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 -