Introduction
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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.
Table of Contents
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.
Table of Contents
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.
Table of Contents
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:
2. Alternative conceptions seem to be independent of age, ability, sex and cultural background. They are tenaciously held by learners and are not usually modified by traditional instruction. Alternative conceptions frequently parallel the conceptions of earlier scientists and philosophers. (Cheek, 1992; Driver & Bell, 1986; Gunstone, 1988; Stepans, 1991; Wandersee, Mintzes & Novak, 1994)
3. Instructional strategies designed specifically to produce conceptual change have shown some success in facilitating construction of conceptions that match those of the scientific community; however, discrepant events during instruction do not always produce the cognitive changes expected, and the alternative conceptions may be maintained even when learners answer questions correctly on tests. (Cheek, 1992; Stepans, 1991; Wandersee, Mintzes & Novak, 1994)
4. Scientific concepts are often presented assuming that learners immediately understand them; however, learners’ alternative conceptions interact with those presented during instruction in unpredictable ways producing unintended learning outcomes. (Cheek, 1992; Stepans, 1991; Wandersee, Mintzes & Novak, 1994)
5. Children can hold contradictory conceptions at the same time. One set can be used to operate in science classrooms and answer science questions, while the other set is used to explain happenings in their experiential world outside the classroom. (Cheek, 1992; Gunstone, 1988)
6. Even after several years of science instruction many adults and science teachers hold the same alternative conceptions as students. (Stepans, 1991; Wandersee, Mintzes & Novak, 1994)
7. Alternative conceptions have their source in each individual student’s complex experiential history, including direct observation of the world, peer culture, and language, as well as, television and formal classroom instruction. Each individual has a unique history; and, therefore, each holds a set of alternative conceptions that is different from other students. (Wandersee, Mintzes & Novak, 1994)
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.
Table of Contents
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.
Table of Contents
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.
Table of Contents
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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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.
Table of Contents
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