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131
Transcript
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TitleNight Session, Pascal’s Identity, Clip 6 of 7: Examples of Pascal’s Identity in the notation for combinations
DescriptionThis is the sixth of seven clips from the night session. After Jeff draws Pascal’s Triangle in what the students call “choose” notation, the researcher asks the students to express an instance...
132
Transcript
Analytic icon 1 Analytic found
TitleNight Session, Pascal’s Identity, Clip 7 of 7: Generating and generalizing Pascal’s Identity
DescriptionThis is the last of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) explain to Brian, a late-comer, the meaning of Pascal’s Identity (the addition rule for...
133
Transcript
Analytic icon 1 Analytic found
TitleNight session, Pascal's identity, clip 2 of 7: making sense of factorial notation and "why you multiply"
DescriptionThis is the second of seven clips from the night session. In it, Jeff, Michael, and Romina, along with Ankur (who has just arrived), use the analogy they call “people on a line” to investigate...
134
Transcript
Analytic icon 1 Analytic found
TitleNight session, Pascal's identity, clip 4 of 7: An example of Pascal's identity
DescriptionThis is the second of seven clips from the night session. In it, Jeff, Michael, and Romina, along with Ankur (who has just arrived), use the analogy they call “people on a line” to investigate...
135
Transcript
Student Work
TitleEarly 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?
DescriptionIn 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...
136
Transcript
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 1 of 9: The Distributive property, Distributing a number over variables.
DescriptionIn the first clip in a series of nine from the first of seven interviews in which 8th grade Stephanie explores Early Algebraic Ideas about Binomial Expansion, the researcher, Carolyn A. Maher, asks a...
137
Transcript
Student Work
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 3 of 9: Making general sense of a(x + y) = ax + ay.
DescriptionIn the third clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, Stephanie, an 8th grade student, reviews her conclusions about...
138
Transcript
Analytic icon 1 Analytic found
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, clip 6 of 9: Testing (x + y)(x + y) = x(x + y) + y(x + y) with numbers.
DescriptionIn the sixth 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 justify her...
139
Transcript
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 4 of 9: Making general sense of x times x.
DescriptionIn the fourth 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 focus on the...
140
Transcript
TitleEarly algebra ideas about binomial expansion, Stephanie's interview one of seven, Clip 9 of 9: Building a geometric model of (x+y)(x+y)
DescriptionIn the final ninth clip in the series from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, Stephanie is presented with a drawing of a square with sides...