Identifying student conceptual resources for understanding physics: A practical guide for researchers

[This paper is part of the Focused Collection on Qualitative Methods in PER: A Critical Examination.] Identifying student ideas about particular physics topics is one of the earliest and longest-standing foci of physics education research. This paper presents a method for identifying common conceptual resources for understanding physics, using large numbers of written student responses to conceptual questions. We walk researchers step by step through how we have done this ourselves, from collecting data, to identifying candidate resources, to turning our lists of candidate resources into a coding scheme that can then be applied to datasets of $>200$ responses. The outcome of these methods are lists of common conceptual resources for understanding particular topics in physics, such as forces, energy, circuits, and heat and temperature.

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Figure 1

Airplane question from the Force Concept Inventory. Reprinted from Hestenes et al., Phys. Teach. 30 141 (1992), with the permission of AIP Publishing. Image description: Sketch of an airplane moving to the right, with five different dotted lines emerging from the bottom center of the plane. The lines represent trajectories of a bowling ball. The leftmost trajectory is a curved line that shows the bowling ball moving backward and landing on the ground behind the plane. The next trajectory is a straight line to the ground, showing the bowling ball landing directly under the plane. The next trajectory is a straight diagonal line showing the bowling ball landing in front of the plane. The next trajectory is a curved line also showing the bowling ball landing in front of the plane. The rightmost, final trajectory looks like a curved letter $\mathsf{L}$ that has been rotated 180 deg, such that the ball moves horizontally forward at first and then abruptly falls to the ground. The trajectories are labeled from left to right: A, B, C, D, and E.

Figure 2

Tension pulse-flick question, originally published in Goodhew et al., Phys. Rev. Phys. Educ. Res. 15 020127 (2019). Image description: Text of the tension pulse-flick question and a figure illustrating a string attached to a wall, held by a hand to the right of the wall. The hand is horizontal, positioned halfway between the top and bottom of the wall, and a pulse moves to the left along the top of the string. The question text reads, “Consider the following two scenarios: In scenario 1, your Teaching Assistant (TA) creates a pulse by flicking the end of a spring, as in the figure at right. In scenario 2, your TA pulls the spring so that it is more taut (i.e., increases the tension in the spring) and then creates a pulse by flicking the end of the spring in the same way. The pulse in scenario 2 travels down the spring faster (i.e., has a larger speed) than the pulse in scenario 1. Why would it make sense for a pulse to move faster on a higher-tension spring? (We’re trying to understand your intuition, not whether or not you can remember particular equations. In other words, we want to know how you make sense of this phenomenon)”.

