across an inclined plane, and two orthogonally moving carts.  He found students used the ground as the predominant frame of reference when describing motion and did not use other frames of reference when determining velocities of the objects.  Students viewed component forces as acting separately rather than together, and generally confused component and resultant velocities.  Aguirre pointed out that teachers need to be aware of these student alternative conceptions to be able to design effective instructional strategies.
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General Characteristics of Students’ Alternative Conceptions
    The “Alternative Conception Movement” (ACM) (Gilbert and Swift, 1985, p.682) has carried out research exploring student alternative conceptions in most areas of science, including biology, chemistry, physics, and earth science.  Miller (1989) stated that the ACM had made significant contributions to science education research by helping us appreciate the complexity of the processes involved when students learn science.  The following is a summary of characteristics of alternative conceptions as they appear in the literature:

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Incorporating Alternative Conceptions in Teaching Science
    Science educators have developed learning and instructional models which incorporate research on student alternative conceptions and student conceptual development.  One general feature of these models is the development of some mental connection between new classroom experiences and knowledge already held by learners (see for example, Driver, 1983; Driver & Bell, 1986; Pines & West, 1986; Osborne & Wittrock, 1983, 1985; and Wittrock, 1985, 1986).  Some attempts that have been made to produce instructional strategies based on viewing student learning as conceptual development are described below.
    Students should not be viewed as empty vessels or blank slates that can be filled by lecturing about science (Gilbert, Watts and Osborne, 1982; Gunstone and Watts, 1985); rather, they must be actively involved in their learning (Millar & Driver, 1987). The traditional instructional strategy of providing definitions of concepts and statements of principles is not sufficient for learners to perform complex intellectual tasks required to learn in science (Reif, 1985).  Teachers should not respond to student demands for “right” answers, nor should they yield to the temptation to attempt to transmit knowledge directly through lectures and textbooks (Roth, K., 1990).  Pope and Gilbert (1983), and Ebenezer and Erickson (1996) think that effective teachers need some understanding of their students’ conceptions to enable instruction to make classroom facts have personal relevance to students.
    Driver and Easley (1978) maintain that teachers have to consider the individuality of learning.  The authors think that classroom experiences need to be designed to cause conceptual conflict, but that students have to be in a non-threatening, student-centred environment for such conflict to produce successful conceptual change.  Students need to interact with other students and teachers to clarify their own ideas and explore alternative ideas through techniques such as small group discussion (Driver & Bell, 1986) and student debates (Gilbert, Watts & Osborne, 1982; Roth, K., 1990).  Other common features of constructivist classrooms frequently include discrepant events (Nussbaum, 1985), experiences designed to distinguish scientific conceptions from everyday views, peer discussion and analogies (Driver, 1989: Glynn, Duit & Thiele, 1995). Julyan and Duckworth (1996) think students should articulate their ideas, test them through experimentation and conversation, and consider connections between their lives and concepts being studied.
    Posner, Strike, Hewson and Gertzog (1982) concluded that student learning in science “is best viewed as conceptual change (p.212)” and “teaching science involves providing a rational basis for conceptual change (p.223).”  Driver & Bell (1986) and Gunstone & Watts (1985) concurred that learning in science can be profitably viewed as conceptual change rather than reception of knowledge from a teacher.  K. Roth (1990) advocated questioning as a means of exploring student conceptions
    Millar (1989) has credited the ACM with making important contributions to understanding learning in science; however, he does not accept that a constructivist view of learning implies a single typical instructional strategy.  He argues that all teaching strategies can lead to student learning and that regardless of the strategy restructuring of concepts can take place in the heads of learners.  Millar has challenged the constructivist movement with creating workable applications that can be used in a class of twenty-five or more students.
    Dykstra (1996) has developed a different way of teaching physics to first year college students.  Based in part on an earlier work (Dykstra, Boyle & Monarch, 1992), Dykstra teaches classes of about twenty-five physics students in a different way than most traditional university instructors.  First, students explore their conceptions of physical quantities, such as velocity, force and acceleration.  Groups of students record their predictions and explanations about the way objects will behave in certain conditions.  Students then perform laboratory activities and evaluate their data using computer graphing programs.  Experimental results are compared with their predictions and discussed with others in the class.  Conflicts between experimental results and predictions are resolved through discussion led by Dykstra who carefully avoids judging any proposed solution; rather, he allows class members to decide on resolution.  He reports success with his technique, as well as, some frustration among students who are used to instructors providing answers directly.  He believes the learning experienced through this style of instruction is superior to that in traditional classes and finds a greater sense of personal satisfaction with the new instructional strategy.
    Alternative conceptions research has influenced other areas of science education.  For example, Gilbert and Watts (1983) have proposed that curriculum development in science could start by reviewing descriptions of alternative conceptions and using them as a foundation for curricula.  Driver and Bell (1986) argue that a spiral curricula is required because of the length of time required to achieve conceptual change in students.  Spiral curricula revisit concepts and allow more detail and complexity to be added on each cycle.  Driver and Oldham (1986) argued that curricula should incorporate conceptual development as part of the documentation.  They believe conceptual development should be included as an integral part of each curriculum document rather than remaining external to curricula as an instructional strategy.
    A few authors have suggested that students in science should be taught metacognitive (thinking skills) strategies to assist them in constructing and reconstructing their concepts in science.  Reif (1985) suggests that we should strive to teach students more generic skills about how to learn a new concept and knowledge related to it.  He believes that students could benefit from instruction aimed at teaching them about thinking (metacognitive) skills in general.  Pope and Gilbert (1983) take a slightly different slant by advocating that learners learn to reflect on their own views and “recognize their roles as theory builders (p.193).”  These authors argue that students need to be aware that they construct their own theories and these theories can be refined through reflection and additional experiences.  Millar and Driver (1987) accept that pedagogy has to account for the effect of learners’ prior knowledge on learning activities, but see pedagogy being designed to empower people to act more effectively in their daily lives, in their involvement with natural events and with technological artifacts.
