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Move over misconceptions and make way for resources: a wave motion example

Title: Student conceptual resources for understanding mechanical wave propagation

Authors: Lisa M. Goodhew, Amy D. Robertson, Paula R. L. Heron, and Rachel E. Scherr.

First Author’s Institution: University of Washington

Journal: Physical Review Physics Education Research, 15 020127 (2019)


Physics Education Research has had considerable success in improving student learning in physics classrooms, both in schools and in colleges. One technique that has contributed to this success is the study of student difficulties and misconceptions. That is, researchers give students a particular situation to work with and then they analyze student responses to identify common mistakes, which are then viewed as difficulties or misconceptions. Such studies have resulted in a large collection of research-based and research-validated materials and resources for use by instructors. Resources such as Tutorials in Introductory Physics, Modeling Instruction, Peer Instruction, and many more are results of such inquiries by education researchers over many decades(1).

While the success of traditional educational research is undeniable, it does have some limitations. At a very basic level, research that focuses on difficulties and misconceptions do not account for productive ideas that students already have. In addition, the terms difficulties and misconceptions are too narrow and rigid to explain aspects of student behaviors such as how students respond differently when a question is asked in different ways (4). Education researchers characterize this aspect of traditional research by dividing education research into two broad categories: deficit-based models and asset-based models. In deficit-based models the focus is on confronting, remedying, and overcoming incorrect ideas. Such models are characterized by behaviors such as looking for what is missing or wrong, assuming a normative standard, trying to fix what isn’t up to standard and an emphasis on outcomes. In contrast to deficit-based models, asset-based models look for what it present and useful. Asset-based models focus on multiple pathways, tries to build from what is good, and places emphasis on growth and processes. In short, where a deficit-based model looks for difficulties, an asset-based model looks for strengths and potentials(1). The crucial difference between these two models is captured in the question “Is it a student who can’t sit still or a student who has lot of energy?”(2).

The paper we discuss here focuses on how a particular asset-based model, called the Resources Framework, provides instructionally useful insight into knowledge of student ideas. In this framework, student ideas are considered as potential input to the process of conceptual growth rather than as obstacles to learning. Pedagogically, such research aims to build from existing knowledge rather than confront, remedy, or overcome incorrect ideas(3).

Resources framework

Resources framework, also known as the resources theory of knowledge, “models cognition in terms of pieces of knowledge – i.e., resources – that are activated in the moment in a context-sensitive way to construct arguments, theories, and concepts.”(3). For our purposes, this idea is best illustrated via an example(6).

Suppose we ask 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?

Most students answer this question incorrectly. Instead of answering that the forces are equal, most students answer that the truck exerts more force. A deficit-based model would classify this as a difficulty and would try to find methods for helping students overcome this difficulty. Elby(5), though, took an asset-based approach and carefully analyzed student responses. He noted that what students are really saying is that the car ‘reacts’ more than the truck, and then they associate force with the notion of ‘reacts’ which leads them to their incorrect conclusion. With this observation in mind, Elby created follow up questions such as the following:

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 instincts.

Now most students managed to get the right answer! Possibly due to contextual clues, students managed to associate ‘acceleration’ with ‘reacts’, and that got them on the right track. The student idea that ‘car reacts more than truck’ is a conceptual resource that they presumably built up from day-to-day experiences or from prior learning. When applied to force the resource misleads the students, but when applied to acceleration the resource helped students get on the correct path. Such analysis is difficult with notions such as ‘misconceptions’ and ‘difficulties’.

Hammer(4) offers the analogy of a programmer armed with a library of routines to illustrate what a resource is. In any given situation a programmer has several routines at their disposal. If the programmer has already seen the situation before then they can readily pick the routines they want and apply them. If not they have to think through and choose the set of routines that are applicable to the given context. Similarly, resources are ideas and concepts we have built over our lifetimes. In any given situation, we have access to many resources, and some of them might lead us to contradictory findings, forcing us to analyze the situation to either refine the resources or extend them to new ones.

In the context of the research presented here, the authors highlight three important features of resources. The first important feature is that resources are sensible to the user. Sensible here means that learners have a good reason for thinking in a particular way, and is possibly informed by their experiences in the real world and prior learning. The second feature is that resources tend to be context sensitive. Context sensitivity here means that whether a learner uses a particular resource or not depends on a constellation of conditions related to the learner, the environment as well as the question or task at hand. The third important feature of resources is that they are continuous with formal knowledge to some extent. What this means is that within a resource we can find ideas or concepts that can make a connection with formal understanding of the topic, even if the resource as a whole may be incorrect from a formal viewpoint. This feature also implies that learning, as seen from the resources perspective, involves changing resources in many ways: making them more formal, changing their structure or role, changing the connectedness of resources and so on. All three of these features are well illustrated in the car-and-truck example described above.

