On items requiring algebraic generalization, experimental students tended to express rules algebraically and reason with variable quantities, while comparison students gave single numeric answers, left items blank, or treated the number line as static¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r1 · q2
Currency · newest study 2013 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? On item O5, which asked students to generate an algebraic rule from a story in natural language, experimental students tended to express the rule algebraically while comparison students tended to give a single numeric answer or leave the question blank. → Brizuela 2013 q2 i? On item T2, many comparison students failed to express the transformation story as starting at K and treated the number line as static, while experimental students even in 3rd grade expressed the relationships in terms of a variable quantity. → Brizuela 2013 (2)

Evidence¶

Brizuela 2013¶

Brizuela, B.M., Martinez, M.V., and Cayton-Hodges, G.A. (2013). The Impact of Early Algebra: Results from a Longitudinal Intervention. Journal of Research in Mathematics Education, 2(2), 209-241. https://doi.org/10.4471/redimat.2013.28

q2 · i? · causal · r1

Qualitative analysis of students' written work on item O5, which asked students to generate an algebraic rule from a story expressed through natural language; experimental students "te nde d to e xpre ss the rule alge braically" while comparison students gave a single numeric answer or left the question blank.

"E xpe rim e ntalstude nts te nde d to e xpre ss the rule alge braically (se e F igure 5) w hile com parison stude nts te nde d to e xpre ss this as a single num e ric answ e r,or le ft the que stion blank (se e F igure 6)."

Brizuela 2013 (2)¶

Brizuela, B.M., Martinez, M.V., and Cayton-Hodges, G.A. (2013). The Impact of Early Algebra: Results from a Longitudinal Intervention. Journal of Research in Mathematics Education, 2(2), 209-241. https://doi.org/10.4471/redimat.2013.28

q2 · i? · causal · r1

Qualitative analysis of work on item T2, involving transformations on a K-number line: many comparison students "tre ate d the num be r line as static", giving -4 or another numerical answer when the correct answer was K-2, while experimental group students even in 3rd grade expressed the relationships in terms of a variable quantity.

"M any com parison stude nts faile d to e xpre ss that this w as a story that be gan at K and inste ad tre ate d the num be r line as static"

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it

Related Claims¶

• The EA intervention made the most difference on assessment items involving variables, functional relations, intra-mathematical contexts, tables, and algebraic expressions — a broader claim this one bears on
• The authors conclude that elementary students are capable of sophisticated functional thinking and that this calls into question the lack of focus on covarying quantities in many elementary curricula and standards — a broader claim this one bears on