TY - GEN
TI - Early algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 2 of 9: Distributing a variable over other variables, Does it check out with numbers?
DO - https://doi.org/doi:10.7282/T3765DC4
AU - Maher, Carolyn Alexander
PY - 2012-04-10
AB - In the second clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, researcher, Carolyn A. Maher, asks Stephanie, an 8th grade student, whether a variable "a" could be distributed over a quantity composed of the sum of two other variables and how this would be represented symbolically. Stephanie, after conjecturing that a(x + y) would be the same as ax + ay, begins by substituting the numbers 2, 3 and 4 for "a", "x" and"y" in each expression to test her conjecture. When asked whether her conjecture will always work, she questions the usefulness of distributing multiplication over addition in cases where there are numbers, rather than variables, to express the sum. She then tests her conjecture by substituting the numbers 2 and 4 for "a" and "y", setting the resulting expression equal to 14, the result of the earlier substitution, and solving for "x".
The problem as presented to Stephanie:
a (x + y) is written on Stephanie's paper. The researcher asks: What do you think this might be?
Stephanie's equation for checking her conjecture:
2(x + 4) = 14
KW - 6-8
KW - Mathematics education
KW - Learning, Psychology of--Case studies
KW - Critical thinking in children--New Jersey--Case studies
KW - Algebra
KW - Problem solving
KW - Reasoning and proof
KW - Communication
KW - Connections
KW - Work view
KW - Student view
KW - Algebra
KW - Simplify expressions
KW - Color markers
KW - Informal learning
KW - 8
KW - Direct reasoning
KW - Additive reasoning
KW - Considering a simpler problem
KW - Female
KW - White
KW - Public school
KW - Distributive property
KW - Human sample
KW - Representation
ER -