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 -