Analogical scaffolding and the learning of abstract ideas in physics: An example from electromagnetic waves

Abstract

This paper describes a model of analogy, analogical scaffolding, which explains present and prior results of student learning with analogies. We build on prior models of representation, blending, and layering of ideas. Extending this model’s explanatory power, we propose ways in which the model can be applied to design a curriculum directed at teaching abstract ideas in physics using multiple, layered analogies. We report on a recent empirical study that motivates this model. Students taught about electromagnetic waves in a curriculum that builds on the model of analogical scaffolding posted substantially greater gains pre- to postinstruction than students taught using a more traditional (non-analogy-based) tutorial (21% vs 7%).

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Analogical Scaffolding and the Learning of Abstract Ideas in Physics:
An example from electromagnetic waves

Noah S. Podolefsky and Noah D. Finkelstein
University of Colorado at Boulder

Abstract
This paper describes a model of analogy, analogical scaffolding, which explains present and
prior results of student learning with analogies. We build on prior models of representation,
blending, and layering of ideas. Extending this model’s explanatory power, we propose ways the
model can be applied to design curriculum directed at teaching abstract ideas in physics using
multiple, layered analogies. We report on a recent empirical study that motivates this model.
Students taught about EM waves in a curriculum that builds on the model of analogical
scaffolding posted substantially greater gains pre- to post-instruction than students taught using a
more traditional (non-analogy based) tutorial (21% vs. 7%).

PACS: 0140FK

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Introduction
Analogies are ubiquitous in both the practice and the teaching of physics. There are many
historical examples, from Rutherford’s planetary model of the atom [1] to Maxwell’s application
of fluid theory to electromagnetism. [2] Analogies are commonly used to teach physics in
lectures and in textbooks. [3] Because analogies are so common in physics education, there is
clearly a need to understand how analogies work, as well as when and why analogies are
productive or not for learning physics. Researchers have proposed models of analogy [4] [5] [6]
[7] which have advanced our theoretical understanding, but we argue these models are
insufficient to explain students’ use of analogy in practice. Teaching with analogy has been
shown to be sometimes productive for learning, but sometimes not, and the reasons for this
inconsistency are not well understood. Spiro et al [8] suggest teaching with multiple analogies in
order to circumvent the drawbacks of single analogies, (e.g., single analogies may be misleading
or incomplete) especially when teaching complex and difficult topics. Broadly, our efforts build
on prior work in order to better understand how, when, and why analogies can be used
productively to teach physics, particularly in the context of using multiple analogies. Our prior
work revealed implications for the productive use of analogy and called for a new explanatory
model. [9] Building on prior theoretical models of analogy, we extend other researchers’ efforts
to study mechanisms of analogy and general features of teaching with analogy that lead to their
productive use for learning physics. This paper presents a model of analogy, analogical
scaffolding, which extends these prior efforts and examines sample data supporting this model.
Our research efforts address the need for further study of teaching with analogy in three
ways. (1) The existing literature reports mixed success of teaching with analogy (e.g., [6] [10]).
Existing models of analogy suggest general approaches to, but do not specifically inform,

