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This is a report on some recent research papers.
Some Considerations about Teaching Force
to High School Students
Scientific literacy is an expected and necessary outcome in education; however, such a
competence involves a grasp of fundamental physical principles, a technical understanding
of specific scientific terms and a commitment to what we loosely refer to as the
scientific method. The concept of force within Newtonian mechanics is illustrative of the
gap between the scientific priesthood (including some but not all science teachers) and
the laity (which include many undergraduate science majors). The concept of force
is further complicated by the fact that it is a "phenomenological primitive"
like time. Thus, although we experience forces and the passage of time, their
precise meaning is evasive and now even fraught with the mathematical complexities of
string theory, hyper-dimensionality and quantum mechanics. The power and beauty of science
in general and physics in particular is the ability of precise definition, careful
reasoning within consistent mathematical frameworks and experimental corroboration to
increase our understanding of our natural world. Within this framework several studies of
student’s conceptions of force will be considered in light of promoting effective
learning.
Children’s Dynamics1
When one understands Newtonian mechanics the entire scheme seems straightforward
but research shows that "even university physics students have problems with some of
the most basic ideas." Osborne cites an example of students successfully solving a
multidimensional unit vector force problem while having more difficulty with analyzing the
forces on a projectile (golf ball). Further analysis showed that many students seem to
utilize an "impetus" theory that conflates momentum and force, as well as other
Aristotelian notions. How do students come to have these non-Newtonian frameworks?
Osborne cites literature that argues that children begin forming
"mini-theories" from birth which enable them to make predictions and decide on
certain actions. Young soccer players show that these mini-theories are quite effective in
dealing with their common experiences. This "gut mechanics" is based on direct
experience and often not articulated. Children might counsel each other to "hit the
ball closer to the top of the bat and it will not jar so much", but no explanatory
role is offered or asked for in "gut dynamics" (this is a craft type knowledge).
As children grow they develop "lay dynamics" which is language mediated from the
culture at large. Explanations begin to play a role in the framework but lack consistency
or mathematical rigour of "physicists’ dynamics". The sources of
information for lay dynamics come from the media, science fiction, Discovery Channel and
so on. Consequently, this elaboration of gut dynamics contains a mixture of helpful
concepts and definitions as well as pure horse hooey.
Finally students learn physicists’ dynamics in school settings. The language and
mathematical structures of this framework is novel and sometimes even counter-intuitive.
Unfortunately, this new learning often forms a (thin) veneer of scientific reasoning over
a recalcitrant core of previous frameworks. Students compartmentalize their knowledge (use
gut dynamics to improve your slapshot, lay dynamics to talk about Star Trek, and
physicists’ dynamics for physics exams and contrived physics experiences such as air
track experiments). Osborne’s analysis is persuasive and resonates with my
experience. Students do have some intuitive ideas about force from their experience but
their language is imprecise. The explanations and vocabulary they do pick up come from an
eclectic group of sources. They often fail to integrate this vocabulary with their
experiences because they and no one else can—their lay dynamics is to flawed to
become a generalized powerful explanatory scheme. Finally, they learn real physics;
unfortunately, this physics is applied to highly idealized situations. Air tracks or other
situations that ignore the real experiences they actually have familiarity with (friction,
loss of kinetic energy in interactions) and other messy real world phenomena. Physics also
postulates immeasurable quantities such as the upward motion of the earth as a ball drops
down as well as some highly incredible claims such as those within both Special and
General Relativity.
So what should we do about this sad state of affairs? Osborne suggests some general
strategies and some very concrete actions. First, he suggests that developing
"real-world ideas about dynamics" from an early age. This should not be a
physicists’ understanding since elementary students are not ready for the
mathematics, rather, their own gut dynamics should be refined and proper vocabulary should
be introduced to counter some of the lay dynamics fallacies. Furthermore, high school
science should aim at developing consistent frameworks and practical applications of
Newtonian mechanics to facilitate the transformation of gut dynamics to a more scientific
view. Osborne also cites several examples of how this could be done such as introducing
students to the concept of momentum early on and exposure to "frictionless"
motion apparatus such as air tracks or air tables.
