TY - GEN TI - Early algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 5 of 9: Beginning to make sense of (x + y)(x + y) DO - https://doi.org/doi:10.7282/T3GM8696 AU - Maher, Carolyn Alexander PY - 1995-11-08 AB - In the fifth clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion researcher Carolyn Maher asks Stephanie to multiply (x + y)(x + y). Stephanie conjectures that this would be x "squared" plus y "squared", symbolically represented by the exponent 2 above x and above y, only to disprove her conjecture by substituting numbers. Stephanie then concludes that, since a(x + y) = ax + ay, (x + y)(x + y) could also be represented as x(x + y) + y(x + y). The problem as presented to Stephanie: What about (x + y)(x + y) ? What would that be? KW - Human sample KW - 6-8 KW - Critical thinking in children--New Jersey--Case studies KW - Learning, Psychology of--Case studies KW - Mathematics education KW - Algebra KW - Problem solving KW - Reasoning and proof KW - Communication KW - Connections KW - Representation KW - Work view KW - Student view KW - Algebra KW - Binomial expansion KW - Color markers KW - Informal learning KW - 8 KW - Direct reasoning KW - Additive reasoning KW - Reasoning by contradiction KW - Substituting numbers for variables KW - Mathematical expressions KW - Female KW - White KW - Public school KW - Distributive property ER -