    A key participant in any science classroom is a teacher.  Regardless of how learning is viewed, a teacher is an integral part of the process of learning in science classrooms, and is responsible for implementing instructional strategies that facilitate learning by students.  Gunstone (1988) has argued that teachers have reacted positively to alternative conception research because it better informs teachers’ own classroom experience.  The results and descriptions of learners are more consistent with teachers’ practical experience than were earlier types of research.  In spite of this acceptance by teachers, direct applications of research results to classroom teaching have not been easy to achieve nor are they prevalent.
    Driver (1988) suggests that instructional strategies should be developed using a process of action research directly involving classroom teachers.  The resulting strategies could be tested in classrooms during their development.  She argues that this procedure would be a natural development of accepting a constructivist view of student learning.  If teachers are to adopt strategies designed for conceptual change they must be part of the research programs that develop them (Driver, 1989).  Driver maintains that students cannot develop scientific conventions by themselves; rather, they must be constructed with assistance from teachers who are part of the scientific community.
    K. Roth (1990) points out that teachers have to undergo their own conceptual changes about teaching and student learning if they accept a constructivist model of learning.  Recognizing conceptual change is required by teachers, Ebenezer and Erickson (1996) make a plea for teachers and researchers entering into collaborative teaching and research projects.  They believe the most effective means of promoting change in classrooms is to involve teachers in the design of change.
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Constructivism in Science Education
    This research project and much literature on learning and instruction in science are based on a constructivist model of learning and knowing.  This adoption of constructivism as an epistemological base for research in science education has taken place over a number of years.  As learning in science began to be viewed as an individual student process of concept development a need for a different view of learning and knowing became necessary.  Learning came to viewed as an individual process carried out in each student’s mind.  Learning was described as individual knowledge construction and concept development.  As this view spread constructivism began to be used in the science education literature to describe and explain learning.
    Solomon (1994) credits “Driver and Easley’s (1978) memorable article” with creating the tools necessary “for the accelerated rise of constructivism in science education (p.3).”  Osborne (1996) recognizes the same paper as initiating the view that successful learning in science depends more on prior experiences than on cognitive levels of development.  In spite of this Driver and Easley did not directly advocate constructivism as an epistemological foundation for learning in science.  Magoon (1977) is frequently cited (see for example, Cheek, 1992; Driver & Oldham, 1986; Gilbert & Swift, 1985; Gunstone, 1988) as one of the first to advocate a constructivist model of learning to direct educational research.  In his view Piaget’s research and publications, Chomsky’s research on linguistic development in children, and Kuhn’s (1970) descriptions of paradigms in science were the driving forces behind the shift to a constructivist view of educational research and learning.  He thought these works showed the constructed nature of knowledge in a range of fields.
    Posner, Strike, Hewson, and Gertzog (1982) argued that no well articulated theory of conceptual change yet exists.  They described the process in learners as analogous to Kuhn’s paradigm shift and incorporated Piaget’s processes of accommodation and assimilation to explain how concepts changed.  Pope and Gilbert (1983) traced the constructivist position to Kelly (1969, cited in Pope & Gilbert) and concluded that he drew on constructivist principles when formulating his Personal Construct Psychology.
    Osborne and Wittrock (1983), and Pope and Gilbert (1983) held the position that learning in science could best be viewed as knowledge construction with learners having an active role in the process.  Osborne and Wittrock (1983, 1985) incorporated individual knowledge construction to describe the generation of links between stored memories and new experiences in order to explain alternative conceptions by students.  Driver and Erickson (1983) argued that viewing students as actively constructing knowledge was based on a “constructivist epistemology”  (p.39), but made no reference to constructivism as described by von Glasersfeld (1984, 1988, 1995).  Strike and Posner (1985) described an epistemology similar to constructivism, and Driver and Bell (1986) referred to a “constructivist view” of thinking and learning in science; however, none of these authors made any reference to von Glasersfeld’s prolific writing about constructivism.
    Driver and Oldham (1986) cited von Glasersfeld directly in their description of a constructivist approach to curriculum development.  As well, von Glasersfeld (1984) was cited by Bodner (1986) in his article describing a constructivist model of knowledge and its implications for teaching.  Driver (1988, 1989) drew on von Glasersfeld’s view of constructivism as a foundation for viewing individual knowledge construction, but argued that his view was not sufficient to describe social aspects of learning in science.  In a similar manner Millar (1989) acknowledged the value of constructivism in describing individual knowledge construction, but argued that constructivism was not a sufficient explanation for the social aspects of knowledge construction in the scientific community.  Wheatley (1991) drew on Von Glasersfeld’s work when advocating the adoption of constructivism as an epistemological base for science.  He maintained that constructivism fulfilled many requirements for understanding learning in science.
    Cheek (1992) asserted that von Glasersfeld’s version of radical constructivism should be adopted as a theoretical foundation for Science-Technology-Society (STS) education.  By the 1990s the constructivist learning model was being described in literature aimed at practising teachers (see for example, Yager, 1991) and in teacher education texts (see for example, Trowbridge & Bybee, 1996).  When viewed from a constructivist perspective student learning activity during class becomes very important to teachers.  To a constructivist, student verbalizations of ideas and concepts function as a window onto student conceptualizing, thinking and concept development.  As effective teachers have long realized student dialogue assists in understanding how students are thinking about particular concepts in science or physics.
