Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 5 of 11: Developing the correspondence between towers 4-cubes tall, selecting from two colors, Pascal's Triangle and the symbolic algebraic expansion of (a+b) to the 4th power

In the fifth clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie responds to questions from researchers Carolyn Maher and Robert Speiser about the correspondence between towers 4-cubes tall, selecting from blue and green cubes, and the symbolic binomial expansion of (a+b) to the 4th power. After developing the correspondence for Unifix-cube towers with no blue cubes, exactly one blue cube and exactly three blue cubes, Stephanie refers to her Pascal's Triangle chart to determine the number for choosing exactly two from a set of four and then completes the set. She then rewrites the symbolic expansion to correspond to her five cases of towers and indicates the combinatorics notation for the subset of towers with exactly two of each color. The problems as proposed to Stephanie are: What is the expanded expression for (a+b) to the 4th power? How does the symbolic expansion correspond to the Towers selecting from two colors? How would combinatorics notation describe the expansion and the Towers?Robert B. Davis Institute for Learning. (1996). Early algebra ideas about binomial expansion, Stephanie's interview six of seven, Clip 5 of 11: Developing the correspondence between towers 4-cubes tall, selecting from two colors, Pascal's Triangle and the symbolic algebraic expansion of (a+b) to the 4th power. [video]. Retrieved fromTranscript and student work are also available