Conceptswk1/Conceptswk3
This scatterplot compares concept scores in Week 1 (conceptswk1) with concept scores in Week 3 (conceptswk3). Each dot represents one student. There is a positive trend, meaning students who performed well in Week 1’s concept section generally also performed well in Week 3’s concept section. There are clusters forming, students performance tends to be stable over time, students who were strong at week 1 likely maintained or improved it, while weaker students also remained weaker. students could be grouped into high, medium, and low performance clusters for conceptual knowledge.
equationswk1/equationswk3
This scatterplot compares concept scores in Week 3 with equation scores in Week 3. There is a looser positive correlation, meaning students who did well on concept questions in Week 3 were more likely to also do well on equation questions.
conceptswk1/equationswk1
This would track students’ equation performance from Week 1 to Week 3. This chart would help identify whether some students improved significantly in their equation-solving abilities. It would highlight a potential “improver” cluster, students who started with low scores but made notable progress. This would reinforce the idea that some students might fall into a “low-to-high” improvement cluster.
conceptswk3/equationswk3
This would compare how students’ concept understanding at the start of the course relates to their equation-solving ability in the same week. Seeing some students who are good at concepts but bad at equations would suggest mixed abilities.
K-Means clustering Biplot
The K-Means clustering analysis grouped students into four clusters, which align well with the initial interpretation from the scatterplots. These clusters likely represent:
High performers who consistently did well across all quizzes.
Medium performers with average scores across both weeks.
Low performers who struggled across both weeks.
A group with inconsistent performance or notable improvement in Week 3, especially in equations.