CALCULATOR EXPERIMENT

Modeled after a 1980 experiment (Reys, Bestgen, Rybolt, & Wyatt)

and a subsequent 1996 experiment (Reys & Glasgow)

 

           

            Students will be “shown one computation at a time and asked to estimate the answer, record their estimate on a sheet of paper, use the calculator to compute the exact answer, and then record the answer provide by the TI-82 (in this case a TI-83) calculator.” The TI-83 will be programmed to give incorrect answers (see below). The questions are not timed – the students may take as much time as needed.

 

            Questions 1 – 3, the interviewer doesn’t ask any questions and doesn’t make any comments.

 

Question

Problem

Calculator Error

1

2

3

 

 

           

            Questions 4 – 5, the interviewer asks the student, prior to the student using the calculator, how he made his estimate and whether the calculator answer would be more or less that his estimate

 

.

Question

Problem

Calculator Error

4

5

 

 

           

            Questions 6 – 7, the interviewer asks the student, prior to the student using the calculator, to mark on the scale (see below) how confident he is of his estimate and also to record what his “upper bound” for the calculator should be.

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

 

 

Question

Problem

Calculator Error

6

7

 

 

            The experiment ends either when the student questions the calculator’s results or after the last question.

 

Instructor Worksheet

 

Inform the student that we are conducting a test on her mental math and estimation skills. This is not a timed test – the students may take as much time as they want. Explain that you may be taking notes so that we can see how each person estimates.

 

You will show the student one problem at a time.

 

Instruct the student that they are to:

 

Questions #1 – 3: Instructors should not ask any questions or make any comments.

 

Questions #4 – 5: Instructors should ask the student, prior to the student using the calculator, how she made her estimate and whether the calculator answer would be more or less that her estimate.

 

Questions #6-7: Instructors should ask the student, prior to the student using the calculator, to mark on the scale (see below) how confident she is of her estimate and to record what her “upper bound” for the calculator should be.

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

 

The experiment ends either when the student questions the calculator’s results or after the last question at which time you would tell the student about the experiment.

 

Student Worksheet                                                          

 

Name ________________________

 

 

Estimation

 

1.

 

2.

 

3.

 

4.

 

5.

 

6.

 

Confidence Level:

 

7.

 

Confidence Level:

 

 

 

 

 

 

 

 

Calculator

 

1.

 

2.

 

3.

 

4.

 

5.

 

6.

 

 

 

7.

 

Instructor Worksheet                                   Name of Student  ________________

 

1.                          

 

 

2.                                 

 

 

3.                                       

 

 

4.             

 

 

5.                                         

 

 

6.              

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

 

7.                                      

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

 

 

1.   

 

 

 

2.  

 

 

 

3.  

 

 

 

4.  

 

 

 

5.  

 

 

 

6.  

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

7. 

 

Absolutely Not Confident

Moderately Not Confident

Slightly Not Confident

Slightly Confident

Moderately Confident

Very Confident

 

Instructions

 

“We are conducting a test on how students estimate. This is not a timed test – you may take as much time as you want. I will be taking notes so that we can learn about the estimation process.”

 

 “There are only seven problems. I will show you one problem at a time. I want you to estimate the answer (I am NOT looking for an exact answer), and write it down on your sheet. Then use the calculator to confirm your answer and write the exact answer down.”

 

1.  Ask no questions, make no comments

2.  Ask no questions, make no comments

3.  Ask no questions, make no comments

4.  After estimation ask:

§        “How did you make your estimate?” 

§        “Do you expect the calculator’s answer to be higher or lower?”

5.  After estimation ask:

§        “How did you make your estimate?”

§        “Do you expect the calculator’s answer to be higher or lower?”

6.  After estimation ask:

§        “How confident are you of your estimate?” (Show scale)

§        “What do you think the upper bound for the calculator should be?” 

     (Record answer)

7.  After estimation ask:

§        “How confident are you of your estimate?” (Show scale)

§        “What do you think the upper bound for the calculator should be?” 

     (Record answer)