Figure 3

Sample (partial) list of question-specific candidate resources for the tension pulse-flick question (Fig. 2). Bolded text is the list of fine-grained, candidate resources, and subsequent plain text shows examples from student responses. Image description: List of bolded, bullet-pointed sentences, representing candidate resources, and italicized student responses underneath each one. The first bullet reads, “Lower mass density means it takes less energy for the pulse to travel,” and the italicized example underneath it reads, “Pulling a spring (creating tension) decreases the number of coils in a given distance. This in turn lowers the mass density of the same length of spring. With a lower density and the same energy a wave uses less energy to travel through the medium and more energy to “create” its speed.” The second bullet point reads, “Increasing the tension of the spring increases the potential energy (which can then be transformed into kinetic energy, and the pulse can move faster).” The italicized example below this bullet point reads, “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 higher tension spring by the law of conservation of energy.” The third bullet point reads, “The restoring force is bigger in a higher tension spring.” The example student response underneath this bullet point reads, “From just thinking about the scenario, I think it makes sense for a pulse to move faster on a higher tension spring, because as the pulse travels through, each part of the higher tension spring will [be] displaced less than the normal spring would and would return to equilibrium faster. The pulse would not create such a large amplitude, which would slow it down, which is what happens when you decrease the tension.” The fourth bullet point reads, “The wave speed is determined by a force that is the sum of the tension and the hand force.” Underneath this bullet is a drawing with two sets of vector diagrams. The vector diagram on the left is labeled, “By using a FBD,” and there are three vectors, one pointing straight up, one pointing horizontally to the right, and one that is the sum of the two. The vector pointing straight up is labeled, “${\mathrm{F}}_{\text{Hand}}$,” the horizontal vector is labeled, “${\mathrm{F}}_{\text{string}}$,” and there is a bracket between the horizontal vector and the vector sum labeled, “This magnitude represents wave speed.” The vector diagram on the right is labeled, “By [up arrow] tension,” and has similar vectors to the diagram on the left, except the horizontal (${\mathrm{F}}_{\text{string}}$) vector is longer, and thus so is the vector representing the sum of the vertical and horizontal vectors. On this diagram, the student has indicated that the vertical vector is the same, the horizontal vector greatly increases, and so the magnitude of the resultant vector also increases. The fifth bullet point reads, “Increasing tension means energy is transferred more quickly.” The example response below it reads, “Higher string $\mathrm{tension}=\text{quicker}$ transfer of energy. I think a pulse would move faster with higher tension. The string would move less, therefore leading to less displacement, overall leading to the ability for faster pulses.” The sixth bullet point reads, “The speed of the wave is related to how fast the particles of the spring return to equilibrium after being disturbed.” The example response below it reads, “A wave is basically a disturbance in a medium, in this case, the string. The speed of the wave moving through the medium is directly related to how fast the particles of the string can return to equilibrium position after being disturbed. The more tense the string, the faster the ability of the particles to return to equilibrium position. This is why wave speed increases with increase in tension. Greater $\mathrm{tension}=\text{greater}$ restoring $\mathrm{force}=\text{greater}$ wave speed.” The seventh (final) bullet point reads, “Greater tension means a greater force between the particles of the spring.” The example response below it reads, “The wave pulse speed would increase when the tension of the spring increases because higher tension means there’s a higher force between the particles in the string. When the wave is displaced, there is a greater restoring force to bring the particles back to equilibrium. Therefore, there’s a greater tendency to pass the displacement along, resulting in a higher wave speed”.

Figure 4

Sample reduction of preliminary list of candidate resources (left, orange box) into a smaller set of common conceptual resources for understanding mechanical wave propagation (bolded sentences in blue box on right). Image description: On the left is an orange box with a bold, underlined title at the top that reads, “(Subset of) fine-grained resources for understanding mechanical wave propagation:.” Under this title is a list of resources including, “a) Increasing the tension of the spring increases the potential energy (which can then be transformed into kinetic energy) and the pulse can move faster.”; “b) A pulse has to move further in a slack string, so increasing tension will allow it to move faster.”; “c) The restoring force is bigger in a higher tension spring.”; “d) The speed of the pulse depends on the medium through which it travels/properties of the spring.”; “e) Lower mass density means it takes less energy for the pulse to travel.”; “f) Increasing tension means amplitude is less and energy is transferred more quickly.”; “g) The speed of the wave is related to how fast the particles of the spring return to equilibrium after being disturbed.”; “h) A lighter string has less inertia or resistance to the motion of the pulse, so a pulse will move faster.”; “i) It takes less energy to move a pulse through a lighter spring.”; and “j) Greater tension means a greater force between the particles of the spring.” On the right is a blue box that includes the resources from the orange box [a) through f)], grouped into clusters that represent coarser-grained resources, with each coarse-grained resource listed under each cluster. At the top, resources “c) The restoring force is bigger in a higher tension spring”; “f) Increasing tension means amplitude is less and energy is transferred more quickly”; “g) The speed of the wave is related to how fast the particles of the spring return to equilibrium after being disturbed”; and “j) Greater tension means a greater force between the particles of the spring” are listed one after another. Underneath this cluster of fine-grained resources is a horizontal blue arrow pointing to the right, with text beside it that reads, “The speed or duration of transverse motion affects pulse speed.” Under this is another list of fine-grained resources: “b) A pulse has to move further in a slack string, so increasing tension will allow it to move faster”; “d) The speed of the pulse depends on the medium through which it travels/properties of the spring”; and “h) A lighter string has less inertia or resistance to the motion of the pulse, so a pulse will move faster.” This cluster of resources is also followed by a blue arrow, next to which is the text, “The properties of the medium impede or facilitate pulse movement.” Following this is a final list of fine-grained resources: “a) Increasing the tension of the spring increases the potential energy (which can then be transformed into kinetic energy) and the pulse can move faster”; “i) It takes less energy to move a pulse through a lighter spring”; and “e) Lower mass density means it takes less energy for the pulse to travel.” Below this cluster is a final blue arrow, next to which is text that reads, “Pulse speed is affected by the kinetic energy of the pulse”.

