Student resources for learning introductory
Physics and Curriculum &
University of Maryland at College
College Park, MD
Hammer, D. (2000). Student resources for learning introductory physics.
American Journal of Physics, Physics Education Research Supplement, 68
AbstractWith good reason,
physics education research has focussed almost exclusively on student
difficulties and misconceptions. This work has been productive for curriculum
development as well as in motivating the physics teaching community to examine
and reconsider methods and assumptions, but it is limited in what it can tell us
about student knowledge and learning. This article reviews perspectives on
student resources for learning, with an emphasis on the practical benefits to be
gained for instruction.
IntroductionBy and large,
physics education research has been dominated by studies of student
misconceptions and difficulties. The former are more specifically defined as
stable cognitive structures; the latter notion is theoretically non-committal;
but both are concerned with understanding aspects of students' knowledge and
reasoning that that present obstacles to learning.
Without question, this
work has been and continues to be productive, for curriculum development as well
as for motivating the physics teaching community to examine and reconsider
conventional methods of instruction. Nevertheless, as views of student knowledge
and reasoning, misconceptions and difficulties are limited in two important
respects. First, they provide no account of productive resources students have
for advancing in their understanding. Second, descriptions of student
difficulties provide no analysis of underlying mechanism, while the perspective
of misconceptions cannot explain the contextual sensitivities of student
reasoning1, 2, such as the empirical fact that substantively
equivalent questions, posed in different ways, can evoke different responses
from the same student.3
purpose in this article is to review current ideas for thinking about students
in terms of the resourcesthey bring to learning. In this description I will
emphasize how these resources can be productive, but this view of resources is
not complementary to that of difficulties. Rather, an account of student
resources should provide theoretical underpinnings to understanding difficulties
I begin in this introduction with
a rough description of the general notion of a resource. Then I discuss
"conceptual resources" students bring to understanding physical phenomena and
concepts, emphasizing how an understanding of these resources may be of direct,
practical benefit for instruction. I then present some initial ideas about
"epistemological resources" students have for understanding knowledge and
learning, again emphasizing instructional utility.
The rough ideaPresented
with a sufficiently unfamiliar problem, physicists generally begin by searching
their knowledge and experience, trying out different ways of
thinking.4 As an example, consider
Suppose you place a box in a stream of water, and suppose the
temperature of the water is 20 °C. If the temperature of the box is less than
20 °C, then the effect of water flowing over the box will be to raise its
temperature; if the temperature of the box is greater than 20 °C, then the
effect of the water flowing will be to reduce its temperature. Of course,
there may be other factors as well: The box may have an internal source of
energy; it may be in thermal contact with the air or with the ground, either
of which could have a different temperature. Still, if the box is warmer than
20 °C the water cools it, and if the box is cooler than 20 °C the water warms
you have not seen this question before it may be useful to pause and work on it
a little before reading on, to conduct an informal case-study of your own
Now suppose you place the box in a "stream" of sunlight, and here is the
question: What is the corresponding temperature of the box, if there is one,
such that if the box is cooler than that temperature the effect of the
sunlight is to warm it, and if the box is warmer than that temperature the
effect of the sunlight is to cool it (more rapidly, that is, than the box
would cool in the absence of sunlight)?
The question invites
you to compare a stream of sunlight to a stream of water. Applying that analogy
brings the idea that the "break-even" temperature is the temperature of the
sunlight. Readers of this journal have a variety of relevant resources. Perhaps
you know this temperature offhand; perhaps you will apply your knowledge of
blackbody spectra and your knowledge that the light from the sun looks
But there are other
ways you could think about the problem. Rather than think of the sunlight as a
material flowing over and past the box (like water), you may think of it as a
form of energy the box absorbs. Among the resources you would apply in this way
of thinking is one for understanding an accumulation, in this case an
accumulation of energy in the box. If you apply this way of thinking, you may
conclude that the incident sunlight can only add to the energy of the box, and
thus the effect of the sunlight would always be to increase the temperature of
the box (or to decrease the rate of cooling).
Both of these ways of
thinking consider the sunlight acting on the box. Of course, the
box can emit light as well as absorb it; like the sun the box's emissions depend
on its temperature. Thinking of an equilibrium between absorption and emission
of light makes it difficult to think of the stream of sunlight as analogous to
the stream of water, as the question suggested. It may be useful to stop
thinking about the sunlight as the other object in the interaction, and to think
of the sun as the other object, that is to think of the sun and the box
as acting on each other, through light.