In summary, resources framework aims to move beyond the notions of ‘misconceptions’ and ‘difficulties’, even-though these have provided many benefits to physics education research. The notion of ‘misconception’ suggests a single stable cognitive unit that is leading the student astray(4) and the notion of ‘difficulty’ suggests something to be overcome and left behind. On the contrary, the resource framework argues that instructors should expect student thinking to be dynamic and sharing features with complex-systems(3), and the productive use of student resources can help instructors better support student learning.

What this paper is about

In this paper the authors present research that they have conducted to try to answer the following two questions: What are some of the common conceptual resources that introductory university physics students use to reason about mechanical wave propagation? How does student use of these resources vary across questions about mechanical wave propagation?

Figure 1: Three questions used to probe student ideas about motion of a pulse.

To answer these questions the authors use a resources perspective to analyze student responses to three questions related to how a single pulse moves along a string. The three questions are shown in figure 1. The first question , the pulse-flick question (‘original question’), asks two sub-questions: how can someone make a pulse travel faster along a string while keeping their hand motion the same, and how they can do this if they are only allowed to change the material of the string.. After analyzing responses to these questions, the authors decided to form two more questions that further explore two of the most common student answers. In the tension pulse-flick question (‘tension question’) the answer to the first part of the original question is given and the student is asked to explain why the answer makes sense. In the mass density pulse-flick question (‘mass density question’), the answer to the second part of the original question is given and the student is asked to explain why the answer makes sense. The three versions were given to students enrolled in introductory physics classes at 5 US universities as part of their required course-work. At-least 70% of students enrolled in each class participated in the survey, and the authors analyzed 851 responses covering all three questions.

Identifying conceptual resources in an objective fashion is difficult, since conceptual resources are ideas that exist in students’ minds. Researchers have to use their subjective interpretations to come to some agreement on what the resources are in any set of student responses. The authors of the papers go to great lengths to identify the many preferences and ideas they themselves bring to the analysis, so that readers have a good understanding of why certain choices are being made.

First, the authors describe how they identified resources. To identify conceptual resources, the authors conduct an iterative content analysis process to create a scheme to label resources. A response is considered to have a resource only when the first author and the second author both agree to a high degree. The authors find 5 resources of which 3 are common and are presented in this paper. Second, the authors give a description of the physics of wave motion along a string. In this description they highlight the important points they found useful as they analyzed student responses. This is important, since an emphasis on a different approach to the problem might not reach the same conclusions. A summary of these keys points are listed in table 1 for completeness.

Summary of the physics of a pulse moving along a string
Table 1: Summary of the physics of a pulse moving along a string
We can treat a shape preserving pulse as an abstract entity traveling at a constant speed.
We can model wave motion as a series of particles connected by springs. Each particle only
moves up or down but the connections cause the disturbance to move in a perpendicular
direction to the movement of each particle.
The speed of a pulse is given by , where T is the tension in the
rope and is the mass density of the rope. That is, speed depends on the properties of
the medium.
The wave speed is a property of the medium, frequency can be manipulated at the source, and
wavelength is determined by these.
The wave carries with it both kinetic and potential energies. The stretching of the rope results in
potential energy and the transverse movement of parts of the rope results in kinetic
energy. A pulse with greater kinetic energy must also have greater potential energy.
Amplitude of the motion is related to kinetic energy but does not affect the speed of the wave.

Resources associated with the motion of a pulse along a string

The main result of this paper is the three resources identified by the authors: the “medium resource”, the “transverse speed resource” and the “energy resource”. To illustrate the resources, consider the following student responses.

[so] the speed of propagation of the pulse
is directly related to the square root of the tension.”
(original question)

“Because tension is directly related to speed in waves,
higher tension means that the pulse and speed can travel
faster because higher tension makes a more linear path
to travel.” (tension question)

“It takes more energy to move something of greater
mass. The pulse also must travel through more particles
per unit of distance therefore it makes sense intuitively
that it would take longer.” (mass density question)

In the first response above we see that the student is using an equation to make the qualitative argument that speed is related to tension, a property of the medium. In analyzing the second example, the authors suggest that even though the idea of a “linear path” is incorrect, the student still links tension, a property of the medium, to the pulse. The authors interpret the third response as the student trying to come up with a casual mechanism by which the medium affects the pulse. These and similar interpretations form the medium resource: students see pulse propagation as an interaction between the pulse and the medium.

The “transverse” motion resource acknowledges that the pulse is a propagation of disturbances of parts of the medium and that speed of pulse is linked to the transverse motion of the medium. That is, the resource represents an initial mechanistic model for propagation. A few responses that the authors interpret as having this resource are shown below.

