Part 2: What you did during the rehearsal
For this part of the reflection regarding what I did during my rehearsal, I have chosen to analyze how I Elicited and Responded to Student Thinking and how I Represented Students’ Mathematical Thinking.
Eliciting & Responding to Student Thinking
To demonstrate how I elicited and responded to student thinking, I have chosen to examine my video from 2:45 – 3:25. During this time, I asked students for their answers to the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to state their response, I questioned their thinking and reasoning behind it in the hopes that they would use their prior knowledge to explain their solution in the appropriate terms and mathematical language. I was also hoping to target the students’ use of square root functions in solving for the inverse of a function, as well as the domain and range of both the function and its inverse. In doing so, I wanted to test their knowledge of whether they knew and understood specific math terms, such as domain and range, and whether these are useful to know when determining the inverse of a function and whether this inverse is or is not a function. Ultimately, I was hoping to target more specifically for “Goals for students’ learning of mathematical concepts—Students will learn about inverses” and for “Goals for students’ learning of mathematical practices—Students will analyze the situation given to them and with their prior knowledge, figure out and explain what is the best way to go about it”. I decided to begin the rehearsal with a broad question regarding what were the answers the students came up with, with regards to the problem. At 2:44: “I want to know where you guys think the mistake is.” At 2:47: Kassandra: “I don’t think there is a mistake.” Between 2:50-2:59: After choosing Kassandra for her answer regarding where she believed the mistake in the solution was, I further said: “Could someone, or actually Kassandra, could you explain to me why there is no mistake?”. In this manner, I was hoping to press for evidence or a reason. In essence, I was asking Kassandra to explain her reasoning behind her thinking. By asking this question, I was hoping to target the instructional goal “Students will analyze the situation given to them and with their prior knowledge, figure out and explain …show more content…
I was targeting the mathematical instructional goal, “Students will develop their critical thinking skills by listening to their peers when they state their reasoning for their choices and by analyzing what they say”. The goal of this question was to see if the students were able to figure out that Kassandra’s answer was incorrect. In doing so, this would have demonstrated their mastery of inverse functions, the properties of functions, and what was the best way to solve this particular situational problem. Moreover, in receiving the answers of the rest of the class, this would have allowed me to visualize whether more time needed to be spent on the inverse of quadratic functions or related topics, such as square root
For this part of the reflection regarding what I did during my rehearsal, I have chosen to analyze how I Elicited and Responded to Student Thinking and how I Represented Students’ Mathematical Thinking.
Eliciting & Responding to Student Thinking
To demonstrate how I elicited and responded to student thinking, I have chosen to examine my video from 2:45 – 3:25. During this time, I asked students for their answers to the problem given to them and their reasoning for this answer. In essence, I was hoping to target students’ knowledge of inverse functions and how they applied it to solving a situational problem. More specifically, if they were able to find the error in a solution of an inverse algebraic problem and explain their reasoning for this error. Moreover, once a student was able to state their response, I questioned their thinking and reasoning behind it in the hopes that they would use their prior knowledge to explain their solution in the appropriate terms and mathematical language. I was also hoping to target the students’ use of square root functions in solving for the inverse of a function, as well as the domain and range of both the function and its inverse. In doing so, I wanted to test their knowledge of whether they knew and understood specific math terms, such as domain and range, and whether these are useful to know when determining the inverse of a function and whether this inverse is or is not a function. Ultimately, I was hoping to target more specifically for “Goals for students’ learning of mathematical concepts—Students will learn about inverses” and for “Goals for students’ learning of mathematical practices—Students will analyze the situation given to them and with their prior knowledge, figure out and explain what is the best way to go about it”. I decided to begin the rehearsal with a broad question regarding what were the answers the students came up with, with regards to the problem. At 2:44: “I want to know where you guys think the mistake is.” At 2:47: Kassandra: “I don’t think there is a mistake.” Between 2:50-2:59: After choosing Kassandra for her answer regarding where she believed the mistake in the solution was, I further said: “Could someone, or actually Kassandra, could you explain to me why there is no mistake?”. In this manner, I was hoping to press for evidence or a reason. In essence, I was asking Kassandra to explain her reasoning behind her thinking. By asking this question, I was hoping to target the instructional goal “Students will analyze the situation given to them and with their prior knowledge, figure out and explain …show more content…
I was targeting the mathematical instructional goal, “Students will develop their critical thinking skills by listening to their peers when they state their reasoning for their choices and by analyzing what they say”. The goal of this question was to see if the students were able to figure out that Kassandra’s answer was incorrect. In doing so, this would have demonstrated their mastery of inverse functions, the properties of functions, and what was the best way to solve this particular situational problem. Moreover, in receiving the answers of the rest of the class, this would have allowed me to visualize whether more time needed to be spent on the inverse of quadratic functions or related topics, such as square root