    From a constructivist perspective the function of teacher instruction is viewed differently than from other models of learning.  Rather than being seen as transmitters of knowledge, teachers are viewed as facilitators of student knowledge construction.  von Glasersfeld and Steffe (1991) recommend that teachers work to develop skills to create conceptual models of individual student learning to aid them in assisting students with their learning.  Teachers can use these conceptual models in choosing instructional strategies to provide individual assistance to students in their knowledge construction.
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Social Construction of Knowledge
    Even though Driver and Easley (1978) were credited with beginning the move to constructivism, they did not see an individual constructivist model as sufficient to explain learning in science.  Because science is a consensually agreed upon body of knowledge, the authors argue that students cannot independently discover the rules and definitions of the scientific community.  Driver (1988) continued to emphasize that science is public knowledge that is better described as “carefully checked construction (p. 136)” than as discovery.  Learning in science involves individuals being initiated into the ways of seeing of the scientific community (Driver, 1989).  Without the presence of a teacher as member of the scientific community, students would have no way of knowing a particular viewpoint was shared with the scientific community.
    Driver, Asoko, Leach, Mortimer & Scott (1994) view learning science as involving a combination of personal and social processes.  “Individuals must engage in a process of personal construction and meaning making (p.8)” before they can enter “into a different way of thinking about and explaining the natural world” and become socialized in the practices of the scientific community.  Learners have to acquire rules to manipulate the symbols of science, a process which is impossible without contact with the community of scientists or their representatives.  Concepts learned in science classrooms must be similar to those of the scientific community, because there is little value in students carrying away ideas that are significantly different (Millar, 1989).
    Cobb (1996) argues that both individual knowledge construction and enculturation occur when learning a body of knowledge located in a community.  He concludes “that the sociocultural and constructivist perspectives each constitute the background for the other (p.48).”  In a similar manner Fosnot (1996) maintains that sociocultural and individual constructivist processes are interwoven because individuals do not act alone; they are social beings and, as such, interact with others to construct mutually shared knowledge and meaning.
    Welch (1985) described the state of research in science education and made recommendations for future research programs.  He concluded investigations of teacher behaviors had produced very little in the way of improvement in classroom teaching; however, he remarked, “If one thinks of the students as the primary actors in the learning process instead of the teachers, then the study of appropriate behaviors seems highly desirable” (p.443).  He noted the lack of research on student behaviors and suggested a great deal could be learned by investigating students while learning science.
    Welch (1985) maintained that one important finding in cognitive psychology was that learning is influenced by previously-held student knowledge and stated “cognitive researchers believe that understanding how children learn will lead to improved instruction” (p.436).  He also noted that “It is difficult to separate student behaviors from teacher behaviors because they often occur simultaneously” (p.431).  Seeing teaching and learning as mutually effecting each other seem obvious to practising teachers, but to this time research attempted to isolate the two process and study them independently.
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Part II - Significant Findings of the Study

Student Views on Learning and Physics
    From the first day the participants arrived with a desire to learn about physics and throughout the project generally looked forward to being in class.  They were motivated by a variety of factors, including personal interest and knowing that Physics 30 was a prerequisite for certain career choices.  At no time during the study did I deliberately have to spend time motivating them to engage in learning physics.
    The students had some perceptions about how they learned and the role that teachers had in that process.  For the most part they were receptive learners at the beginning of the study and were not comfortable being actively involved in their own learning.  They expected me to provide instruction in a direct manner, either through notes or by directly answering their questions.  Their expectation was that the notes and answers would explain the physics concepts and that they would develop understanding from these explanations.  Initially they were uncomfortable when the instructional strategy did not fit their receptive style of learning.
    When the students became comfortable with being actively involved in their learning, they were incredibly active.  Although there were only nine students in the class, interactions between participants were numerous.  Conversations erupted spontaneously among students and between students and teacher.  They discussed ideas with each other and openly argued about interpretations and meanings of definitions, concepts and problems.  The high frequency of interactions about physics was a revelation to me.  The participants were more talkative during their attempts to understand physics concepts than I had expected.  All students were involved in these interactions.  Without the videotape records the large number of these learning interactions would not have been fully appreciated.
    The participants believed that natural ability was an important factor in their own and others success or lack of success in physics.  They believed that some of them had more ability than others to do physics.  On occasion individuals assumed that they did not have the ability to use the mathematics which they believed were required in physics.  While a range of ability did exist among members of this group of students, they were not always correct in their assessment of their own ability or of other individuals.  Their main tool for assessing ability was the marks that they received on tests and assignments.  They undoubtedly viewed these marks/grades as a measure of ability as well as an indication of achievement.
    Their understanding of the structure of physics knowledge caused them some problems.  They perceived that there were knacks or tricks to doing questions and searched for a system of steps to follow that would lead them to correct answers.  The participants wanted an all-purpose algorithm (set of steps to follow in solving a problem) which they could use to solve all types of questions. Rather than viewing theory as underlying principle, they appeared to view scientific theories as algorithms which could be used to answer problems.  Theories were thought of as providing understanding of phenomena in the world by answering their questions.  This interpretation is consistent with their reliance on experiential knowledge to understand phenomena and with their lack of development of conceptual knowledge.
    Their use of algorithms was non-discriminatory; that is, they picked an algorithm that matched the variables in the problem.  They demonstrated, for example, considerable difficulty answering questions involving kinetic energy or momentum because both concepts depend on mass and velocity.  They looked for a formula that contained mass and velocity and solved the resulting equation, rather than basing their analysis of a problem on underlying physics principles.  Since both kinetic energy and momentum formulas contain an m and a v, they often chose the incorrect formula for solving a problem.  Once they employed an algorithm and determined an answer, they did not reflect on whether the answer was reasonable or not.