All of these suggestions are salutary but the brief article leaves much room for a more
thorough development of the main themes. For instance, how do we structure our tests,
curriculum, and labs to test for and develop a coherent consistent dynamics? When and how
should some advanced physics concepts like momentum be taught? How can labs be changed to
facilitate real understanding of Newtonian mechanics? What conceptual schemes cause the
most problems or are the most fruitful in developing a physicist’s dynamics? I also
think the introduction of the air track to elementary students might foster the dualism of
physics type phenomena versus real world experiences. Real world labs (even if they are
messy and don’t yield neat answers) in secondary school physics could also bridge the
gap. For instance, labs incorporating accelerated motion with friction could also help
bridge the chasm between the student’s world and Newtonian mechanics.
Students’ concepts of force as applied to related physical systems: A
search for consistency2
Finegold and Gorsky investigated 534 students (university and high school) to
search for consistent "misconceptions". Their study consisted of a ten-item test
to "elicit their beliefs about the forces acting on" pendulum bobs at rest and
in motion, a book at rest and in uniform motion across a table, a cannon ball in
mid-flight and a ball thrown straight up. Students were asked to use arrows to show
forces, to name forces and some students were interviewed to provide explanations for
their answers. They examined and found their test to be reliable and valid. Their results
were categorized according to error so a students score card would be graded with a C for
correct, G for only gravity was (correctly) indicated, and G + Fm which indicated gravity
was correctly indicated but a non-scientific force of motion was added, and so on. These
results were analyzed in a database (Lotus 123) and 280 queries were examined.
The database query method allowed a fine-tuned analysis of the results to answer
questions such as, "Do students who have not taken a physics course answer questions
inconsistently (showing lack of a coherent unified framework) more than students who have
take a physics course". They also were able to assess the prevalence of
"impetus" theories of motion and the false belief that no forces act on objects
at rest. Their results showed only limited support for these two often-quoted
"alternative frameworks" being consistently applied among students. Evidently,
when students make these mistakes they make them inconsistently in two ways. First, the
same student will use the impetus theory for one situation but not for another analogous
situation. Secondly, not all pre-physics students attempt to use these two alternative
frameworks. This echoes Reif’s findings that no general laws govern the thinking of
these non-Newtonian students. Yet most students who completed advanced high school or
University physics courses did have conceptual schemes which were internally consistent.
Thus, a student would apply Newtonian mechanics to projectiles in motion but revert to
impetus theories for objects undergoing uniform motion. This indicates the stubbornness of
some previous ideas about forces and the difficulty of inducing a global conceptual
change/modification to a completely Newtonian framework. Students who studied no physics
or merely physics at a general (ORD) level did not have a consistent meaningful conception
category to respond to the questions. It remains to be seen which group of students is
more amenable to the formation of a fully consistent Newtonian framework for application
to all situations. This result also suggests that formal physics instruction inculcates
the application of general principles to many phenomena although not all students could
maintain such a Newtonian rigour in all test questions.
The study seems both aided and limited by their methods and tools. The database
programme is a powerful tool for searching for patterns. But it also requires simple
inputs such as "G + Fm" so the test had to be structured and then subjectively
evaluated to categorize student responses into the 6 or 7 categories. This enabled the
analysis to detect consistent or inconsistent explanatory schemes as well as Newtonian and
Newtonian plus alternate schemata. However, the role of interview and student-generated
explanations (and situations and questions!) was limited or non-existent. This study
suffers from lack of qualitative and narrative richness offered by more language and
explanation and concept mapping approaches. But it does offer a powerful tool to assess
difficulties in analyzing forces. It also avoids the limitations of multiple-guess tests
in the requirement to label and identify forces including fictional forces which students
mistakenly invent and apply to many situations. Interestingly, some of these fictional
forces have entered our lexicon (lay dynamics) exemplified by "Coriolis force"
or "centrifugal" force.
This study showed that Israeli students, like their counterparts abroad, "after
studying physics, either do not understand, or have great difficulty in applying,
Newton’s laws to drawings of systems. They posit that students need the "ability
to apply general rules to particular instances and to extract general rules from
particular instances." The researchers are currently designing software simulations
to "refute students’ prior knowledge" and to help them grasp "the
general applicability of physical laws over a wide range of topics and situations";
for instance if a student neglected to indicate the normal force on a screen shot of a
book resting on a table the book would fall right through the table top.