What I am describing
are a variety of ways of thinking about the question. If you paused to think
about the problem, it is not unlikely you came up with some I have not
mentioned. The important point here is that, as a physicist, you have developed
a range of resources for thinking about physical situations. Given a familiar
problem, you already know which of these resources to apply, and you do so
efficiently. Given an unfamiliar problem, you need to search through your
resources, perhaps trying several of them out before you arrive at those you
find to be useful. Often, as may happen with this problem, you have active at
the same time multiple ways of thinking about a problem that conflict with each
other, and much of the work you need to do is to reconcile that conflict. Here,
the "sunlight can only add energy" reasoning conflicts with the "thermal
equilibrium" reasoning; reconciling that conflict entails finding a flaw in one
or the other line of reasoning.
Sometimes you make a
mistake in applying a resource, by supposing it is useful for solving a problem
in a way that it turns out not to be. But that does not mean the resource itself
is invalid, as this problem illustrates. The notion of equilibrium, for example,
is a powerful and important resource, but it does not turn out to be useful for
thinking about the box in sunlight in the way it is for thinking about the box
in water. To apply that resource, it would be necessary to think of the box as
in constant thermal contact with the electromagnetic field, but their
interaction is very far from equilibrium.
A computational metaphorThis
use of the word "resource" derives loosely from the notion of a resource in
computer science, a chunk of computer code that can be incorporated into
programs to perform some function. Programmers virtually never write their
programs from scratch. Rather, they draw on a rich store of routines and
subroutines, procedures of various sizes and functions. Depending on their
specialization, different computer programmers would have assembled for
themselves different sets of procedures. Those who specialize in graphics have
procedures for translating and rotating images, for example, which they use and
reuse in a variety of circumstances. And, often, a programmer will try to use a
procedure in a way that turns out to be ineffective.
This metaphor of the
mind as a computer?and certainly for some it is more than a metaphor?has been
developed explicitly by researchers in artificial intelligence. The essential
point here is that mental phenomena are attributed to the action of many
"agents"5 acting in parallel, sometimes coherently and sometimes not,
rather than as resulting from the action or properties of a single entity.
Thinking about the sunlight problem, for example, activates many resources at
once; much of the challenge is to bring these activations into coherence. This
differs from the notion of a "misconception," according to which a student's
incorrect reasoning results from a single cognitive unit, namely the
"conception," which is either consistent or inconsistent with expert
instructors have at least a tacit sense of student resources. In fact, much of
naïve instructional practice is characterized by inappropriate presumptions
regarding the resources students have available. The emphasis in the physics
education research literature on difficulties and misconceptions is largely by
design, to address and debunk these presumptions. It is now abundantly clear
that students do not have well-formed, prerequisite conceptions, such as of
"mass," "air," "force," and "velocity," as instructors often unknowingly assume.
Nor, as it has become trite to admonish, are students "blank slates" on which
instructors can inscribe correct ideas. To the contrary, students have a great
deal of knowledge about the physical world formed from their everyday
experience, and physics instructors are prone to underestimate the extent to
which that knowledge differs, in substance and structure, from what they hope to
However, that students
lack productive resources in the form naïve instructors presume does not mean
that they lack productive resources entirely. There is broad consensus among
physics education researchers that students' "construct" new knowledge from
prior knowledge; this obviously implies that students have in their prior
knowledge the raw material for that construction. Nevertheless, in its emphasis
on difficulties and misconceptions, physics education research has mostly
overlooked the task of studying and describing this raw material.
It is to the
interest both of progressing toward a theory of physics learning and of
designing and implementing effective instruction that physics education
researchers come to understand the resources students bring to learning
introductory physics. Because effective instructors already have a rich, tacit
sense of these resources, there is much to be gained from mining for insights
embedded in their practices. In this section, I will discuss some instructional
practices that are tied to insights into student conceptual resources.
