Solving inversion problems increases adults' self-reported use of associativity shortcuts on three-term problems¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r3 · q3
Currency · newest study 2018 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? Adults who first solved 20 inversion problems ('a + b – b' and 'a + b – a') were more likely than a two-term arithmetic control group to self-report using an associativity shortcut on a subsequent 'a + b – c' test problem (phi = 0.29). → Joanne Eaves 2018 q3 i? The effect was also significant on a closed-format self-report question (phi = 0.23), with more shortcut users in the inversion condition. → Joanne Eaves 2018 (2)

Evidence¶

Joanne Eaves 2018¶

Joanne Eaves, Nina Attridge, Camilla Gilmore. (2018). Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts. Learning and Instruction. https://figshare.com/s/230ee9491e0b67d9d3f3

q3 · i? · causal · r3

Pre-registered between-subjects classroom experiment with 109 first-year psychology undergraduates randomly allocated to solve 20 inversion problems or 20 two-term arithmetic problems before a self-report test on '33 + 9 – 5'. Chi-square showed "more shortcut users in the inversion condition" (phi = 0.29); no standardised effect size beyond phi was printed.

"For the open-ended question, the frequencies of users to non-users was significantly different between the two conditions, X2(1, N = 103) = 8.57, p = 0.003, phi = 0.29, with more shortcut users in the inversion condition."

Joanne Eaves 2018 (2)¶

Joanne Eaves, Nina Attridge, Camilla Gilmore. (2018). Increasing the use of conceptually-derived strategies in arithmetic: using inversion problems to promote the use of associativity shortcuts. Learning and Instruction. https://figshare.com/s/230ee9491e0b67d9d3f3

q3 · i? · causal · r3

Same Study 1 sample, closed-format self-report question offering three response options. "More shortcut users in the inversion condition" (phi = 0.23). Exploratory Bayesian analysis gave BF10 = 2.65 (anecdotal evidence).

"This difference was also significant for the responses to the closed question, X2(1, N = 104) = 5.27, p = 0.022, phi = 0.23, with more shortcut users in the inversion condition."

Discussion¶

Learner Variables¶

• Problem Solving — outcome: instruction changes it

Related Claims¶

• Solving only 'a + b – b' inversion problems replicates increased self-reported associativity shortcut use in a new sample — a narrower finding that bears on this claim
• Inversion intervention did not significantly increase problems solved or attempted on a timed problem-solving measure — related
• Self-reported shortcut users solve substantially more conducive problems than non-users, validating the problem-solving measure — related