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¶

Claim · All claims
Evidence · 1 study · causal r1 · q3
Currency · newest study 2011 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? After a year-long early algebra intervention, experimental students showed significant improvement in constructing function tables, identifying patterns or relationships, and representing functional rules verbally and symbolically. → Stephens 2011

Evidence¶

Stephens 2011¶

Stephens, A. C., Isler, I., Marum, T., Blanton, M. L., Knuth, E. J., & Gardiner, A. M. (2011). From recursive pattern to correspondence rule: Developing students' abilities to engage in functional thinking. https://eric.ed.gov/?id=ED585054

q3 · i? · causal · r1

The article's conclusion summarizes the study's significant pre-post findings by grade and states these findings support prior work asserting elementary students' capability for functional thinking, calling into question curricula that omit covarying quantities.

"([perimental stXdents shoZed significant improveme nt in this stXdy in their abilities to constrXct fXnction tables in grades 3 and 4 , identify patterns or relationships in tables in grade 3 , and represent a fXnctional rXle verbally in grades 3 and 4 and sy mbolically in all grades ."

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it

Related Claims¶

• After an early algebra intervention, the number of kindergarteners giving a relational definition of the equal sign went from one to nine, and acceptance of non-standard equation forms rose, as reported from the authors' earlier study — related
• After the intervention, posttest differences in identifying patterns in a function table were only marginally significant at grade 3, but experimental fifth graders more often described covariational relationships than recursive patterns — a narrower finding that bears on this claim