Folding back to inner layers of understanding supported Grade 10 learners' geometric reasoning on proof tasks¶

Claim · All claims
Evidence · 1 study · qualitative r3 · q2
Currency · newest study 2018 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? In a teaching experiment with two Grade 10 groups, learners folded back to the property noticing level and returned to formalising without external prompts to conclude two triangles were similar. → Mabotja 2018

Evidence¶

Mabotja 2018¶

Mabotja, S., Chuene, K., Maoto, S., & Kibirige, I. (2018). Tracking Grade 10 learners' geometric reasoning through folding back. Pythagoras, 39(1), a371. https://doi.org/10.4102/pythagoras.v39i1.371

q2 · i? · qualitative · r3

Qualitative teaching-experiment analysis of Extract 1, in which two learners (John and Koena) proved that triangle PST is similar to triangle PQR. The authors interpret the pair's use of the F-shape mnemonic as folding back to property noticing, after which they returned to formalising without external prompts.

"After folding back to the property noticing level through using the F shape mnemonic and thickening their understanding through successfully applying the mnemonic on the given problem, the learners returned to the formalising layer without external prompts to conclude that the two triangles were similar."

Discussion¶

Learner Variables¶

• Geometric Reasoning — outcome: instruction changes it

Related Claims¶

• Learners' critical sharing of ideas and the teacher's intentional intervention were the two critical factors for effective folding back — related
• Discontinuities during folding back, including algebraic errors while working outside the geometry topic, did not prevent effective folding back — related
• Teacher interventions that are not explicit encourage learners' self-awareness of the limitations of their current understanding without prescribing a solution — related
• Embodied collaborative construction can build shared geometric reasoning — related