Anchoring conceptions and bridging analogiesClement, Brown & Zeitsman6 highlighted the
existence of productive resources in students' understanding, noting that "not
all preconceptions are misconceptions." They described "anchoring conceptions"
in which student understanding typically aligns well with physicists' and how
these may serve as targets of "bridging analogies" to help students apply that
understanding in other contexts.
strategy for helping students understand the Newtonian idea of a passive
force, such as the force exerted upward by a table on a book is a core
example. Students generally have difficulty with the idea that the table can
exert a force. Asked, for example, to draw a free-body diagram for the book,
students often draw a downward gravitational force but omit the upward contact
force exerted by the table. Many explicitly contend that a table cannot exert a
force, but rather, "gets in the way" or "blocks" the book from falling. In other
words, students have difficulty understanding the table as having a causal role
in the interaction, because the table seems to be an inherently passive object:
How can a table "exert"?
Students do not,
however, typically have that difficulty when thinking about a spring. They
readily see a compressed spring as "exerting" force against its compression;
they can "see" it pushing. Minstrell's7 strategy uses students'
understanding of springs as a productive resource, the anchoring
conception6 from which to build an understanding of passive forces.
Specifically, he uses a series of bridging analogies6 to help
students learn to see a table as an extremely stiff spring.
In sum, students have
resources for thinking about springs that, if activated, are productive for
their developing a Newtonian understanding of passive forces. An instructor such
as Minstrell who is aware of these resources can design instruction to help
bring about that activation.
Refining "raw intuitions"Elby8 describes another instructional strategy that
illustrates a resources-based view of student knowledge. The context for this
example is a lesson on Newton's 3rd law. As part of the lesson, Elby
posed to students the following question:
A truck rams into a parked car, which has half the mass of the
truck. Intuitively, which is larger during the collision: the force exerted by
the truck on the car, or the force exerted by the car on the truck? That most students responded that the truck exerts a larger
force on the car than the car exerts on the truck is not surprising; this is a
commonly recognized "misconception."Elby
then posed them another question:
Suppose the truck has mass 1000 kg and the car has mass 500 kg.
During the collision, suppose the truck loses 5 m/s of speed. Keeping in mind
that the car is half as heavy as the truck, how much speed does the car gain
during the collision? Visualize the situation, and trust your
instinctsThis time, most of the students
answered correctly; and by working through follow-up questions, they came to the
conclusion that their "instincts" agree with Newton's 3rd law. Elby
identified students' correct answer to this question as reflecting their "raw
intuition" that "the car reacts twice as much during the collision," and he lead
them to the idea that they could "refine" this raw intuition in one of (at
least) two ways. Figure 1 depicts the diagram Elby drew on the blackboard during
this discussion, to show the two options for refining the raw intuition and the
implications of each refinement.
Figure 1: From Elby8 Elby identified the
notion that "the car reacts twice as much" as a resource from which students
could build their understanding. Depending on how they used this resource, how
in Elby's terms they "refined" it, the idea could contribute to a Newtonian
understanding or it could pose a difficulty for that understanding. In this way,
what Elby loosely characterized as a "raw intuition" provided the raw material
for students in building their understanding. Like a subroutine for a
programmer, the intuition itself is neither correct nor incorrect; it becomes
correct or incorrect in its use.
What this meant in
class for Elby was an instructional strategy explicitly designed to help
students refine their intuition toward a coherent understanding. He guided them
to see the consequences of the two alternatives: If they apply their "car reacts
twice as much" intuition to the concept of force, their reasoning leads to a
contradiction with Newton's Third Law; if they apply it to the concept of
acceleration, their reasoning is consistent with Newton's Laws.
In this way, a
resources-based account of student knowledge and reasoning does not disregard
difficulties or phenomena associated with misconceptions. Rather, on this view,
a difficulty represents a tendency to misapply resources, and misconceptions
represent robust patterns of misapplication.
A similar view of
student knowledge motivated Minstrell to coin the term "facet"; Elby's raw
intuition here would constitute a facet of student understanding that students
could apply productively or counter-productively. Understanding the students in
this way, the task for instruction becomes helping students "unravel" and
"reweave" the strands of their knowledge and understanding, in Minstrell's
metaphor,10 rather than removing or replacing conceptions.
Toward a more precise model of conceptual
resourcesThese are not technical terms:
Minstrell and Elby chose "facet" and "raw intuition" largely for pedagogical and
practical reasons, to make the general notion accessible to a broad audience,
including secondary students. This general level of description is useful, but
developing a model of physics knowledge and learning will eventually require
more precise ideas and terminology.
has pursued a technically more precise model, beginning with his account of
"phenomenological primitives," or "p-prims," as one form of cognitive structure.
To return for a moment to the computational metaphor, a programmer writes
routines from subroutines, and subroutines from smaller subroutines, and so on.