    The participants were aware of difficulties and inconsistencies in their knowledge construction.  When a topic was presented and not understood, they asked questions in an attempt to reduce or eliminate their confusion.  Initially they were somewhat reticent to talk about their confusion; however, as they became more at ease, they openly discussed their confusion with me and the other students.  For example, when learning about momentum they knew that they did not understand the concept in spite of having done a laboratory activity which was designed to explore momentum.  Although achieving good results on the activity they knew that they did not understand momentum.
    They appreciated the non-judgmental atmosphere of the classroom, including my own reactions to their struggles and the reactions of their classmates.  There were very few cases of students “putting each other down” during the months of the study.  In reviewing the tapes and transcripts no cases were identified where students had to be reminded not to discourage each other.  They had trouble describing their thinking and problem solving as they learned but without a supportive classroom environment they would never have attempted to do so.
    The participants employed a variety of strategies to construct physics concepts but did not appear to attack knowledge construction in a planned or coordinated manner; that is, I do not think they had identified principles of learning that they applied to the process.  While other examples occurred the most clearly documented case illustrating different strategies of knowledge construction were exhibited during the discussion on momentum.  Four different individual attempts at constructing the concept were evident in a twenty minute discussion.  The students clearly learned about momentum differently, even though they had shared common classroom experiences.
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Students’ Experiential and Conceptual Knowledge
    In this report experiential knowledge refers to knowledge that students bring to class as a result of their life experiences.  This knowledge includes all experiences they have had during their lives and the thinking that they have done to organize their knowledge to help them operate in their world.  On the other hand conceptual knowledge is theoretical in nature.  This knowledge is formed in the mind as a result of reflection about experiences and generally has principles that can be used to explain a number of experiences.  Science requires both types of knowledge, but the conceptual knowledge is the abstract part of science which serves to organize knowledge using laws and theories.
    The participants relied on their experiential knowledge to an enormous extent when learning physics.  They had not developed conceptual (theoretical) knowledge that was useful in physics and did not seem to understand the process of using conceptual knowledge to explain and understand natural phenomena.  Although they used mathematical formulas in calculations, they did not understand the process of representation that has been used to create the formula.  When the mathematics became more complex, they did not trust a model to provide interpretations of situations; for example, when asked to calculate the change in velocity of a car which went around a corner at constant speed, they did not think that there had been a change in the velocity, and did not understand what the calculated answer meant.  The mathematical model was not useful in assisting them to understand the situation.  A second example of the lack of use of conceptual knowledge was displayed when they solved a force board problem near the end of the project.  Even those participants who used vector mathematics properly were unable to state an adequate reason for using vector mathematics in their solution.  Their choice was determined by intuition and previous examples rather than realizing that vector mathematics are required to represent the properties of forces.
    The participants did not reflect to any extent on the application of physics principles in their everyday experience.  They had not thought about the action of curling rocks or the place of numbers in science until asked to do so during the study.  Initially I was concerned that my interaction was not skilled enough to reach the limits of their reflection about such concerns; however, I no longer think this to be the case.  The life experiences of the participants had not created any need to think about the nature of knowledge or what it meant to learn.  Generally the participants seemed to be positivist in their view of the world and believed scientific laws were discovered in nature.  Their belief was that physics concepts really existed in nature, rather than being constructed by humans to organize and understand their world.  On occasion they talked as if they had a constructivist view of the world, but they did not understand the ramifications that such a viewpoint had for learning science and other subjects.
    The participants worked well with laboratory apparatus.  On several occasions they demonstrated their ability to operate laboratory equipment skillfully.  They understood what the equipment was meant to do and the measurements that they were supposed to make during the experimentation; however, this understanding of the operation of laboratory apparatus did not appear to translate into understanding at a conceptual level.  This outcome was disappointing because a traditional argument for the use of laboratory activities in all science classes had been to provide concrete examples of concepts that are being studied.  These concrete examples were expected to help students develop more understanding of the concepts involved.
    On one occasion students were asked to lift a heavy bucket of sand using two ropes and pulling them at various angles.  This activity illustrated their lack of understanding of the process of mathematical representation of concepts identified in everyday situations.  They were able to describe the relationship between the angle of the rope and the force needed to lift the bucket with considerable accuracy in a qualitative manner; however, they made no headway in representing that relationship using vector mathematics.  The ability to perform this difficult representation process was never demonstrated during this activity.  Their struggle with conceptual knowledge, its use and development, was ongoing throughout the study.
    When asked what concepts were easiest to learn, the participants listed those that they could visualize or identify in their everyday experiences.  They were unable to visualize concepts which they considered to be difficult to learn, and wanted me to provide “hands-on” activities and practical examples of abstract concepts.  They thought that if they could understand how a concept was used in their experience, then they would be able to understand the concept in physics.  In spite of this belief the students did not demonstrate very much development of conceptual knowledge as a result of the hands-on activities.
    Although the participants at times exhibited some characteristics of meaningful learning, more extensive probing of their understanding revealed that they had mainly achieved rote learning.  The learning that occurred as the result of the momentum cart lab was a good example of this type of mimicry.  The manner is which they manipulated the equipment and lab reports submitted indicated they understood some aspects of momentum.  Their lack of understanding was identified only when they tried to answer questions which probed their conceptual development.  The instructional sequence produced the expected results but these did not accurately indicate the level of student understanding.  The assessment items used during this activity, student observation and submitted report, did not correlate well to their conceptual understanding of momentum.
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Student Alternative Conceptions and Communication
    As was expected the students showed confusion over the use of words which are used in everyday language but have separate and distinct meanings in physics.  Separation of vector addition and subtraction from algebraic addition and subtraction was difficult for the participants who, at times, used the algebraic operations when using vectors.  Equally apparent was their confusion between the terms balanced and equal when using vector components.  They wrote equations for relationships between components which indicated that they thought balanced meant equal.  They looked only at the magnitude of the component vectors and did not consider the directions of the components as significant.