The study can be questioned on some technical points such as the question design, test
format, small number of interviewed subjects… but the general results are compelling.
The theorist may often create these alternative frameworks, whereas the student merely
guessed or offered an answer from incoherent and even contradictory conceptions. Secondly,
not only do students not develop a consistent Aristotelian framework, the development of a
coherent Newtonian framework is also difficult for students. The authors acknowledge the
need for effective conceptual change strategies but only offer one rather flimsy one. To
be fair, their study did not focus on how to change and improve student’s conceptual
frameworks. Finally, I take exception to the aim of "refuting student’s prior knowledge"
on both epistemic and psychological/moral grounds. I prefer the metaphor of modifying, or
extending the range of application, or refining their prior "frameworks".
Making Productive Use of Students’ Initial Conceptions in Developing the
Concept of Force3
Dekkers and Thijs conducted a two-part study in pre-university classes in
Botswana and South Africa. The first phase (wherein teacher introduced the scientific view
after the experimentation to help resolve cognitive dissonance) used a "cognitive
conflict strategy" and was somewhat successful but not consistent with the
"assumption that most students based their reasoning either on correct or alternative
concepts." The second more successful phase revised the teaching sequence to develop
conceptual tools to perceive and resolve cognitive dissonance before they
experienced it.
Cognitive conflict approach is a common tool within a constructivist view of
learning. Conceptual growth can either be assimilative (use existing concepts to account
for new phenomena) or accommodative (replace existing concepts with new concepts to
account for new phenomena). Accommodation occurs when the learner becomes dissatisfied
with the existing conception or the new conception is seen as more intelligible, fruitful
or plausible. However, the replacement is not always complete (see previous paper).
The researchers suggested three problems with the "classic" cognitive
conflict approach. First, the learners were not prepared prior to the conflict or
discrepant event. Second, the learner’s prior concepts were not fruitfully mined for
aid in developing a more adequate scientific conception. Finally, the students’
"misconceptions" were often not so false as imprecise; the students’ use of
"force" was often not precisely defined and in some contexts functioned as a
term for momentum or energy. Thus, the teacher and student are actually speaking different
languages (incommensurate) and communication and deep learning is difficult. Consequently,
the research aimed at refining the students’ "prior correct concepts" and
"expanding the contexts" wherein those concepts could be applied.
The teaching sequence in this second phase was revised to incorporate:
- Find a shared meaning of "force" in limited contexts.
- Refine that partial concept of "force" and expand those contexts until the
meaning is no longer shared (these labs form the main thrust of the
cognitive conflict strategy employed in the first phase).
- Resolve dissonance: compare and find shared meanings.
The transcriptions and observations of student dialogue showed that students were able
to construct a Newtonian view of "force" within the revised teaching sequence as
opposed to requiring the teacher to aid in resolving the cognitive conflict. Furthermore,
the students improved with time (23% gain as opposed to 7% loss) which indicates a real
understanding of Newtonian force occurred although it required some additional time
(1-week). Finally, the answer patterns were more consistent with the assumption that
student reasoning was based on correct reasoning. The positive approach to a
student’s alternate conception resulted in improved learning. The correct theory was
not taught prior to the experiment (as in Dawson, 1985), merely tools were developed for
solving the problem by refining the students existing knowledge.