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curriculum design. We make progress towards understanding successful cases, describe specific
mechanisms by which analogies can be used productively to teach, and propose a model with
direct implications for the design of learning materials using analogies. (2) Often, no single
analogy is sufficient for teaching a new idea in physics, especially if that new idea is highly
abstract. We propose a mechanism of student use of analogies to learn abstract ideas in physics,
specifically by using multiple, layered analogies. (3) We believe models of student learning in
physics should begin to explain they complex dynamics of student thinking, allowing for on-the-
fly variations in students’ thinking that depend crucially on salient factors in the environment.
Our model proposes one such mechanism of student reasoning, focusing on how multiple
analogies and representations used to teach those analogies interact to influence student thinking.
In this paper, we broaden the scope from a strict definition of analogy to consider the idea
of domain comparisons, of which analogy, [4] metaphor, [11] and conceptual blends [12] are
particular cases. In all of these cases, mappings of object attributes and relations, as well as other
types of connections, are made between two (or more) domains. In the literature dealing with
domain comparisons, a domain is often represented by a mathematical set, and a comparison
between domains is represented by a mapping, isomorphism, union or another related operation
on the two sets. We draw on a range of prior work, focusing on Fauconnier and Turner’s theory
of conceptual blending, [12] to develop the analogical scaffolding model. As we will
demonstrate, blending includes several features that extend traditional models of analogy. For
instance, contrasted with traditional “two-domain” models of analogy, blending is a “multi-
domain” model, making it a promising model for dealing with multiple analogies. According to
Turner and Fauconnier, allowing for multiple domains “introduces a higher degree of variability
and a loss of parsimony, but with a corresponding increase in sensitivity and generality. The two-

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domain model is in fact a special case of the many-space model.” [13] [14] At the same time we
build on work in semiotics [15] to frame meaning making with representations, and on the work
of layering meaning [16] to see how analogies can scaffold one another. More details on these
prior theoretical frameworks will be provided in the next section. Following this section, we
briefly describe a selection of the empirical work on which we base our model of analogical
scaffolding. Next, we describe this model, which builds on prior models of analogy and
addresses some outstanding questions on teaching with analogies. We explore the utility of this
model by applying the model to explain sample data. Finally, we suggest future studies and
curriculum design which lead naturally from an application of this model.

Previous Analogy Theory
A prevailing view of analogy in physics is due to Gentner. [4] [5] Her model, referred to
as Structure Mapping, defines an analogy as a mapping from a base domain to a target domain.
Gentner defines attributes of (e.g. color) and relations between (e.g. revolves around) objects,
and proceeds to define an analogy as a domain comparison in which, predominantly, relations
are mapped rather than attributes. For example, in Rutherford’s planetary model of the atom, the
solar system is the base domain and the atom is the target domain. The sun, an object,
corresponds to the nucleus, the planets correspond to the electrons, and the relationship planets
revolve around the sun maps to electrons revolve around the nucleus. There are other possible
mappings as well, for instance, the color attributes of the sun and planets could map to the
associated components of the atom. According to Gentner’s definition of analogy, these
attributes do not generally map. Instead, Gentner defines a literal similarity, in which attributes,
rather than relations, predominantly map from base to target. An example is the literal similarity

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between our solar system and another planetary system somewhere else in the galaxy. This
delineation between analogy and literal similarity is consistent with expert thinking, but may not
describe student thinking about analogies. Indeed, when presented with an analogy (as defined
by an expert), students may consider attributes equally (or more) valid to map from base to target
compared to relations.
Gentner and Gentner [10] showed empirically that student reasoning about electric
circuits was associated with analogies that were generated by the students. Students who used a
water analogy out-performed students who used a moving objects analogy on questions about
batteries, while students who used a moving objects analogy out performed students who used a
water analogy on questions about resistors. However, in a second experiment, the explicit
teaching of water or moving object analogies to students was not found to be as effective as
when the students created the analogies themselves. Explanations for this mixed success in
teaching with analogies include inadequate student understanding of the base domain, a failure to
use the analogy correctly, or a failure to use the analogy at all.
In order to overcome difficulties with teaching analogies, Brown and Clement [6] suggest
bridging as a method to foster productive analogy use. A bridging analogy provides one or more
intermediate steps between the base and target intended to help students connect the two. The use
of bridging analogies has had mixed success. [6] [17] Researchers attribute student difficulties to
the use of analogical comparisons that were too abstract and therefore difficult for students to
apply productively. Other studies [18] [19] have confirmed the difficulty in fostering
spontaneous analogy generation and productive use by students.
Existing models of analogy have difficulty explaining why analogies are only sometimes
successful for affecting student reasoning. In particular, it is not well understood how one knows