    Confusion over the meaning of pairs of words provide strong evidence for the necessity of clear communication between teacher and students.  While this need is always assumed by teachers, the apparent insignificance of an item that can cause a breakdown in communication can not be underestimated.  Confusion can arise over seemingly minor points resulting in learning blockages which either produce faulty knowledge construction, or block it altogether.  The most important feature documented in this research is that many of these causes of confusion are not identified in the classroom as instruction occurs.  Students may be aware of some blockages, especially those that stop learning completely, but are unaware of others because knowledge construction continues but in a wrong direction leading to some form of alternative conception.
    Student transfer of knowledge about vector mathematics between mathematics classes and physics was almost nonexistent.  No student in this group brought sufficient understanding of vector mathematics to be of practical use in physics.  Some had learned algorithms for addition and subtraction of vectors but could not recall them completely.  They brought only a poorly developed concept of what a vector is, and no one came with conceptual understanding of what it meant to add or subtract vectors.  Teaching the rudiments of vector mathematics in physics classes is likely to continue for the foreseeable future, at least until a different approach is used in teaching these concepts in mathematics classes.
    This inquiry has reinforced my understanding of the value of using student questions and comments to build models of their knowledge construction and conceptual development.  Students ask questions and make comments on the basis of what they think they understand about a concept.  The structure of their knowledge is indirectly revealed in the way that they phase their questions.  By using their questions and asking others I was able to explore their knowledge development.  Student responses on tests and quizzes, and work at the board provided additional sources of data for development of these models of student knowledge construction.  For teachers to develop such models of student knowledge construction, interactions among students and teacher have to occur openly.  In a classroom which is highly teacher-centred, this type of model development is not possible, because students do not have opportunities to talk about their developing concepts with the teacher or each other.
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Mathematical Representation of Concepts
    The detailed analysis of student thinking made in this research confirmed that the participants did not understand the process of mathematical representation of physics concepts well enough to apply the process to new concepts and situations.  Because of this research and my teaching experience I think the majority of secondary school physics students do not have a fundamental understanding of this important process.  Students learn to manipulate formulae that are part of the course curricula but, in general, do not understand the relationship between the formulae and the concepts which the variables in that formula represent.  Students treat physics formulae as algebraic expressions to be manipulated mathematically rather than representations of certain quantities identified in nature.  To some extent I have fostered this attitude in my students by providing algorithms for problem solving and clues in the questions to help students choose the correct pathway to the solution.  In this study I attempted to provide the participants with a different view of this relationship by looking at the place of numbers and mathematics in science, but the results of the study are strong evidence that this change was not enough to create understanding of the representation process.
    The enhancement of student understanding of the process of mathematical representation cannot be achieved in grade 12 physics classes alone.  Students need experience with the principles of mathematical representation much earlier in their formal education than the last year of secondary school.  Courses in math and science taken before grade 12 physics will have to begin to develop these skills and understanding.  The curricula of those courses will have to be restructured to provide students with primary experiences constructing mathematical representations, rather than observing them as secondary experiences from a teacher or text book.  Classroom experiences could be formulated so that their successful solution is dependent on students developing mathematical representation for the concepts under investigation.  Computer software and graphing calculators have potential to provide simulations of this process and to perform those mathematical manipulations in which students tend to get bogged down.  The use of computers and the Internet in assisting students in constructing physics concepts is an area for further research.
    Post-secondary educators would also benefit from students who had a better understanding of the process of mathematical representation.  In post-secondary science courses the representation process is essentially the same; however, more complex mathematics, such as statistics and calculus, are required to represent the relationships between concepts with accuracy.  Students entering subject areas such as biology, chemistry, ecology and economics, as well as, physics would benefit from a more complete understanding of the use of mathematics in representation.
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Recognizing Direction as a Characteristic
    I reflected for some time about the students’ inability to identify direction as a significant characteristic of certain physics concepts before gaining even a hint of insight.  In their lives most experiences and problems did not require the awareness of direction that is needed in physics.  All participants had driven cars which would seem to be an experience requiring some knowledge of direction; however, closer examination reveals that this was not so.  When beginning a trip a driver must start out in a particular direction, but after choosing the correct road few navigational skills are required to arrive at a destination.  Students tended to see direction as a means of relating positions on the earth and not a characteristic of certain concepts in physics.  Their conception of direction was not the same as that of practising physicists.
    The participants memorized algorithms to solve problems that involved direction and used clues in the problems to identify which algorithm to apply.  These clues were normally present in the questions as part of the written description.  Educators have assumed that successful problem solving of this nature would lead to the development of understanding as experience was gained.  Over the years this approach appeared to be an effective way to teach students because they successfully answered problems.  This research study has helped to show that this instructional approach did not produce the depth of understanding which was traditionally thought to have been created.
    This lack of identifying the importance of direction in physics concepts adds to the inability of students to understand applications of vector mathematics in physics.  Without identifying direction as a fundamental characteristic of certain quantities students cannot be expected to see any reason to use vector mathematics in solving problems; and, vector mathematics will make little sense to them until they are able to understand why direction must be part of some mathematical representations.  The participants did not benefit a great deal from separate instruction about vector mathematics in geometry-trigonometry classes as was shown by their unanimous surprise that vector mathematics could be used to represent anything in physics.  None of the students in this research had developed sufficient understanding of vector mathematics in their mathematics classes to be able to make use of that knowledge in our physics class.