At the lowest level of this progression are the "primitives" of the given
computer language (e.g. Fortran), the smallest units of code. Similarly, a
"primitive" resource would be the smallest chunk of cognitive structure.
diSessa11 conjectures p-prims as one form of primitive cognitive
For example, asked to
explain why it is hotter in the summer than in the winter, many students will
respond that it is because the earth is closer to the sun.12 The
usual interpretation attributes this response to a faulty conception students
have formed, by which the earth moves in a highly eccentric ellipse around the
sun, and in some cases this may be the case. An alternative interpretation,
however, is that some students do not have this previous conception regarding
the cause of the seasons but generate it on the spot. Asked the question, they
conduct a quick search in their knowledge and reasoning for a way to think about
it. One of the first resources they identify is the general notion that getting
closer to a source increases the intensity of its effect: Closer means
As a p-prim, Closer
means stronger is a resource productively activated to understand a number
of phenomena: The light is more intense closer to the bulb; music is louder
closer to the speaker; an odor is more intense closer to its source. Students'
tendency to explain seasons in terms of proximity to the sun may be seen as a
faulty activation of this resource, rather than as reflecting a faulty,
previously existing conception.
account affords a more fine-grained analysis of Clement and Minstrell's bridging
analogy. The situation of the book on the table tends to activate a primitive
Blocking: The table blocks the book from falling. As a primitive element
of student reasoning, Blocking needs no explanation, and its activation
in this context represents a difficulty. Meanwhile, springs tend to activate
Springiness, a primitive notion of a restoring agency acting in response
to a deformation. The bridging analogy helps to activate Springiness to
the situation of the book on the table; that activation can be reinforced by a
demonstration to show the table's deformation.7 Springiness
would cue other primitives as well, including Maintaining Agency, by
which the students understand the deformation of the table as causing and
maintaining an upward force on the book, and Balancing by which students
see an equilibrium between the weight of the book downward and the upward force
by the table. As important, these activations would tend to deactivate
Blocking, and students have arrived at a new understanding of the book on
the table. (The account predicts that as they become robust in their new
understanding, students should have difficulty remembering what it was they had
been thinking earlier: With Blocking deactivated, they would not have
access to the sense it had provided of the situation.)
In sum, on diSessa's
view, the function of an anchoring conception is to activate productive
resources, and the function of a bridging analogy is to carry those activations
back to the problem at hand. Of course, this account of p-prims activations is
conjectural. I present it to illustrate the possibilities in a resource-based
account. Brown13 discussed this role of analogies as "refocusing core
intuitions," with p-prims a model of a core intuition. In principle, this model
of primitives activations could be developed and tested computationally, with
p-prims at nodes of a connectionist system.Similarly, one could depict the raw
intuition in Elby's example as a set of p-prims. The different posings of the
question activate the same set of primitives but apply them differently. The
details of that account are not important here, and they would again be
conjectural, so I leave them as an exercise to the reader.
Instructional designElby's8 example illustrates an advantage for
instruction of having insight into student resources: Instruction can be
designed to help students use their resources more productively. Here I discuss
two other examples to illustrate how that design may be sensitive to details of
analysis of student reasoning about waves suggests that many of their
difficulties arise from their misapplying resources for thinking about objects.
Their behavior fits diSessa's and Sherin's15 account of object
as a "coordination class," another form of cognitive structure, a coherent set
of associations and strategies, which they developed again toward technical
precision for thinking about what may constitute one form of "concept." The
coordination class of object, for example, consists of particular
expectations and strategies for reasoning and obtaining information. That is, to
think about X as an object is to expect it to have properties of form,
location, permanence, mass (in an intuitive sense), and velocity; and it is to
expect that one can find out about X through various strategies, such as by
looking for it (if it is within sight), touching it (if within reach), hefting
it, and so on.
That resource, however,
is not productively applied to waves, and a number of difficulties arise.
Students expect, for example, that the impact of a sound wave will propel a dust
particle across the room, or that "flicking your hand harder" will cause a wave
pulse to move more quickly down a string. The insight that these difficulties
originate in students thinking of waves as objects is useful in designing
a tutorial: Exercises in the tutorial can specifically highlight differences
between the behavior of waves and the behavior of objects, to help
students stop thinking in this way.