“In increasing the tension, the TA puts more force on the
spring towards making it follow a straight line. This
makes its acceleration towards the center greater, and
thus, each individual point does ‘the wave’ more quickly.
For the pulse to complete one length of the string, each
point must complete the ‘wave’ motion. Therefore, since
the points complete the wave more quickly, the pulse
moves more quickly.” (tension question)

“The higher tension will decrease the amplitude if the
same amount of force is used, which means each
displacement is shorter, [and] tak[es] less time to do
[therefore] moving faster.” (original question)

In the first response above the student considers the medium to be discrete and tries to link the transverse motion of parts of the medium to the propagation of the wave. The second statement is incorrect but the authors argue that this particular use of the resource is continuous with formal physics, as it expresses the correct connection between the transverse motion of the medium and the propagation of the pulse.

The second statement above, and how the researchers have interpreted it, is a very good illustration of how asset-based and deficit-based approaches differ. This statement resembles previously reported difficulty or misconception: a faster input makes the pulse move faster. This classification is true, but the authors interpret the above example as a resource where the student is employing a mechanistic reasoning similar to how scientists reason. That is, students are engaged in a modeling attempt at treating a pulse as sequential and local disturbances of a medium connected via interactions between parts of the medium. The student may have reached an incorrect conclusion, but we shouldn’t neglect the fact that they are attempting such a connection.

A response is considered to be an instantiation of the energy resource when the response uses energy accounting to explain or predict changes in the pulse speed.

“There is kinetic energy being transferred into the
spring when the professor creates the pulse. Since the
mass of the second string is increased, it would make
sense for the second spring to move slower because it
has less velocity (if the amount of energy transferred is
kept the same).” (mass density question)

“If the tension of the string is greater, the system would
have more potential energy, then once the system is
given a pulse, that potential energy is converted to
kinetic energy which is a function of velocity. Therefore
it would make sense for a pulse to move faster on a high-
tension spring by the law of conservation of energy.”
(tension question)

“[You can generate a faster-moving pulse] by adding an
enormous amount of motion that gives the motion a
small “T” period per wave cycle {because] the more
energy you add, the faster the wave will travel.”
(original question)

The first example above relates velocity to kinetic energy and mass density. In the second one a clear association is made between potential energy, kinetic energy and the pulse. The authors assert that while the third response is incorrect in saying that more energy leads to faster wave (in fact, change in energy changes the shape of the pulse), the response still connects energy with the propagating pulse and reasons about speed using energy principles.

In addition to identify conceptual resources, the authors also investigated the frequency of resources across the three questions. The three resources do not occur in the same frequency for all three questions. For example, the medium resource appears frequently in the ‘original question’ where as responses to the other two questions contain a variety of resources. The difference could be due to the type of question: the first asks students to predict where as the second asks students to explain. The authors hope to explore such factors and others in future work.

Conclusions

One of the important ways in which this paper contributes to physics education research is by illustrating how detailed analysis of student responses, without too narrow a focus on outcomes, can reveal strengths that students bring to a situation. For example, in the quotes classified as examples of the transverse motion resource, we see that from a purely outcome based analysis the student is incorrect and needs correction. But from an asset-based perspective, here the resources perspective, we do see the mistake but do not miss out on the relevant ideas that the student bring to the table.

It is important to keep in mind that, as the authors point out, the resources that the authors bring to the study influence the results, and hence, different researchers may find similar or different resources in the student responses. The aim here is to bring to light productive ideas that students bring to a particular situation that may otherwise get lost in a deficit-based model of analysis.

The authors mention several ways for using the knowledge that we gain from such interpretations to improve student learning. For example, instructors might first engage in sense-making with the students and then follow up on the resources that show up, whether they match the ones described in this paper or not. A common theme in the examples presented in the paper is the use of mechanistic reasoning and modeling — instructors might focus on more detailed explanatory models (not just an equation) for pulse speed. The authors report that they themselves are in the process of designing instructional materials based on the insights gained from this study.

References

1) Consequences of asset-based models for physics education by Dr. Eleanor Sayre, https://www.phys.ksu.edu/news/colloquia/f19/sayre.html; retrieved on October 9 2019.

2) An Asset-Based Approach to Education: What It Is and Why It Matters. https://teachereducation.steinhardt.nyu.edu/an-asset-based-approach-to-education-what-it-is-and-why-it-matters/; retrieved on October 9, 2019.

3) Lisa M. Goodhew, Amy D. Robertson, Paula R. L. Heron, and Rachel E. Scherr, Student conceptual resources for understanding mechanical wave propagation, Phys. Rev. Phys. Educ. Res. 15, 020127 (2019); the paper under discussion.

4) D. Hammer, Student resources for learning introductory physics, Am. J. Phys. 68, S52 (2000).

5) A. Elby, Helping physics students learn how to learn, Am. J. Phys. 69, S54 (2001).

6) This example comes from the discussion presented in Hammer(4), who discusses original work done by Elby(5).

Figures used under Creative Commons Attribution 4.0 International. Header image by Frits Ahlefeldt [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons.

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