Interview Transcript with Subject A

Interview Transcript with Subject A

Female

Level: Integrated Mathematics I

10th grade

Received score of 88 percent on the unit test.

Received a final grade of B in the class.

Interviewer: Define in your own words the mathematical concept of a function. (Wait time: 6 sec) Analysis

Subject A: A function is on a graph whether or not a vertical line crosses two dots. That is what it is on a graph. I do know about the equations at all. (Responding/Stucturing)

Interviewer: If it crosses two dots is it a function? (Wait time: <3 sec) Knowledge

Subject A: It is not a function. (Responding)

Interviewer: What are the parts of a function? (Wait time: 6 sec) Analysis

Subject A: Oh my gosh, umm, I can’t remember. I just cannot remember. (Responding)

Interviewer: You answered how you know data is a function is? (Wait time: < 3 sec)

Subject A: If a vertical line crosses two dots then it is not a function. (Responding)

Interviewer: If I gave you a table of data how would you tell me if it is a function? (Wait time: 4 sec) Analysis

Subject A: I don’t know. (Responding)

Interviewer: We are going to go over some graphs. Application

Subject A: (Responding)

A. Function

1. Not a function
2. I think it would be a function.
3. Function
4. Function
5. Not a function If it crosses two dots it is not a function.

Interviewer: Which of these equations indicate y is a function of x? (Wait time: <3 sec) Application

Subject A: A, B I think, I don’t think C and D are. (Responding)

Interviewer: Why would you say C and D are no? (Wait time: <3 sec) Application

Subject A: Because this one is xy = 8 there is nothing else in there so you would not be able to graph it. (Structuring)

Subject A: D looks more like an algebraic expression than a function. (Responding)

Interviewer: Can’t an algebraic expression be a function? (Wait time: < 3 sec) Analysis

Subject A: These are both algebraic expressions, but y is always the equals and that one isn’t. (Structuring)

Interviewer: If y is by itself then it is a function? (Wait time: < 3 sec) Comprehension

Subject A: Yes, that is the way I understood it. (Reacting)

Subject A: I am going to guess on this one and say yes. (Responding)

Interviewer: That one (e.) is using the table and you say “ yes it is a function”. How did you guess that? (Wait time: 9 sec) Analysis [REALLY EXTENDED WAIT TIME!]

Subject A: Well, it wait, actually that wouldn’t be a function it is one of those graph things, like a scatter plot, so it wouldn’t be a function. I am understanding things I did not get in pre-algebra last year. (Structuring/Reacting)

Interviewer: What would be the difference between a scatter plot and a function? (Wait time: < 3 sec) Analysis

Subject A: A scatter plot graphs like if it were temperature and time it would graph how much the temperature would go up in a certain amount of time. It is like the difference between two variables. It is like a positive and negative thing. (Responding/Structuring)

Interviewer: A scatter plot is two variables plotted. What would a function be? (Wait time: 7 sec) Analysis

Subject A: Ohh! Something that looks like this (pointing to graph on sheet) I can do these, I just cannot explain them. (Reacting)

Student reads last question relating to caterpillar. Analysis

Subject A: I don’t understand that. I think it would be function, you would have to guess at the amount of time it would take to get to that point. You are going to have an x and y in the problem anyway. (Structuring)

Interviewer: You are going to have an x and a y? (Wait time: < 3 sec) Application

Subject A: Y could be the time and x could be the point he starts at. (Responding)

Interviewer: So you would say that could be a function and x could be the point he is at and y could be the time? (Wait time: < 3 sec) Analysis

Subject A: The number that is in the problem could be how many squares he needed to go to get that point. (Structuring)

Interviewer: You would not apply the vertical line test to this drawing, you would graph it separately. (Wait time: < 3 sec) Application

Subject A: Yes. (Responding)

Interview Transcript with Subject B

Male

Level: Integrated Mathematics I

10th grade

IEP student learning challenged in language arts

Received score of 88 percent on the unit test.

Received a final grade of C in the class.

Interviewer: Define in your own words, the mathematical concept of a function. (Wait time: 7 sec) Synthesis

Subject B: Of a function. Umm. I would have to see like the graph and if I saw a vertical line cross two times, that is not a function. (Structuring)

Interviewer: Is there any other way you could determine something is a function? (Wait time: 4 sec) Analysis

Subject B: If it goes through. The same up and down quadrants, the top and bottom ones, it would not be a function. (Structuring)

Interviewer: What are the parts or pieces of a function? (Wait time: <3 sec) Analysis

Subject B: Lines and a graph. (Responding)

Interviewer: If you had raw data or numbers how would you know if they are a function? (Wait time: 4 sec) Analysis

Subject B: Like points on a grid? (Wait time: < 3 sec) (Soliciting)

Interviewer: No, you had numbers, like year and population. For Junction City year in one column and population in another. How would you tell if that is a function? (Wait time: < 3 sec) Analysis

Subject B: I am not too sure. (Responding)

Interviewer: Show student the worksheet.