Still, this insight
raises the question: What resources do students have in their prior knowledge
that are productive for thinking about waves? Staying within diSessa's and
Sherin's framework, if student difficulties arise from their coordinating their
expectations and strategies by the class of object , what other
coordination class would be a productive starting point from which to develop a
One possible answer,
worth exploration, is the coordination class of "event." To think about X as an
event16 is to expect it to have a location, a time of
occurrence, a duration, and a cause; and it is to expect that one can find about
X by looking for it (at the moment it is occurring). But one does not think of
touching or hefting an event, strategies appropriate for objects.
This may be a productive coordination class to bring to bear on reasoning about
waves, and if so it would be useful to design a tutorial to help students think
of waves as events rather than objects. Thus a tutorial might
include a comparison to a series of dominoes toppling, a succession of
events, one causing the next, propagating through space.
provided another example, similar to Wittmann's, of a difficulty arising from
the application of an otherwise useful resource. Rosenberg spoke of a "Principle
of Exclusivity" as a generally useful resource for thinking about values: A
quantity can hold only one value at any time. This resource is applicable, for
example, for constructing an understanding of the mathematical concept of a
function. An object can be in only one location at a time; thus its location can
be written as a function of time. Student difficulties in quantum mechanics,
Rosenberg conjectures, arise in part from their applying the Principle of
Exclusivity to their thinking about values, including location, to quantum
objects such as electrons.Here is an example in which a more precise
understanding of the nature of the resource could have dramatic implications for
instruction.18 If, for example, this resource is a p-prim, then its
activation is highly sensitive to context, and it should be possible to
deactivate through manipulations of contexts, such as through bridging analogies
or confrontation. Another possibility is that this resource, when it is fully
described, will be another form of cognitive structure, more distributed and
constitutional than a p-prim (more like a property of the operating system than
like a chunk of code), and if this is the case "deactivation" may not be an
Instructors' tacit knowledgeOf
course, teachers and curriculum developers are guided by their sense of what
students know that may contribute to their learning. As a prominent example,
Hewitt's text19 is rich in common sense explanations of physics
concepts. Embedded in these explanations are insights into what students know
that may be productively applied to their learning. For example, his strategy of
writing equations with exaggerated or diminished symbols, such as in Figure 2,
is motivated by a sense of students' productive intuitions for balancing. There
are many examples to be found in current instructional texts.20, 21,
the physics education research community has devoted substantial attention to
studying the nature of student difficulties, it has paid little attention to
documenting and systematizing extant ideas about student resources. Without that
attention, this knowledge remains mostly tacit and unexamined. I am arguing that
it should become a primary agenda of the physics education research community to
develop explicit accounts of student resources, to allow their exchange, review,
Figure 2: Hewitt-style depiction of how
the impulse of a large force over a small time can equal that of a small
force over a large
If, for example,
students' intuitive sense of balancing is well described as a p-prim in
diSessa's framework, then its activation may be temporary for many students
reading Hewitt's textbook: The figure may be effective at cueing the p-prim, and
students will have a sense of understanding; later, in another context, the
p-prim may no longer be activated and students would no longer have access to
the sense they experienced looking at the figure. How instructors appeal to
student resources, and what they expect will result, depends critically on how
they understand the nature of those resources.
This is relevant not
only to curriculum development but also to how teachers interact with students
in specific moments of learning and instruction. In earlier work1,
23, I compared the perspectives of misconceptions and p-prims with respect
to how they may influence what an instructor perceives in student knowledge and
reasoning. Instructors who expect productive resources will be inclined to look
for those resources in their students' reasoning, engaging them in ways that are
not limited to confrontation,24 and, like Minstrell, Elby, and
Hewitt, helping students find and build from those resources. Again, it is
essential to articulate, examine, and refine instructors' sense of student
resources, because the details of this understanding may have significant
consequences in how instructors attend and respond to student thinking.
