Students with very different prior math achievement generate similar numbers of representations and solution methods during Productive Failure¶

Claim · All claims
Evidence · 1 study (2 entries) · associational r2 · q3 · i0–i2
Currency · newest study 2023 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i0 In the variance unit, schools differing greatly in prior math achievement showed no significant difference in number of RSMs (d = 0.03). → Manu Kapur 2023 q3 i2 In the ratios unit, the higher-achieving school generated modestly more RSMs (d = 0.48), far less than its prior-achievement advantage (d = 2.12). → Manu Kapur 2023 (2)

Evidence¶

Manu Kapur 2023¶

Manu Kapur, Janan Saba and Ido Roll. (2023). Prior math achievement and inventive production predict learning from productive failure. npj Science of Learning 8:15. https://doi.org/10.1038/s41539-023-00165-y

q3 · i0 · associational · r2

Quasi-experimental variance-unit study of eighth graders from two schools with significantly different PSLE profiles. ANOVA on group-level RSM counts found no significant school difference (d = 0.03), despite schools differing in prior achievement.

"An ANOVA did not reveal any significant difference between the two schools on the number of RSMs, for school A: M = 5.23, SD = 1.50, for school B: M = 5.19, SD = 1.49, F(1, 103) = 0.015, p = 0.903, d = 0.03."

Manu Kapur 2023 (2)¶

Manu Kapur, Janan Saba and Ido Roll. (2023). Prior math achievement and inventive production predict learning from productive failure. npj Science of Learning 8:15. https://doi.org/10.1038/s41539-023-00165-y

q3 · i2 · associational · r2

Ratios-unit study of seventh graders: the higher-achieving school generated significantly more RSMs, d = 0.48. The discussion notes this was "less than a quarter of their pre-existing difference in their prior math achievement (d = 2.12)".

"An ANOVA revealed a significant difference between the two schools on the number of RSMs in ratio unit, for school A: M = 6.83, SD = 1.44, for school B: M = 6.16, SD = 1.38, F(1, 110) = 5.669, p = 0.019, d = 0.48."

Discussion¶

Learner Variables¶

• Prior Knowledge — predictor: learners who differ on it differ in outcomes

Related Claims¶

• Prior math achievement has at most a small effect on learning from Productive Failure, and topic-specific prerequisite knowledge has none — related
• Mixed-ability groups generated a broader range of RSMs than all-low and all-high ability groups, relating to better uptake of the canonical formula — related
• Diversity of student-generated representations and solution methods is significantly correlated with learning from PF — related
• The two schools differed drastically in prior math achievement as measured by the PSLE — related
• The control and experimental schools did not differ significantly in PSLE entrance scores — related