    In a sense the confusion is the result of students’ alternative conceptions of direction.  Students have a conception of direction in their vocabulary and use this meaning in the physics environment.  Their meaning is based more on using direction to describe the location of some object or destination with respect to some fixed point.  For example, a car is located to the left of the doorway, or Canada is north of the United States.  They do not understand the concept in the manner that is required for success in physics in that they do not associate concepts such force and velocity with having direction.  Without a more appropriate comprehension of direction as physicists use it, grade 12 physics students will continue to struggle with the use of vector mathematics.  Conceptual development strategies, as described earlier, may produce some of the reconstruction required for successful problem solving involving direction, but more study and research are required before a practical classroom solution can be developed.
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Applying Vector Mathematics in Physics
    The students did not understand the process of mathematical representation to any great extent, nor did they understand that direction is a fundamental characteristic of many physics concepts.  These two factors combined to make the use of vector mathematics even more difficult for the participants and most grade 12 physics students.  The participants lacked a perception of any need for vectors or vector mathematics.  They did not have a sense of why they had been taught about vectors in other courses nor could they describe any practical applications when we talked about vectors early in the study.  Some were able to perform addition and subtraction using algorithms but they did not exhibit understanding of the mathematical principles involved in these processes.  This deficiency was illustrated when they drew vector diagrams to help with adding and subtracting vectors as part of solving problems.  Most students did not view these diagrams as aids which showed a resultant vector; rather, they saw the diagrams as separate problems which made the problems more complicated.
    The research results show that the difficulties experienced by students learning to apply vector mathematics are very complex.  Three elements of the struggle have been described, mathematical representation, alternative conceptions of direction, and not understanding the function of vector mathematics.  A simple solution to this problem does not exist because of the complexity of the learning processes that have to be achieved by students.  The three elements must be dealt with together and successful resolution can not be achieved in one five-month semester in grade 12 physics.  Solutions to student difficulties in applying vector mathematics in physics have ramifications for science and mathematics courses at earlier grade levels.  Students must be assisted on three fronts: first to understand the representation process; second, to develop a different conception of direction; third, to develop an understanding of the purpose of representing certain concepts with vectors.  Resolution will take considerable time and innovation to create instructional strategies and experiences to accomplish these goals.
    I have discussed the three elements separately but any solution will have to incorporate their interdependent nature.  While the concerns described are fundamentally cognitive in nature, they must be addressed in curricula to some extent because curricula largely determine what is taught in science classrooms.  Resolution will have to start much earlier in science and mathematics education.  Elementary and middle years science teachers will have to begin to provide experiences that develop student understanding of these ideas and relationships.  Students need opportunities to test their own knowledge in real-life experiences and then to reconstruct it in light of them.  Most science teachers do not have the arsenal of instructional strategies and experience necessary to create these experiences for students because the type of instruction that I am advocating had not been used to any extent in science education.  This result will also have ramifications for teacher education programs.
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Part III - Considerations and Recommendations
    Abstract concepts, such as momentum, energy and entropy, are currently a part of the Physics 30 curriculum and are likely to remain so.  The nature of these concepts cannot be changed, but instruction can be modified to assist students in achieving something closer to meaningful learning instead of simply memorizing formulae and definitions.  Different instructional strategies can be developed to facilitate student construction of conceptual knowledge.  Learning about this group of concepts will never be a simple matter, but students are likely to develop better understanding if they learn more about the structure of physics knowledge and the process of mathematical representation than is currently expected in secondary school curricula.
    Secondary physics curriculum guides usually describe student learning in terms of outcomes or objectives, but do not provide guidance to teachers in promoting student conceptual development.  Physics and other science curricula are not designed to have students explore the relationship between science concepts and mathematics, or the process of mathematical modeling.  Science and mathematics courses are developed with little attempt to coordinate content/topics in mutual support.  Some mathematics courses may be required as prerequisites of physics courses, but students can not be assumed to understand the process of mathematical representation used in science as a result of those mathematics courses.
    One objective of physics curricula is to have students understand the nature of science knowledge and the processes of science/physics (Saskatchewan Education, 1992).  To achieve this goal student learning should be meaningful and new knowledge should be connected to what the learner already knows.  This research indicates that reducing the amount of content in physics curricula, making content more relevant and meaningful for students, and increasing connections between mathematics and physics would be constructive changes in assisting students to achieve meaningful learning within secondary school physics.
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Amount of Content in Secondary School Physics
    Throughout my teaching career and this research project I have been aware that students did not develop the depth of understanding of physics concepts for which I was aiming.  Because of pressure to cover the content in the grade 12 physics curriculum, additional time was not spent helping students develop a conceptual knowledge base to inform their experiential knowledge.  I have found it impossible to help students develop conceptual physics knowledge in the time allotted; however, the length of time spent on a given concept is not the only issue.  Alternative teaching strategies and learning experiences must be developed to increase learning success.  Using the same instructional strategy for a longer period to time will not increase student knowledge development.  When curricula are designed with coverage of concepts as a major driving force, the pressure to move on to the next topic or unit dominates teacher decision making.  Until a change in curriculum focus is made, the pressure to “cover the course” can not be ignored by teachers.  Good pedagogy should direct teachers to ensure an adequate level of student understanding before moving onto a new concept or unit; however, good pedagogy is rarely the driving force in these decisions because of the overwhelming pressure to cover the content.
    If students can answer problems and “do the math,” then they are assumed to understand the function of mathematics and mathematical representation in physics.  This research has illustrated the inaccuracy of that assumption.  These participants did not demonstrate understanding of the process of mathematical representation even when instruction was designed to enhance it.  Little time is allotted to examine this relationship in most physics, science and mathematics courses.  Without making the connections between physics concepts and fundamental processes of physics, students can not achieve adequate understanding.  New curricula in physics have to reduce the number of physics concepts explored and allow students more time to develop understanding of the processes and relationships in physics.  If changes are made only in grade 12 physics, then success is unlikely. To ensure better exploration of the mathematics/science relationship changes to the curricula of other science and mathematics courses taken prior to Physics 30 are required.  Most student knowledge of the place of mathematics in science and physics was obtained in the courses taken previously.  Changes in teaching science and mathematics in earlier grades could provide the background for application of mathematical models necessary to physics.  The rush to move on and cover the content in physics might be alleviated if understanding of the processes was learned earlier in students’ formal education.