Epistemological resourcesPhysics education research has traditionally focussed on student
conceptual understanding. In recent years, however, some researchers have paid
significant attention to student epistemologies, including the development of
three different instruments25, 26, 27, all designed to assess what
students believe about knowledge and learning in introductory physics. Some
physics students, for example, may believe learning consists of memorizing facts
and formulas provided by the teacher, while others may believe it entails
applying and modifying their own understandings.28 For teachers,
awareness of these beliefs provides an alternate perspective into students?
behavior.29 Rather than see students as lacking in common sense,
e.g., a teacher could see them as believing common sense is irrelevant to
The study of
epistemologies has generally emulated the study of conceptual understanding in
presuming essentially unitary structures, "beliefs," as components of
essentially stable epistemologies.30 Construed in this way,
epistemological beliefs are analogous to the concepts posited as elements of
cognitive structure, and research on epistemologies has mostly focused on
students' "misbeliefs" about physics and physics learning (e.g. that learning
consists of memorizing) that differ from expert beliefs. Like misconceptions,
these misbeliefs could not be understood to contribute to productive
beginning to develop an account of context-dependent epistemological resources,
at a finer grain-size than "beliefs." Like conceptual resources, these
epistemological resources are activated in some contexts but not others, and are
productive in some contexts but not others. For example, many students appear to
view scientific knowledge as coming from authority. At the same time, it is
clear even small children have epistemological resources for understanding
knowledge as invented ("How do you know your doll's name is Ann?" "I made it
up!") or knowledge as inferred ("How do you know I have a present for you?"
"Because I saw you hide something under your coat!").
To appreciate the role
of these resources in physics reasoning, consider again the question of the box
in the sunlight. Discussing it above, I focused on various sorts of conceptual
resources physicists might apply. But that reasoning involves other sorts of
resources as well, including some developed for the tasks of managing the
These resources might
entail a sense of knowledge as connected and constructable (and
reconstructable): You expect that the answer to this question can be constructed
using knowledge you already have in place. In other contexts, such as answering
the question "What is the capital of Lithuania?," you may do better to activate
resources for thinking of knowledge as factual and communicable. That is, rather
than choose to search within your own knowledge and experience you would choose
to search for that information from documents or other experts.
Having chosen to
conduct a search within your own knowledge and experience, you have further
resources for evaluating the results of that search. You know, for example, not
necessarily to trust the first idea you find; you know to compare different ways
of thinking with each other; you know to monitor for coherence in your
understanding and to address inconsistencies when you find them. For example,
you may have quickly decided that the sunlight can only add energy to the box,
and from there spent most of your time trying to identify specifically why it
does not work to reason in terms of equilibrium. In other contexts, such as in
deciding what to have for dinner, once you decide on an answer you would stop
thinking about the question; it would be odd to spend time trying to identify
specifically what would be wrong with choosing lasagna, e.g., once you had
chosen grilled salmon. For some students, the two situations may activate the
same epistemological resources, and they may consider it odd to continue
thinking about a physics problem once they have chosen an answer.
learning physics thus involves learning when to activate which epistemological
resources. To help with this, instructors need understanding of these resources,
but there has been very little research. In developing our account, we are
drawing insights from Minsky,5 whose agents include a number
concerned with epistemology, as well as from Collins and Ferguson31,
who described various "epistemic forms" (e.g. lists, stories, rules) and
"epistemic games" (e.g. listing, categorizing, guessing) as everyday
We are also, as I
suggested above, mining for insights embedded in instructional practices.
Reasoning in terms of students' epistemological resources provides a new
interpretation of existing strategies and may guide the implementation and
refinement of those strategies. Here I sketch several examples of relevant
Modifying the instructional contextOn this view of student epistemologies, difficulties generally
attributed to stable beliefs may also be understood in terms of
counter-productive resource activations. Rather than think in terms of
confronting misbeliefs, an instructor could think in terms of modifying the
resources students activate. A core difference between conventional and reformed
physics instruction may be in the epistemological resources the different
instructional contexts tend to activate.
Encouraging debates in
science class for example, certainly not a new practice, may be understood as a
means of helping students activate a set of epistemological resources they have
available for understanding argumentation and differing points-of-view. The
class may become a context in which students understand it as important to
explore a variety of perspectives, as opposed to looking for the "one right way"
of thinking about the issue at hand. These are resources they activate (or
should!) in the contexts of debates about, e.g. politics and history, and they
may be productively activated in physics as well.
Much of the benefit of
innovative pedagogical approaches can be understood in these terms: They change
the context in such a way as to invoke productive epistemological resources.
Another example is engaging students in activities of design and construction,
such as building gadgets or writing computer programs that accomplish some task.
Students have resources for understanding these sorts of activities, of what it
means to make something, try it, and adjust it to improve
performance.32 That understanding may also be used to activate
resources productive for learning.