Figure 5

Resources identified in previous work from our research team, by topic. Image description: A series of nine underlined phrases (all topics in physics, followed by journal citations) and bullet-pointed lists to accompany each one. The title of the box is “Resources identified in previous studies by our team.” The first underlined topic is energy, with an accompanying citation of Sabo, Goodhew, & Robertson, 2016. Under this topic are five bullet-pointed resources: “Students account for energy transfers and transformations in a scenario”; “Students associate (i) forms of energy with indicators and (ii) changes in energy with indicators of change”; “Students relate energy to forces and/or work”; “Students implicitly use the second law of thermodynamics”; and “Students quantitatively represent energy scenarios.” The second underlined topic is mechanical wave propagation, with an accompanying citation of Goodhew et al., 2019. Under this topic are three bullet-pointed resources: “Properties of the medium either impede or facilitate the motion of the pulse”; “The speed or duration of transverse motion affects pulse speed”; and “The speed of the pulse is affected by its energy.” The third underlined topic is superposition, accompanied by a citation to Bauman, Goodhew, & Robertson, 2019. Under this topic are four bullet-pointed resources: “Localization: Superposed effects must be co-located”; “Independence: Effects must be independent of each other”; “Quantifiability: Superposed effects can be described quantitatively”; and “Additiveness: Effects add together.” The fourth underlined topic is kinematics, with an associated citation of Broadfoot et al., 2020. Under this topic are four bullet-pointed resources: “Acceleration is present when there is a change in the velocity of an object”; “The magnitude of acceleration is related to the magnitude of the change in velocity”; “The directional relationship between an object’s velocity and acceleration determines what is observed about its speed”; and “Gravity changes the speed of objects.” The fifth underlined topic is forces, accompanied by the citation Robertson et al., 2021. Under this topic are six bullet-pointed resources: “Moving objects keep moving”; “Forces influence the motion of objects”; “Imbalanced forces change the motion of objects (and balanced forces do not)”; “It takes more effort to overcome a given force than to match it”; “It takes more effort to overcome a bigger (net) force (and less effort to overcome a smaller one)”; and “It takes more effort to change the motion of an object than to sustain it.” The sixth underlined topic is linear momentum, with the associated citation Hansen et al., 2021. Under this topic are four bullet-pointed resources: “Conservation: Momentum is conserved”; “Direction: Momentum has a direction”; “Collisions: The type of collision an object undergoes matters”; and “Properties: The properties of an object matter.” The seventh underlined topic is heat and temperature (macroscopic), with the associated citation Abraham et al., 2021. Under this topic are three bullet-pointed resources: “Heat transfer is directional”; “An object’s physical properties matter in thermal processes”; and “Hotter objects have more energy.” The eighth underlined topic is heat and temperature (microscopic), with the associated citation Alesandrini et al., 2022. Under this topic are three bullet-pointed resources: “Differences will eventually even out”; “Macroscopic changes connect to microscopic collisions”; and “When something is hotter (colder), its molecules are moving faster (slower).” The ninth and final underlined topic is circuits, with the citation Bauman et al., under review. Under this topic are four bullet-pointed resources: “Current is responsive”; “Voltage drives current”; “Resistance opposes current”; and “The way elements are connected within the circuit matters”.