Factors affecting learning of vector math from computer-based practice: Feedback complexity and prior knowledge

In experiments including over 450 university-level students, we studied the effectiveness and time efficiency of several levels of feedback complexity in simple, computer-based training utilizing static question sequences. The learning domain was simple vector math, an essential skill in introductory physics. In a unique full factorial design, we studied the relative effects of “knowledge of correct response” feedback and “elaborated feedback” (i.e., a general explanation) both separately and together. A number of other factors were analyzed, including training time, physics course grade, prior knowledge of vector math, and student beliefs about both their proficiency in and the importance of vector math. We hypothesize a simple model predicting how the effectiveness of feedback depends on prior knowledge, and the results confirm this knowledge-by-treatment interaction. Most notably, elaborated feedback is the most effective feedback, especially for students with low prior knowledge and low course grade. In contrast, knowledge of correct response feedback was less effective for low-performing students, and including both kinds of feedback did not significantly improve performance compared to elaborated feedback alone. Further, while elaborated feedback resulted in higher scores, the learning rate was at best only marginally higher because the training time was slightly longer. Training time data revealed that students spent significantly more time on the elaborated feedback after answering a training question incorrectly. Finally, we found that training improved student self-reported proficiency and that belief in the importance of the learned domain improved the effectiveness of training. Overall, we found that computer based training with static question sequences and immediate elaborated feedback in the form of simple and general explanations can be an effective way to improve student performance on a physics essential skill, especially for less prepared and low-performing students.

Figure 1

Examples of each question type used during training. From left to right, top to bottom: Dot product determine sign, dot product determine magnitude, dot product compare magnitudes, cross product determine direction, cross product determine magnitude, and cross product compare magnitudes.

Figure 2

Examples of EF images used in dot or cross product training.

Figure 3

Experiment 1 mean assessment scores for each condition.

Figure 4

Experiment 1 mean assessment scores for each condition, for students with high and low course grades.

Figure 5

Mean assessment scores for experiment 1 feedback conditions, split by high and low scores on the first six training questions. The dotted line represents the mean control score.

Figure 6

Experiment 2 mean assessment scores for each condition.

Figure 7

Mean assessment scores for experiment 2 students for each training condition, split by high or low scores on the first six training questions (prescores). The dotted line represents the mean control score.

Figure 8

Experiment 2 mean scores for EF present or absent and for students with high or low score on the first six questions of training.

Figure 9

Median explanation times for each training trial within a question type and for correct or incorrect responses in each trial.

Figure 10

Box plots indicating 1st, 2nd, and 3rd quartiles of explanation times on the first three cross product compare magnitudes questions, split by student response patterns on the first three questions.

Figure 11

Experiment 2 mean assessment scores by score on first 6 training questions (prescore), separated by perceived importance of the topic for the course.