Representing Students’ Mathematical Thinking
Initially, before the lesson began, I split the chalkboard into three parts: 1) the inverse algebraic problem with each line representing a step, 2) Students’ answers, and 3) Reasoning. In doing so, I was planning to write down the answers of the students and their reasoning behind their answers. Therefore, the two moments in which I represented students’ mathematical thinking are as followed:
Between 2:45—3:21: Kassandra’s answer and reasoning written on the chalkboard
By writing Kassandra’s answer and reasoning on the chalkboard, I was hoping to target the mathematical instructional goal: “Students will describe the process used in determining their choices for the error. Therefore, by representing students’ mathematical thinking in an open …show more content…
Anita: “Can you tell me what your mistake was? Maybe someone can help you?”
Danny: “My answer is different from the one on the board.”
Anita: “Okay.”
Danny: “I guess I didn’t square root the nine.”
Anita: “Okay, can you explain why you didn’t?”
Danny: “I don’t know what I was thinking.
Anita: “Can you explain to me what your mistake looks like? What did you write? Or can you come to board and write it down what your mistake is?
Danny: “I would rather not…From step 4 to step 5, I point to step 4 and then to step 5 of the steps written on the board, instead of square rooting the whole thing, I just square rooted the x.
Anita: “Okay. So he is saying that from here to here, instead of taking, I’ll just write it over here.” Draws a square to write what Danny is saying. “He wrote something like”, writes on board, √x/9 then underneath, writes (√x)⁄9.
Danny: “Yes”.
Anita: “Can you explain to me why you wrote that?”
Danny: “I don’t know”.
Anita: “What was your thinking behind it?”
Danny: “I have no idea”.
Anita: “Can someone try to think what maybe Danny did or someone who made the same mistake as him could tell me what his process might
Initially, before the lesson began, I split the chalkboard into three parts: 1) the inverse algebraic problem with each line representing a step, 2) Students’ answers, and 3) Reasoning. In doing so, I was planning to write down the answers of the students and their reasoning behind their answers. Therefore, the two moments in which I represented students’ mathematical thinking are as followed:
Between 2:45—3:21: Kassandra’s answer and reasoning written on the chalkboard
By writing Kassandra’s answer and reasoning on the chalkboard, I was hoping to target the mathematical instructional goal: “Students will describe the process used in determining their choices for the error. Therefore, by representing students’ mathematical thinking in an open …show more content…
Anita: “Can you tell me what your mistake was? Maybe someone can help you?”
Danny: “My answer is different from the one on the board.”
Anita: “Okay.”
Danny: “I guess I didn’t square root the nine.”
Anita: “Okay, can you explain why you didn’t?”
Danny: “I don’t know what I was thinking.
Anita: “Can you explain to me what your mistake looks like? What did you write? Or can you come to board and write it down what your mistake is?
Danny: “I would rather not…From step 4 to step 5, I point to step 4 and then to step 5 of the steps written on the board, instead of square rooting the whole thing, I just square rooted the x.
Anita: “Okay. So he is saying that from here to here, instead of taking, I’ll just write it over here.” Draws a square to write what Danny is saying. “He wrote something like”, writes on board, √x/9 then underneath, writes (√x)⁄9.
Danny: “Yes”.
Anita: “Can you explain to me why you wrote that?”
Danny: “I don’t know”.
Anita: “What was your thinking behind it?”
Danny: “I have no idea”.
Anita: “Can someone try to think what maybe Danny did or someone who made the same mistake as him could tell me what his process might