The authors do not articulate how they ascertained the students’ prior conceptions
of force. Did they use interviews (formal/informal/class/group/individual) or written
tests? How much more time would the revised teaching sequence require? Are pre-university
students in Botswana similar to Gr. 11 students in Ontario? Yet, the emphasis on working
with what the students know (or think they know) resonates within my liberal heart. Much
cognitive conflict theory smacks of brainwashing or cult-like to me; create a conflict,
then come through with the "answer" for the confused adolescent and recruit them
into the cult. The role given to the teacher with the "correct" view and the
younger learner with the "misconception" seems somewhat dangerous and
misrepresents what learners actually believe. Finally, the creation of the
"conflict" situation involve the learner being induced to articulate a
conception which had previously not been worked out in general terms—the learner is
being setup by the teacher and this seems to perpetuate the chasm between the teacher who
controls and knows everything and the pliant clay-like learner. In contrast, the
authors’ approach seems to make best use of "conflict strategy" while
preserving the value of the learner. This paper is a timely corrective to
mis/over-reliance on a "misconceptions" approach to conceptual change. Moreover,
Fisher and Breuer (1993 Misconceptions Seminar) provide a rationale for not
defeating misconceptions (and then immediately supplying the "correct" answer)
within the process of concept development.
Studying Conceptual Change in Learning Physics4
Dykstra et al. decry the classrooms where the communication is hindered by the
lack of a shared vocabulary and three situations result: the child ignores the teacher, or
the teacher ignores what the child is saying, or the teacher insists the pupil uses the
"correct" words to sound scientific so children are praised for "thinking
like a scientist" when they are actually "making noises which sound
scientific." The authors build upon the work of Dekkers (see previous paper) and
others in the emphasis on making use of students prior concepts and the use of bridging
structures, analogies, or scaffolding to construct a scientific framework after suitable
experiences have disequilibrated the learner. Merely guiding problem solving or more
effective presentation of the correct view fails to take account of student’s
alternative conceptions. Dykstra et al. use the tool of concept mapping to explore
conceptual change and how to foster it effectively.
Students are asked to generate explicit and detailed representations of their beliefs
(about motion and force in this paper). Thus strategy answers the lurking question in the
paper by Dekkers, how do we find out what they know now so we can better inform our
instruction? This approach could pushed even further to allow students to interview each
other to allow them to ask each other questions they find meaningful. However, this is
risky and probably more time consuming. Nevertheless, students were engaged in a
meta-cognitive process which the authors suggest promotes effective conceptual change to
completely scientific dynamics.
They introduce a useful trilogy of conceptual change;
i) differentiation, wherein new concepts emerge from more general
concepts (velocity and acceleration from motion)
ii) class extension, wherein existing concepts thought to be different
are found to be subsumed under a more general concept (rest and constant velocity are both
uniform motion
iii) reconceptualization, wherein a significant change in the nature and
relationship between concepts occurs (force implies motion to force implies
acceleration)..
They provide details and examples of the three types and especially the third. For
instance, they outline the POE (predict, observe, explain) and stress the collaborative
nature of the construction and testing of adequate scientific explanations. They stress
the Socratic nature of learning (in group or class discussion), the teacher’s role is
clearly "an example of leading, even (supplying) provocative questions and
situations, but the development of the ideas and the convincing of the class we try to
leave to the class."
The research is really the reflections and observations of a group of physics students
as they learn about force and Newton’s laws. They do not test any hypothesis
(although they cite many studies) since they are trying to develop a tool for assessing
conceptions and for fostering conceptual change. They distinguish conceptual schemes or
conceptions (force implies motion) from concepts (force) to aid in the construction and
analysis of conceptual maps. The nodes are the concepts and the links form the conception.
They also point out the ontological and structural characteristics of those maps. It is
not just that the student mistakenly thinks motion requires force, but they categorize
force (in some contexts) as an attribute of an object, instead of a result of an interaction
between two objects. More detailed analyses of concept maps can be found in the
literature (Halloun, 1997, Roth et al., 1992) but this paper merely attempted to provide a
framework for such maps within pedagogy. Their taxonomy of conceptual change is offered as
a starting point for further investigation and refinement of teaching methods. Further
research is required to see just how effectively these tools inform teaching and improve
learning.
Interactive-engagement methods in introductory mechanics courses5
Richard Hake is a physicist at Indiana University who has turned his research to
physics and education instruction and learning. He was stunned by the failure of his
traditional "TRAnsmission to Passive Target (TRAPT)" method of
physics instruction; his "brilliant lectures and thrilling demonstrations passed
through the minds of (of his students) leaving no measurable trace." Hake’s
survey of over 6000 students revealed that Interactive Engagement (IE) methods including
Socratic Dialogue Inducing labs (SDI) increased the mechanics course effectiveness in both
conceptual understanding and problem-solving when compared to traditional instruction.