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Increasing the Relevancy of Physics to Students
    The abstract nature of many physics concepts creates considerable learning difficulty for most students.  To master the concepts in Physics 30 students have to expend considerable effort in constructing new knowledge, reconstructing their currently-held knowledge, and making connections between the two.  This research showed that students consistently had considerable difficulty making such connections on their own.  Because of students’ inability to make cognitive connections instructional strategies need to be designed with the aim of assisting students in connecting newly acquired concepts to their currently-held knowledge.
    Without students achieving understanding of physics principles and concepts there is little rationale for students taking grade 12 physics.  For most students little content appears to be remembered for more than a few weeks or, at most, a few months.  Having students understand a few principles deeply and seeing connections to their life experiences is a more sound pedagogical position than covering a large amount of content but knowing that the students will remember little in the future and will be unable to apply these principles anywhere but in the physics classroom.  Secondary school physics teachers should shift the focus of instruction away from covering the curriculum to helping students develop a more complete understanding of a few concepts and an ability to apply them to phenomena in their lives outside the classroom.  The current emphasis on moving through a series of concepts without assuring understanding should no longer be acceptable teaching practice.  To some extent all secondary school science classes suffer from the same concern and all could benefit from a similar shift in emphasis.
    When mathematical formulas are introduced early in classroom experiences, the participants treated formulas as algebraic problems and lost sight of the physics concepts.  Evidence of this weakness was displayed when the three students discussing the momentum exam indicated they never thought about the answers once the calculations were complete.  They showed no indication of understanding the principles underlying the problem, rather they simply followed an algorithm to arrive at a solution.
    When introducing a new concept instruction should first explore students’ current understanding of the concept and then identify the concepts in natural phenomena in a qualitative manner.  Much less emphasis should be placed on mathematical formulas than has traditionally been done.  Experiences should be provided for students to assist them in identifying a concept in nature and determining other concepts that are related to it in cause-and-effect relationships.  For example, when exploring acceleration students could initially examine their own conceptions of acceleration acquired during their lives, especially their experience driving cars.  By first examining their own conceptions students would become more aware of their current understanding of acceleration.  Classroom experiences would then be created to demonstrate the limitations and inconsistencies of their conception and to guide them to reconstructing their conception to resolve their dilemma.  Helping students identify situations where their knowledge fails to produce understanding may create an impetus for restructuring their conceptions to match more closely those of the physics community.
    After students had a sense of their own conception and had compared it with the scientific view of the same conception, they would explore variables which cause changes in the concept; in the case of acceleration, mass and force.  This initial exploration of cause and effect relationships would be qualitative in nature rather than using mathematical representations.  Students would gain through experience and discussion an understanding that acceleration increases as force increases, and decreases as mass increases.  When students understood the qualitative relationship between the concepts, they would determine a means of representing the qualitative relationship using mathematics.  A possible vehicle for this stage could be laboratory problems which require numerical accuracy for satisfactory solution.  If used at all, physics formulae would be the end point of concept development rather than the starting point.  The traditional use of formulae in secondary school physics could be eliminated altogether because this research strongly indicates formulae act as part of an algorithm and can be manipulated correctly without understanding the relationships represented.
    The ideas expressed here require field development in classrooms and would evolve with teacher and student experience.  Students would have to learn to operate within this approach to instruction.  If these strategies were introduced in earlier grade levels, then, by Physics 30, students may have learned to view learning in physics as concept development rather than memorization of facts.
    On different occasions in the research, students demonstrated their inability to recognize reasonable answers to problems.  This lack can be interpreted as a manifestation of students not understanding relationships between concepts in a qualitative manner.  To estimate answers to problems students need to understand the fundamental relationships between variables before they can decide if an answer is reasonable.  Estimation skills need not be developed in physics alone, rather they should be part of instruction throughout secondary mathematics and science courses, as well as, elementary math and science courses.
    Discussions and professional development between science and mathematics teachers could produce results if they focussed on interrelating topics common to both curricula.  Potential benefits exist for both subject areas.  First, students could identify explicit connections between subject matter in the two areas.  These connections would make some mathematics concepts more relevant by providing practical applications for seemingly abstract principles.  Second, such discussions could benefit both mathematics teachers and physics teachers because they could compare instructional approaches and refer directly to each others’ subject in their own classes.  They would develop an understanding of how various topics had been taught and which concepts were most important in each others’ classes.  Lastly, they could discuss instructional problems, and perhaps provide mutual support for each others’ teaching.
    Some topics identified by this research which would benefit from mutual discussion include direction conventions for vectors, vector components and problem-solving applications of mathematics.  If direction conventions and vector components were used in the same manner in both subject areas, then students would not have to perform the mental gymnastics currently necessary to apply concepts from one subject area in another.  To some extent problem solving skills might carry over from one class to another benefiting both students and teachers.
    At a more radical level a different option for curricula development could be explored.  The barriers existing between subject areas are artificially created and are present for convenience rather than out of necessity.  Consideration should be given to eliminating the barriers created by subject areas.  Science and mathematics could be taught as a single subject.  Other barriers are no less artificial.  Science subject areas such as, biology, chemistry and physics could be removed leaving an integrated study of science and mathematics.   I have little doubt that such a radical change would not be readily accepted by many teachers and administrators but some radical change is obviously needed if we are striving for meaningful learning in science students.
