Relational understandings of the equals sign are associated with middle grades mathematics success¶

Claim · All claims
Evidence · 1 study · design r1 · q2
Currency · newest study 2024 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q2 i? Success in middle grades mathematics has been associated with relational understandings of the equals sign and flexible comparison of approaches focused on structure and relation. → Haiwen Chu 2024

Evidence¶

Haiwen Chu 2024¶

Haiwen Chu, Brent Jackson. (2024). Engaging English Learners With Equivalence as a Crosscutting Concept in Mathematics. WestEd. https://eric.ed.gov/?id=ED671702

q2 · i? · design · r1

The brief reports, citing Knuth et al. (2006) and Rittle-Johnson & Star (2009), this association; the brief is a narrative attribution, not a study the authors conducted, and no effect sizes are printed.

"Success in middle grades mathematics has been associated with relational understandings of the equals sign (Knuth et al., 2006) and the ability to flexibly compare approaches that focus more on structure and relation than on mechanical multiplication or numerical evaluation of algebraic expressions (Rittle-Johnson & Star, 2009)."

Discussion¶

Learner Variables¶

• Algebraic Thinking — predictor: learners who differ on it differ in outcomes

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
• In a kindergarten early algebra intervention, the teacher's equal-sign language shifted with lesson focus, from definitions and \"is the same as\" early on to \"balanced\" talk and balance gestures when evaluating and solving 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
• 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
• Comparing cases side by side improves learning and transfer by a moderate average amount, though in one algebra study it raised procedural knowledge and flexibility but not conceptual knowledge — related
• A procedural \"answer is coming\" interpretation of the equals sign leads students to chain arithmetic and errors on missing-number equations — related
• Students' knowledge of equals sign definitions relates to their equation-solving performance at the student level — related