Abstract
Understanding scientific phenomena requires learners to construct mental models of causal systems. Simulation-based discovery learning offers learners the opportunity to construct mental models and test them against the behavior of a simulation. The purpose of this study was to investigate sequential patterns of learner actions and utterances associated with outcomes of simulation-based guided discovery learning. We conducted a sequence analysis of data gathered from 11 undergraduate students engaged in discovery learning. Three related methods were used for the sequence analysis: Levenshtein edit distance, k-means clustering of the Levenshtein distance, and the Kohonen generalized median sequence. The median sequences of high-gaining and low-gaining participants showed qualitative differences in how they gathered evidence, stated claims, and drew explanatory inferences. Differences between the sequences of actions and utterances of high-gaining and low-gaining participants suggested ways that students might be guided to enhance discovery learning. By tracking the learning patterns of learners, researchers can determine the conditions under which prompts should be provided and offer recommendations for transforming less effective learning strategies to more effective ones.
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Acknowledgements
This work was supported by a grant from the Social Sciences and Humanities Research Council of Canada.
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This work was supported by a grant from the Social Sciences and Humanities Research Council of Canada (435-2019-0458) to John C. Nesbit.
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Appendices
Appendix A: Inferencing during prediction phase and observation phase in DC circuit simulation
1. Inferencing (prediction phase) | |
Current throughout the circuit | The current stays the same throughout the resistors because the battery voltage has not changed |
But, the current in the circuit is the result of: the voltage of the battery, and how much that push is impeded: the resistance of the bulb | |
The current does not stay the same throughout the resistors because we have resistors with different magnitudes that impede the flow of electrons | |
But, restricting the flow of electrons might cause the electrons to decrease in the entire circuit because in a one path circuit, the electrons have to go through all the resistors. (Questioning: Would the rate at which charge flows into a resistor be the same as the rate at which charge flows out of the resistor? Would restricting the flow of electrons cause the electrons to slow down in the entire circuit or would it cause the electrons to pile up when entering or exiting a resistor?) | |
The current stays the same because the effective resistance is the value of one or the value of sum of the resistors | |
2. Inferencing (observation phase) | |
Current throughout the circuit | Current is the flow of electrons |
We have a constant voltage supply; No charge is entering or exiting the circuit | |
When we increase the resistance, either voltage must increase (we must give the electrons more energy each, to make up for what is lost in the resistor) or the current will reduce (the same amount of energy per electron is not able to ‘push’ them through the circuit’s resistance as fast) | |
The speed of electrons does not change when the current goes through different resistances. There are no leaks and no accumulated charges at different points of the circuit | |
The effective resistance is equal to the sum of the individual resistance | |
All the electrons have to flow from one resistor to the next resistor. When there is one path for the flow of electrons, there is no chance for more electrons to flow through the less ohm resistance | |
Voltage is different across resistors with different magnitudes but current remains the same when flows through resistors with different magnitudes | |
Appendix B: Possible experiment space and claim space
Experiment space |
|---|
1. Constructing a circuit with one bulb/resistor and a battery |
2. Measuring the change in current (using ammeter) when the resistance is increased/decreased |
3. Observing the brightness of the bulb when resistance of the one bulb/resistor is reduced/increased |
4. Measuring the current through each resistor and throughout the circuit |
5. Without changing the voltage, observing the effect of changing the magnitude of one resistor out of the other resistors with different magnitudes |
6. Observing the brightness of the bulbs with the same value of resistance |
7. Measuring the current in the bulbs/resistors with the same magnitudes |
8. Measuring the current throughout a circuit with multiple resistors that have the same magnitudes |
9. Without changing the voltage, measuring the current (using ammeter) through resistors with different magnitudes |
10. Observing the brightness of the bulbs with different magnitudes |
Claim space |
|---|
1. When the resistance increases, the current decreases; resistance decrease→current increase |
2. The resistance increases, the light bulb gets dimmer; resistance decrease→bulb brighter |
3. When using a circuit with a single bulb and when the resistance is zero, the bulb will stop glowing |