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Implications and Recommendations for Instructional Strategies
    The choice of instructional strategy depends on a number of factors, including teacher preferences, the concept or principle being developed, classroom facilities, available resources and the group of students being taught.  Although not designed to compare instructional strategies, this research showed that some choices facilitate student learning better than others.  While no single instructional strategy should be considered as a panacea for learning difficulties, the small group instruction used in the study appeared to have several advantages.
    The participants unanimously agreed that this type of small group instruction was beneficial to their learning.  Among reasons stated were that the small group provided an atmosphere where they were less concerned about personal embarrassment, and each felt that he or she had sufficient opportunity to express his or her opinions and concerns.  They were more active in the discussions, and were generally more attentive to class activities.  I have tried to create a similar non-threatening environment in my regular classes but in a large classroom with twenty-five to thirty students, it is much more difficult to allow all persons as much time as they would have in a small group to contribute their ideas to general discussions.  In particular girls have been shown to benefit from small groups and less competitive classroom environments than occur in most regular science classrooms; however, I have no doubt that all participants appreciated working in our smaller group.  I do think that the girls and some boys would have been at more of a disadvantage in a larger classroom.
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Using Discussion as an Instructional Strategy
    Throughout the project much of the instruction was orchestrated through student-teacher and student-student discussions.  Although this strategy appeared to be quite time consuming, several objectives was accomplished during these interactions.  First, conversations with students assisted me in developing a mental model or image of how each student was constructing his or her knowledge of physics concepts.  These models provided a background against which to formulate individualized responses for each student’s inquiries.  Identically worded questions from two students could require different responses if the image of their concept development was different.  Second, students benefited by listening to and taking part in these interactions, because they were able to experience part of each others’ struggle to learn.  Stronger students were frequently perceived to be naturally talented in physics leading others to believe that a strong student did not have to work through his or her own confusion to achieve understanding.  Classroom discussions helped to make frequent mental struggle seem to be a natural part of learning.  Third, everyone heard all student questions and inquiries, and was involved in the resolution of each.  Student-student dialogue contributed to individual learning because similar conceptual difficulties were experienced by more than one student.  At times a participant who had already worked through some difficulty in learning was able to identify the source of anothers confusion and help to dissolve it.
    The apparent time-consuming nature of participant discussions may be perceived as a disadvantage.  Considerable care had to be exercised to ensure that each student had an opportunity to make his or her contribution to each discussion.  On occasions when progress was agonizingly slow, I was tempted to answer questions and relieve concerns by providing “correct” answers.  In spite of pressure to complete the curriculum I resisted the temptation as much as possible because on most occasions transmitting correct answers did not produce the meaningful learning for which I was aiming.  For classroom discussions to be successful extended time was required because students needed to reflect at length about the issue being discussed.  They had to reconstruct their knowledge and this process could not be rushed.  While I was able to catalyze their restructuring process by providing experiences to help them to understand, each student had to perform the restructuring individually.
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Questioning and Discussion Skills - Learned Processes
    The research record showed that most students took some time to develop the skills necessary to become fully involved in classroom discussions.  They had to gain experience with my style of questioning and interactive discussion.   Transcripts from the earlier classes showed that the participants were initially quite passive and that they did not expect to participate so actively in their own learning.  They needed time and experience to gain a sense of the value of being personally involved before they readily contributed to the discussions.  Initially, wait times were long and student responses were very brief.  I had to exercise considerable patience while waiting for answers and refrain from answering questions or moving on to other students to reduce tension.  Only when the participants realized that I was not going to provide answers directly did they change their approach to this style of interactive instruction.  During the first few days students were not at ease, and neither was I.  They were not used to having so much responsibility for their own learning.
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Implications for Students Learning
    Students are responsible for their own learning and must expend intellectual effort to engage learning activities (Driver & Bell, 1986; Osborne & Wittrock, 1985).  Novak (1985) agreed the responsibility for learning can not be shared and must be consciously pursued by students.  This view that students are responsible for their own learning seems easily defended, yet the experience in the first week or two of the study with the participants strongly indicated they were used to passively receiving knowledge from books and teachers, and that they had assumed almost no responsibility for their own learning.
    When asked to describe how they learned about physics concepts or solved problems the participants struggled to explain what they were doing or thinking.  They had not thought to any extent about how they learned nor their own place in the process.  This situation was not changed as much as hoped during the study because they did not have sufficient time to learn thinking strategies or develop an understanding of learning, especially considering the lack of such focus over their past twelve years of formal education.
    Metacognitive processes can be as simple as awareness of techniques that assist memory, or as complex as the awareness of one’s knowledge and modifying its structure or content (Gagné, Yekovich & Yekovich, 1993).  Several science education researchers have argued that metacognitive strategies should be taught to students so they realize that they change and construct concepts in their minds (Duit,1991; Gunstone, 1988; Gunstone & Watts, 1985; Roth, 1995).  Students need to understand and control their memory to increase their success at learning complex concepts in science.  This research supports the position that students would benefit from understanding more about how they learn and how metacognitive strategies can help them reconstruct their physics concepts.
    These strategies require time to develop and should be introduced early in their education.  Students need to learn that they are actively learning and that teachers can not transmit knowledge to them directly.  Each student constructs the concepts individually in the social environment of the classroom.  Teachers can assist through their instruction in concept development by providing relevant experiences for students; however, each student is fundamentally responsible for his or her own knowledge construction.  Students need to know as early as possible that they are responsible for what they learn.  The appropriate grade level where introduction of metacognitive strategies should be made is an area for further research, but it is likely students could be successfully introduced to such strategies and begin to take responsibility for their learning at a much earlier age than secondary school.
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