Hestenes and his
colleagues design instruction around the core notion of modeling and "modeling
games",33 an approach that may be understood in terms of activating
epistemological resources for understanding physics knowledge and reasoning in
terms of the formation and application of models, rather than in terms of facts
and procedures for solving problems. Similar resources may be promoted by
instruction designed around the core activity of computer programming. The task,
for example, of writing a computer program to model a Newtonian object, should
activate epistemological resources for understanding knowledge as constructed,
represented formally (as a program), and as an approximation of
general notion of epistemological resources suggests the strategy of looking for
"epistemological anchors" in students' understandings of familiar situations and
activities, an epistemological version of Clement, Brown, and
Zeitsman's6 notion of anchoring conceptions. Again, rather than
understand student epistemologies only in terms of counter-productive misbeliefs
to be exposed and confronted, a teacher may understand students as having
productive epistemological resources they naturally invoke in other contexts.
These anchors may serve as targets for epistemological metaphors or bridging
For a familiar example,
many instructors compare mental exertion to physical exertion, to help students
think of knowledge and ability as developed through effort. In that case, the
context of physical exercise serves as the epistemological anchor, a context in
which students naturally associate effort and persistence with
Elby's "refining raw
intuition" lesson8 provides another example. Elby developed his
strategy specifically toward an epistemological agenda of helping his students
to understand learning as "the refinement of everyday thinking."9
This, again, is a means of activating a different set of epistemological
resources than students would typically invoke in physics, to help them think in
terms of modifying what they already know rather than solely in terms of
receiving new information. By casting the activity of learning as the
"refinement" of "raw intuition," Elby was essentially invoking a metaphor for
learning physics as the refinement of pre-existing material, as opposed to a
replacement of "bad" material by "good" material.
The following is
another example, drawn from a discussion in an introductory physics course. It
is a bridging analogy to interpersonal relationships, designed to promote
metacognitive reflection in physics students:
"Imagine you have met a new person and he irritates you for some
reason you can't put your finger on. So you think about it, trying to figure
out what it is about him that bugs you, and eventually you realize that it's
because he looks and sounds a bit like a character in a movie you saw
recently. Having figured that out, you know that it's not really this new guy
who irritates you, but that movie character, and you don't have to worry about
it any more. In another instance, you may realize that you've met him before
and had an unpleasant interaction, in which case there's good reason for that
feeling of irritation. In this case, the everyday reasoning activity of trying to figure
out why a new person seems familiar serves as an epistemological anchor to help
students understand the phenomenon of having a physical intuition, to motivate a
similar introspection to find its source.
to do something like this in learning physics. Very often you'll have a sense
that a ball or some other object ought to move in a certain way, but you'll
have trouble putting your finger on why you have that sense. Sometimes when
you identify it you'll realize you're using an intuition that doesn't apply in
this case, and you don't have to worry about it; sometimes you'll find you
have an experience that's relevant and useful. In either case, it's important
to try to figure out where these ideas come from."
Other targets of
epistemological analogies could include the activity of figuring out the best
way to arrange the furniture in the living room, to activate resources for
thinking of ideas as logically connected ("If I put the couch on the east wall,
the bookcase won't fit anywhere but next to the window"), and the activity of
giving directions to a traveler, to help activate resources for understanding
the importance of precision.
Closing thoughts: The benefits of "messing
and with good reasons, physics education research has focussed almost
exclusively on student difficulties and misconceptions. I have written this
article to help motivate a shift toward the study of resources, toward better
comprehension of (1) the productive aspects of student knowledge and
reasoning, the raw material from which they may construct a physicist's
understanding, and (2) the underlying dynamics of the difficulties and
misconceptions students often have in that construction.
At this point, there
are only early ideas for how to understand and model these resources, what forms
they may take in the minds of students (and of physicists). Still, I hope to
have illustrated that even these early ideas can be useful in instruction and
that there are clear benefits to be gained from more refined understanding. With
respect to conceptual resources, there are promising directions for that
refinement. Physics education research needs to begin to make progress with
respect to other resources as well, including epistemological resources.
the instructional relevance of developing a view of student resources, I have
focused in this article on the advantages of having a sense of the resources
students have in place: Instructors who expect productive resources will be
inclined to look for them in their students' reasoning, and, as important, to
help students look for them themselves. These strategies presume that students'
resources are mostly in place, a presumption that is probably generally valid
for older students, although there may be some important exceptions.
general view of resources also requires an account of how students, mostly as
children, construct these resources in the first place. This topic, of course,
has long been the domain of research on cognitive development in early
childhood, wherein scholars have often advocated approaches to instruction along
the lines of what David Hawkins's famously called "messing about in
science."35 A resources-based view of student knowledge and reasoning
would support their arguments.