Courses used IE methods such as collaborative peer instruction, computer-based labs,
concept tests, problem based learning units, SDI labs all shared common elements. They
were student centered, involved much dialogue and oral and written explanation on a
qualitative level as well as quantitative, and open-ended. Traditional instruction
included lectures (to passive students), recipe labs (not open-ended), and
algorithmic-problem exams (no conceptual questions). Incidentally, I learned physics in
the traditional manner quite successfully by actively engaging myself with my TA,
professor or fellow student when I perceived the need. Could IE have improved my
performance even more? Or would it have made a difference in my abysmal result in Year II
Statistics? I’d like to think so.
The IE methods produced significant gains (g=%Gain/%Gainmax) measured by
three different tests (Halloun-Hestenes Mechanics Diagnostic, Force Concept Inventory,
Hestenes-Wells Mechanics Baseline test of problem solving ability). The results were
consistent for an individual instructor (before and after implementing IE) and among
instructors (some preferred not to implement IE). Instructors not utilizing IE were often
highly rated by both faculty and students so the results do not merely show the effective
of "good" instructors or those willing to change.
A lengthy discussion and case studies show the diversity of what IE actually is. Due to
the multivariate nature of IE the separate elements of IE could not be reliably compared;
often one school implemented some of the possible 6 or 7 methods described by Hake.
Nonetheless, the gains are statistically significant and the anecdotal evidence is equally
compelling. One could not really evaluate the extent of IE being utilized in any
quantifiable and reliable manner. Some of the lower IE courses could have been compromised
by implementation problems (see Reif at http://cil-andrew.cmv.edu). For instance, if they
are told "in lectures that all that really counts is solving Halliday/Resnick
problems, I think they sometimes just go through the motions" in some of the IE
processes. Similarly, some the high achieving Traditional classes could have been due to
instructors who implicitly engaged interaction in their lectures, tutorials or other
structures within the physics course.
This last point reveals the flexible nature of IE. Lectures or assigned text readings
are compatible with actively involving the learner in constructing a useful scientific
framework. For instance, lectures could involve voting on different options, peer
discussion, class debate and other methods to facilitate a constructive process within the
learner. School culture could also help or hinder the same necessary processes. The
strength of Hake’s review involves the large data set and numerous case studies and
anecdotes from instructors and students. He also points to many web resources so that the
IE methods can be disseminated, refined, and researched. I can’t agree more that
teachers who listen more, and talk less (but effectively) will enable their students to
authentically learn science from well-thought out experiences and methods. From my
experience they will also have a lot more fun and will actually learn something as well.
Ironically, these keys seem appropriate to a lot more than learning science (convergence).
In conclusion, these papers cover significant ground for improving educational
practices within high school science. Once you are comfortable teaching the content it is
time to teach the person. These papers will help.
Selected Bibliography
Dekkers, P. J. J. M. & Thijs, G. D. (1998) Making Productive Use of Students’ Initial
Conceptions in Developing the Concept of Force, Science Education, 82(1),
31-51.
Dykstra, D. I., Boyle, C. F., & Monarch, I. A. (1992) Studying Conceptual Change in Learning Physics, Science
Education, 82(6), 615-652.
Finegold, M. & Gorsky, P. (1991) Students’ concepts of force as applied to
related physical systems: A search for consistency,
Int. J. Sci. Educ., 13(1), 97-113.
Hake, R. R. (1998) Interactive-engagement
methods in introductory mechanics courses, Journal of Physics Education Research, or
from http://carini.physics.indiana.edu.
Halloun, Ibrahim. (1998) Schematic Concepts for Schematic Models of the Real World: The
Newtonian Concept of Force, Science Education, 82, 239-263.
Osborne, R. (1984) Children’s Dynamics, The
Physics Teacher, November 504-508
Roth, W. M. & Roychoudhury, A. (1992) The Social Construction of Scientific
Concepts or the Concept Map as Conscription Device and Tool for Social Thinking in High
School Science, Science Education, 76(5), 531-557.
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