4. When using a single bulb and when increasing the resistance, the light bulb will get dimmer |
5. When the resistance is not changing, the current will be the same throughout the circuit |
6. When using a circuit with multiple bulbs with the same magnitudes, the current will stay the same through each resistor and throughout the circuit |
7. The brightness of the bulbs is the same in multiple resistors with the same magnitude |
8. When the resistance is not changing, the current will be the same throughout the circuit that has multiple resistors with same magnitudes |
9. When using a circuit with multiple bulbs with different magnitudes, the current will remain the same throughout the circuit |
10. The bulb with higher resistance will be brighter |
11. When the resistance is not changing, the current will be the same throughout the circuit that has multiple resistors with different magnitudes |
Appendix C: Median sequence descriptions for cluster 1, cluster 2, cluster 3
E = Evidence C = Claim P = Prediction I = Inference | |||||
|---|---|---|---|---|---|
Median string 1 | Description | Median string 2 | Description | Median string 3 | Description |
R | Reading supplementary information | R | Reading supplementary information | R | Reading supplementary information |
E1.2 | Connecting objects with open switch | C1.6 | Claim about what voltage is | C1.1 | Claim about what circuit is |
E1.1 | Constructing circuit with irrelevant objects | C1.3 | Claim about wire resistivity | C1.2 | Claim about what electrons are |
E1.10 | Playing with the brightness of a bulb | E1.3 | Constructing a circuit with closed switch | E1.7 | Constructing a circuit with a bulb |
E1.3 | Constructing a circuit with closed switch | C1.1 | Claim about what circuit is | E1.10 | Playing with the brightness of a bulb |
E3.6 | Measuring the change in current (using ammeter) when the resistance is increased/decreased | E1.10 | Playing with the brightness of a bulb | C1.7 | Claim about what resistor is |
C3.4 | When the resistance increases, the current decreases; resistance decreases, current increases. There is an inverse relationship between resistance and current | E1.12 | Measuring the increase and decrease of wire or battery resistivity | E1.2 | Observing connected objects with open switch |
E2.6 | Observing the brightness of the bulb when the voltage is reduced/increased | E1.5 | Constructing a circuit with a/multiple batteries without a resistor (battery on fire) | E1.3 | Constructing a circuit with closed switch |
C2.3 | When the voltage increases, the current increases; voltage decreases, current decreases. There is a direct relationship between voltage and current | E1.7 | Constructing a circuit with a bulb | E1.4 | Observing connected objects without a battery |
C3.4 | When the resistance increases, the current decreases; resistance decreases, current increases. There is an inverse relationship between resistance and current | E2.5 | Observing the flow that the electrons have when voltage increased/decreased | E2.1 | Observing the voltage of the battery |
P1 | Predicting effective resistance | E2.4 | Measuring the current (using ammeter) when the voltage is increased/decreased | E2.6 | Observing the brightness of the bulb when the voltage is reduced/increased |
P2 | Predicting similarity/difference of current at locations distributed among the resistors | C1.3 | Claim about wire resistivity | C1.6 | Claim about what voltage is |
P3 | Predicting similarity/difference of voltage across resistors with different magnitudes | C2.1 | When the voltage increases, the light bulb gets brighter; voltage decreases, the bulb gets dimmer | C2.1 | When the voltage increases, the light bulb gets brighter; voltage decreases, the bulb gets dimmer |
E4.1 | Measuring the voltage (using voltmeter) across each resistor | C2.3 | When the voltage increases, the current increases; voltage decreases, current decreases. There is a direct relationship between voltage and current | C2.3 | When the voltage increases, the current increases; voltage decreases, current decreases. There is a direct relationship between voltage and current |
E6.2 | Measuring the current (using ammeter) in resistors with different magnitudes | C2.2 | When the voltage increases, the current flows faster; voltage decrease, current flows slower | C2.2 | When the voltage increases, the current flows faster; voltage decrease, current flows slower |
C6.2 | The current (using ammeter) is the same in resistors with different magnitudes | C1.4 | Claim about the function of a bulb | E1.11 | Observing the brightness of the bulb without resistance |
E3.6 | Measuring the change in current (using ammeter) when the resistance is increased/decreased | E3.1 | Observing the brightness of the bulb when the resistance is reduced/increased | ||
I1.2 | With high voltage and low resistance, the current flows faster | E3.6 | Measuring the change in current (using ammeter) when the resistance is increased/decreased | ||
C3.4 | When the resistance increases, the current decreases; resistance decreases, current increases. There is an inverse relationship between resistance and current | C1.7 | Claim about what resistor is | ||