In particular, such a
view suggests two distinct needs, for the development of a scientific
understanding: (1) the formation of intellectual resources, and (2) the
(re)organization and application of these resources to align with scientific
knowledge and practices. On the view I have summarized in this article, high
school and college students learning introductory physics should mostly be seen
as addressing the second need. It is possible that early science education
should mostly be seen as addressing the first. That is, in whatever form they
may appear, children must develop resources, such as Closer means
stronger or Springiness or the "raw intuition" Elby described, before
they can refine their application toward a physicist's understanding.
children mostly form these resources prior to their correct alignment with
physics concepts. It is at least possible that this priority is necessary.
In other words, a resources-based view of knowledge suggests that students are
not ready to understand a concept until they have developed resources from which
to construct it. Of course, many of these conceptual resources, including
Closer means stronger and Springiness, are likely to develop in
early childhood independent of schooling. Other resources, such as the notion of
equilibrium, may not develop fully prior to schooling. Perhaps more at risk,
however, are the epistemological resources necessary for finding, applying, and
modifying these conceptual resources.
For example, visiting
an elementary class recently, I showed a standard demonstration in which I
sprinkled black pepper over a pan of water and then touched the surface with a
toothpick I had dipped in soap. The students saw the pepper recede quickly from
where I had touched, and I asked them to write out their explanations of what
was happening. Some of the students thought of the phenomenon in terms of the
soap was pushing the pepper away, as it expanded into the space the soap was
taking up. Others knew it had something to do with "surface tension"?they had
earlier seen phenomena with soap and surface tension?but they could not be more
specific. Of course, the latter were more correct: The soap weakens the surface
tension, and the pepper is pulled by the un-soapy water surrounding where
I touched. But I contend that the former students were closer to scientific
thinking, because their explanation was comprised of a tangible mechanism rather
than a phrase they did not understand.
Here, then, is a reason
for students' early education in science to consist largely (and perhaps
primarily) of "messing about"35: It is in this way they can best
develop the resources they will need later. Messing about, in hands-on
activities or in playful, student-controlled conversations36 may be
more productive than experiences crafted to guide students toward correct
understandings of the concepts.
In fact, efforts to
promote students' correct understanding at this early stage, and in particular
their correct use of terminology, may be counter-productive, impeding children's
construction and application of productive resources. One common liability is
that they come to see science learning in terms of remembering "magic
words"37 rather than, e.g., of applying and developing their sense of
mechanism. That students typically arrive at introductory physics with
counter-productive beliefs and expectations about physics and physics
instruction26 can be directly traced to their prior experiences in
A piece of this
argument deserves particular emphasis: For students new to scientific thinking,
"wrong" thinking should be seen as productive if it helps develop resources for
later "right" thinking. To be sure, there have been many examples in the history
of science, of resources having been developed, failing in their original
purpose, but proving to be productive later when used in other ways. It was
Aristotle who first argued that an object cannot exert a force on itself; the
Lorentz transformations were first developed for the ether theory; mathematical
tools for understanding knots, developed in the 1800s as an early and
unsuccessful particle theory, are now useful in non-linear
dynamics.38 By analogy, students may develop productive resource
through "wrong" thinking, especially in early grades. Children who argue that
objects sink or float depending on their weight are incorrect, but in that
incorrect thinking they are almost certainly applying and developing resources
they will be able to use in different ways later.
This is certainly not
to suggest that "messing about" is the entirety of science learning; but it is
very much to suggest that messing about may play an essential early role, and
that educators ignore this role at their students' peril. Learning science
cannot end with "messing about," but it may need to begin there, just as
learning to draw must begin with scribbling: To insist from the beginning that
children's drawings be "correct" (bear a good resemblance to what they say they
are drawing) would be to prevent them from learning to draw. For similar
reasons, science education may need not only to tolerate but to encourage the
equivalent of scribbling in early learning.
AcknowledgementsI am grateful
to Andy Elby, Joe Redish, and two anonymous reviewers for numerous comments and
suggestions, both substantive and editorial.
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38I thank Rajarshi Roy for
this last example.