Students' initial correct answers can mask reasoning based on a subtraction strategy not previously reported for integer order comparisons¶

Claim · All claims
Evidence · 1 study (2 entries) · qualitative r2 · q2
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Nicole gave correct initial answers on all four comparison situations, yet her reasoning drew on subtraction and the minus sign as an operative sign rather than a predicative sign. → Maike Schindler 2017 q2 i? The authors report that such a subtraction-based comparison strategy had, to their knowledge, not yet been reported in empirical research on the order relation for negative integers. → 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

Qualitative analysis of Nicole's preliminary interview. She treated number pairs like 12 and −15 as an arithmetic subtraction problem, drawing on prior school-based experiences with comparing natural numbers by testing if subtraction 'works'.

"Even though she gives the correct answer on the first try in all four situations (see Table 2), the reasoning in the inferentialist setting reveals that she does not interpret the minus sign as a predicative sign"

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

The authors' discussion of Nicole's case states the subtraction strategy is novel to this research area, while connecting it to Bofferding's (2014) finding that students apply whole-number subtraction strategies to negative numbers.

"Such a strategy has — to our knowledge— not yet been reported in empirical research on the order relation for negative integers."

Discussion¶

Learner Variables¶

• Operations and Place Value — predictor: learners who differ on it differ in outcomes

Related Claims¶

• 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 — related
• Students' errors on the desk-scale number line cluster on subtracting a negative number, with fewer errors on subtracting a positive from a negative or adding a negative to a positive — related
• Before instruction, a strong sixth grader infers integer order reasoning from out-of-school thermometer experiences, with zero as a significant concept — related