C3.3 | When the resistance increases, the current flows slower; resistance decrease, current flows faster | C3.1 | When the resistance increases, the light bulb gets dimmer. The resistance decreases, the bulb gets brighter | ||
I1.1 | Increasing/decreasing resistance would affect the current but would not affect the voltage of the battery and vice versa (i.e., Increasing/decreasing voltage would affect the current but would not affect the resistance) | C3.4 | When the resistance increases, the current decreases; resistance decreases, current increases. There is an inverse relationship between resistance and current | ||
P1 | Predicting effective resistance | C3.3 | When the resistance increases, the current flows slower; resistance decrease, current flows faster | ||
I1.3 | With low voltage and high resistance, the current stops or decreases | I1.4 | Current is affected by both the voltage and the resistance | ||
P2 | Predicting similarity/difference of current at locations distributed among the resistors | I1.1 | Increasing/decreasing resistance would affect the current but would not affect the voltage of the battery and vice versa (i.e., Increasing/decreasing voltage would affect the current but would not affect the resistance) | ||
I3.1 | The current stays the same throughout the resistors because the battery voltage has not changed | P1 | Predicting effective resistance | ||
P3 | Predicting similarity/difference of voltage across resistors with different magnitudes | I2.3 | The effective resistance could be the sum of all resistances because the current would slow down less in lower resistances and slow down more in higher resistances | ||
I2.3 | The effective resistance could be the sum of all resistances because the current would slow down less in lower resistances and slow down more in higher resistances | I3.3 | The current does not stay the same in the resistors because we have resistors with different magnitudes that impede the flow of electrons | ||
I4.2 | Because the current is the same throughout the circuit, the voltage will stay the same across the circuit. If the current is not changing, the voltage hasn’t been changed either | P3 | Predicting similarity/difference of voltage across resistors with different magnitudes | ||
E4.1 | Measuring the voltage (using voltmeter) across each resistor | I4.1 | Voltage is a driving force produced by a battery that can drive a current through a circuit. The greater the voltage the greater will be the current flowing | ||
I4.1 | Voltage is a driving force produced by a battery that can drive a current through a circuit. The greater the voltage the greater will be the current flowing | E6.1 | Observing the speed of electrons after going through resistors with different magnitudes | ||
E6.2 | Measuring the current (using ammeter) in resistors with different magnitudes | I6.2 | The resistors slow the overall current but don’t change the current from resistor to resistor | ||
C6.2 | The current (using ammeter) is the same in resistors with different magnitudes | E7 | Without changing the voltage, observing the effect of changing the magnitude of one resistor out of the other resistors with different magnitudes | ||
E8 | Observing the effective resistance by comparing the circuit to the reduced equivalent circuit | I2.3 | The effective resistance could be the sum of all resistances because the current would slow down less in lower resistances and slow down more in higher resistances | ||
C8.1 | We need to add up the resistances | E6.2 | Measuring the current (using ammeter) in resistors with different magnitudes | ||
I4.3 | The current does not stay the same throughout the resistors because we have resistors with different magnitudes. Therefore, the voltage will be different across each resistor | E4.3 | Observing the voltage drop when the order of the resistors is changed | ||
I6.6 | The electrons have to flow from one resistor to the next. The resistors slow down the whole current in total | ||||
I6.3 | When we increase the resistance, we must increase the voltage as well; otherwise, the current will reduce | ||||
E8 | Observing the effective resistance by comparing the circuit to the reduced equivalent circuit | ||||
C4.1 | The voltage is different across each resistor | ||||
E8 | Observing the effective resistance by comparing the circuit to the reduced equivalent circuit | ||||
C8.1 | We need to add up the resistances | ||||
I6.5 | The current is slowed down according to the added-up ohms of all the resistors | ||||
I5.9 | The amount of voltage drop in resistors/light bulbs depends on the voltage supplied to the resistors/light bulbs and their resistance (i.e., magnitude of the resistors) | ||||
E7 | Without changing the voltage, observing the effect of changing the magnitude of one resistor out of the other resistors with different magnitudes | ||||
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Obaid, T., Nesbit, J.C., Mahmoody Ghaidary, A. et al. Explanatory inferencing in simulation-based discovery learning: sequence analysis using the edit distance median string. Instr Sci 51, 309–341 (2023). https://doi.org/10.1007/s11251-022-09614-4
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DOI: https://doi.org/10.1007/s11251-022-09614-4