Interviewer: Can you tell me which of these graphs are functions? (Wait time: < 3 sec) Application

Subject B: (Responding)

1. Function
2. Not a function
3. Function

Interviewer: Why is B not a function? (Wait time: < 3 sec) Application

Subject B: It would not pass the vertical line test. (Responding/Structuring)

Interviewer: C is a function? (Wait time: < 3 sec) Application

Subject B: I think it would be because it could cross like this at that one point and it is a function. (Responding)

Subject B:

1. Function
2. Function
3. Not a function
4. Function, wait, so is goes like the count goes over the line right there.

Interviewer: What do those circles on the lines mean to you? (Wait time: < 3 sec) Knowledge

Subject B: I am not too sure. (Responding)

Interviewer: If it meant the graph went to that point and included that point? (Wait time: < 3 sec) Application

Subject B: Plus that other point? (Wait time: < 3 sec) (Soliciting)

Interviewer: Yes

Subject B: Then it would not be a function. (Responding)

Interviewer: If it did not go to that point and did not include that point? (Wait time: < 3 sec) Application

Subject B: So it would be like ______It would be a function. (Responding)

Interviewer: Given the equations in question 2, which ones indicate y is a function of x? (Wait time: 19 sec) Application

Subject B: I am guessing c.

Interviewer: Is that the only one you think is a function? (Wait time: 8 sec) Application

Subject B: Maybe e. (Responding)

Interviewer: Why do you think those two are functions? (Wait time: < 3 sec) Analysis

Subject B: Because they are different than the other ones. (Responding/Structuring)

Interviewer: On e x = club member’s name and y is amount owed and you think that is a function. Is there anything more that you can tell me that helped you determine that is a function other than it is different? (Wait time: 11 sec) Analysis

Subject B: I don’t really know. (Responding)

Student reads the last question relating to caterpillar. (Wait time 19 sec) Analysis/Application

Subject B: So you are like putting that on graph paper? (Soliciting)

Interviewer: What this is representing is the path of the caterpillar (point to picture). (Wait time 15 sec) analysis

Subject B: I think it would not be a function. Because if you put it on graph paper like it would up and down lines would cross these two lines here. (Responding/Structuring)

Interview Transcript with Subject C

Male

Level: Algebra I

10th grade

Interviewer: You would solve the equation and it would give you what? (Wait time: 3 sec) Application

Subject C: It would give me the plot and the points on the graph. (Structuring)

Interviewer: And then how would you tell if those were functions versus just points? (Wait time: < 3 sec) Application

Subject C: I do not know. (Responding)

Interviewer: If I gave you a table with x and y values as in question 2 e could you tell me if they are a function? (Wait time: 3 sec) Application

Subject C: No (Responding)

Interviewer: Can you tell me if you think A is a function? (Wait time: 4 sec) Application

Subject C: A Yes (Responding)

Interviewer: How about B? (Wait time: 9 sec) Application

Subject C: I am not sure. (Responding)

Interviewer: Guess on C. Application

Subject C: No it is just a point. (Responding)

Interviewer: How about D? (Wait time: < 3 sec) Application

Subject C: No. It is just a flat line. (Responding)

Interviewer: How about E? (Wait time: < 3 sec) Application

Subject C: Yes, I think all of them that are curved like that are functions. (Responding/structuring)

Interviewer: How about F? (Wait time: < 3 sec) Application

Subject C: Yes. (Responding)

Interviewer: How about G? (Wait time: 4 sec) Application

Subject C: No (Responding)

Interviewer: So one of the things in your concept definition of a function is its graph would be curved? (Wait time: < 3 sec) Analysis

Subject C: Yes. (Responding)

Interviewer: Question 2. Which equations indicate y is a function of X? (Wait time: 13 sec) Analysis

Subject C: B (Responding)

Interviewer: Why B? (Wait time: 4 sec) Analysis

Subject C: I do not know, I cannot really explain it. I am just trying to remember stuff from algebra last year. I think x and y should be separated. They should not be on the same side. And I do not think there should be an exponent on x. (Structuring)

Interviewer: If x is club member name and y is club member dues, is y a function of x? (Wait time: 3 sec) Analysis

Subject C: Yes. (Responding)

Interviewer: Do you have any thought on what makes that a function? (Wait time: 14 sec) Application

Subject C: No. (Responding)

Student reads the last question relating to caterpillar.

Subject C: I do not know, it is confusing. (Responding/Reacting)

Interviewer: Going back to what you were saying earlier. If this were on graph paper this would be curved, but would it be a function? (Wait time: 4 sec) Comprehension

Subject C: Umm. I am not sure if it would be a function or not. (Responding)

Interviewer: Go back and lets summarize your concept of a function is a mathematical equation? (Wait time: < 3 sec) Knowledge

Subject C: Yes. (Responding)

Interviewer: And its graph would not be a straight line? (Wait time: < 3 sec) Knowledge

Subject C: It would be a parabola. (Responding)

Interviewer: And problem five might or might not be a function? (Wait time: < 3 sec) Analysis

Subject C: It would help if you graphed it. (Structuring)

Interviewer: So, this actually would not be the graph? The graph would look different that that? (Wait time: 13 sec) Analysis

Subject C: I would have to see the graph like in question 1 to see if it is a function or not. (Structuring)

You had a lot of short answers though out the interview. I think students had a hard time connecting to a strict mathematical concept of function.