Estimated parameters show lower-skill students have more variable performance (correlations typically from r = -0.2 to r = -0.4) and harder problems are more discriminating (r = 0.17)¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q2
Currency · newest study 2015 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Skill θ correlates negatively with per-attempt performance variability σ, with correlations typically in range from r = -0.2 to r = -0.4: students with lower skill show larger variability. → Pelánek 2015 q2 i? Problem difficulty correlates slightly with discrimination (r = 0.17), with weaker correlations of variance with difficulty (r = 0.09) and discrimination (r = 0.16). → Pelánek 2015 (2)

Evidence¶

Pelánek 2015¶

Pelánek, R., & Jarušek, P. (2015). Student Modeling Based on Problem Solving Times. International Journal of Artificial Intelligence in Education. https://doi.org/10.1007/s40593-015-0048-x

q2 · i? · associational · r2

Observational analysis of fitted parameters on real Problem Solving Tutor data; skill estimates were approximately normally distributed with larger variance for educational problems than logic puzzles, and the correlation with per-attempt variability is "in range from r =− 0.2t o r =− 0.4".

"This correlation differs for individual problem types, but typically it is in range from r =− 0.2t o r =− 0.4."

Pelánek 2015 (2)¶

Pelánek, R., & Jarušek, P. (2015). Student Modeling Based on Problem Solving Times. International Journal of Artificial Intelligence in Education. https://doi.org/10.1007/s40593-015-0048-x

q2 · i? · design · r2

Observational correlation analysis of problem parameters a, b, c fitted on real tutor data: "more difficult problems are more discriminating ( r = 0.17)", with weaker variance correlations (r = 0.09, r = 0.16). The authors note the results indirectly support the log transformation.

"There is a slight correlation between the basic problem difficulty and its discrimination – more difficult problems are more discriminating ( r = 0.17)."

Discussion¶

Related Claims¶

• Simulated-data study shows difficulty and skill are estimated from few data, while discrimination and variance require far more (at least 30 solvers; 50 problems and 150 students) — related
• Problem difficulty level relates to metacognitive knowledge level: the more difficult the problem, the higher the metacognitive knowledge required — related