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¶

Claim · All claims
Evidence · 1 study (2 entries) · qualitative r3 · q1
Currency · newest study 2022 · not yet checked against its sources · not reviewed by a person
Evidence quality · No study behind this claim is a peer-reviewed article with a DOI: it rests on an ERIC document (a report, conference paper or thesis). It is kept because 2 design pages cite it; treat it as a lead to check, not an established finding.

Subclaims¶

q1 i? In the authors' earlier report on 20 kindergarteners, students giving a relational definition of the equal sign went from one before to nine after the intervention. → Sung 2022 q1 i? Students accepting 5 = 2 + 3, 2 = 2 and 4 + 2 = 3 + 3 as valid went from nine, three and six before the intervention to 20, 17 and 13 after it. → Sung 2022 (2)

Evidence¶

Sung 2022¶

Sung, Y., Stephens, A., Veltri Torres, R., Strachota, S., Blanton, M., Gardiner, A., Stroud, R., & Knuth, E. (2022). Teacher Language and Gesture in an Intervention Focused on Developing Kindergarteners' Understandings of the Equal Sign. Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. https://eric.ed.gov/?id=ED630361

q1 · i? · qualitative · r3

The article summarises its authors' earlier study (Sung et al., 2021) of 20 kindergarteners, a single group with no comparison class: relational definitions went "from one student prior to the intervention to nine students post-intervention". Descriptive counts; no test reported.

"For example, we found that students grew in their ability to provide a relational definition of the equal sign (from one student prior to the intervention to nine students post-intervention)."

Sung 2022 (2)¶

Sung, Y., Stephens, A., Veltri Torres, R., Strachota, S., Blanton, M., Gardiner, A., Stroud, R., & Knuth, E. (2022). Teacher Language and Gesture in an Intervention Focused on Developing Kindergarteners' Understandings of the Equal Sign. Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. https://eric.ed.gov/?id=ED630361

q1 · i? · qualitative · r3

Same earlier single-group study (Sung et al., 2021), summarised in this article: "only nine students accepted 5 = 2 + 3 as a valid equation" beforehand, and these counts "grew to 20, 17, and 13, respectively" for the three equations. Descriptive counts only.

"For example, prior to the intervention, only nine students accepted 5 = 2 + 3 as a valid equation, only three accepted 2 = 2, and only six accepted 4 + 2 = 3 + 3. At the conclusion of the intervention, these numbers grew to 20, 17, and 13, respectively."

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it

Related Claims¶

• Collaborative critique-and-redesign instruction shifts students from a value-free view of objectivity toward a procedural one — related
• The kindergarten teacher explicitly discussed the forms an equation can take (FORM) with the goal of expanding the range of equations students would accept as valid — related
• A combined language-gesture move, saying \"is the same as\" while pointing to the sides of an equation (ISA + GSIDES), occurred rather frequently in the kindergarten lessons where students wrote equations — related
• Across seven kindergarten equivalence lessons, the teacher's sides-of-equation gesture (GSIDES) was coded 38 times, the most of any language or gesture code — related
• A procedural \"answer is coming\" interpretation of the equals sign leads students to chain arithmetic and errors on missing-number equations — related
• Relational understandings of the equals sign are associated with middle grades mathematics success — related
• Only low-working-memory-capacity students benefited from making pointing gestures when explaining number equations (review attributes this to Marstaller & Burianová, 2013) — related