After a lesson series, two sixth graders could switch flexibly between perspectives when comparing negative integers; one distinguished number-line order from context-based absolute-value reasoning about debts¶

Claim · All claims
Evidence · 1 study (2 entries) · qualitative r2 · q2
Currency · newest study 2017 · checked against its sources 2026-10-19 (automated, 2 of 2 entries) · not reviewed by a person

Subclaims¶

q2 i? In the post interviews, both students inferred their reasoning from the number line and could switch perspectives, drawing flexibly on different prior experiences when comparing negative integers. → Maike Schindler 2017 q2 i? Tom distinguished the mathematically correct number-line reasoning from reasoning on absolute value within the debts-and-assets context, judging which debts are greater. → Maike Schindler 2017 (2)

Evidence¶

Maike Schindler 2017¶

Maike Schindler, Stephan Hußmann, Per Nilsson, Arthur Bakker. (2017). Sixth-grade students' reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Math Ed Res J 29:471–492. https://doi.org/10.1007/s13394-017-0202-x

q2 · i? · qualitative · r2

Authors' synthesis of the two post interviews, in which both students drew on the number line, an external representation crucial in their lesson series, illustrating the impact of school-based experiences on reasoning on the order relation.

"Our results support the finding that students have the ability to switch perspectives, to reason differently, and to be able to draw flexibly on different prior experiences and inferences when comparing negative integers"

Maike Schindler 2017 (2)¶

Maike Schindler, Stephan Hußmann, Per Nilsson, Arthur Bakker. (2017). Sixth-grade students' reasoning on the order relation of integers as influenced by prior experience: an inferentialist analysis. Math Ed Res J 29:471–492. https://doi.org/10.1007/s13394-017-0202-x

q2 · i? · qualitative · r2

Tom's post-interview episode comparing −8 and −12: he gave the mathematically correct number-line answer and additionally noted that in the debts context −12 would be the greater debt, a distinction the authors call reasonable in certain situations.

"the minus eight is greater because it is closer to zero. (5 s) Yes, and when a number is closer to zero, then it is greater. If there stood, however, when, say, er, which number, well which debts are greater, then it would be the minus twelve"

Discussion¶

Learner Variables¶

• Mathematical Flexibility — outcome: instruction changes it

Related Claims¶

• Students' initial correct answers can mask reasoning based on a subtraction strategy not previously reported for integer order comparisons — related
• Before instruction, a strong sixth grader infers integer order reasoning from out-of-school thermometer experiences, with zero as a significant concept — related
• Walking the body-scale number line disrupted students' prior misconceptions and erroneous rules, which resurfaced when they returned to the desk-scale number line — reports the opposite
• Students who got stuck on the desk-scale number line proactively returned to the body-scale number line to validate their answers, achieving perspectival mutuality — related