Interview A

Student Interview Protocol Instructions

Interpretations of Rational Numbers

Attached are the masters for four problems you will use in your interview with three students from among your math classrooms. The attachments are as follows:

• Teacher recording sheet (You will need to make one copy for yourself to use for each student you interview.)

• Blank paper for student work. Copy of number line for Question 4.

Do not discuss the problems with students prior to presenting the tasks. Give all of the problems to the student in one sitting if at all feasible.

Take as many notes as you can on your recording sheet as to how the student explained their thinking. Ask questions of the student to clarify their thinking. This interview will be a teaching interview. Your goal will be for your students to get correct answers for these problems and you are able to use guiding questions to get your students to answer correctly. The main findings from the interviews are the questions you use to guide the students and their reaction to your questions. You are welcome to try to interview a pair of students at the same time. The students seem to feel more comfortable discussing their strategies when they work in pairs. If you try this approach you may want to allow only one pencil per pair to encourage them to work together.

Each question has goals and the teacher recording sheets reflect the goals for each question.

Teacher Recording Sheet
Interview Protocol – Combining Fractions Level A
Directions: Present these items to your student one at a time. Read each question aloud before he or she begins to work on each problem. Ask the student to think out loud as they work. Write down the strategies he or she describes. You are able to use guiding questions to guide the students to accomplish the desired goals. Write down what you said that guided your student(s) accomplish the goals.
  1. Provide student with a blank sheet of paper and pencil.
a)Say: “Draw a picture of the number one-half.”
After the student has drawn the picture of ,
b)Say: “Draw a picture of the number three-fourths.”
Goal: To determine type of mental image the student uses to show these numbers (i.e. circle, number line, dots…).The pictures can be used by students to help with later questions in this interview, as well.
2.Say: Someone told me one-half is the same as two-fourths, do you agree?
Ask student to explain his/her thinking.
Goal:To determine if students have a mental image of being the same as for the same size whole. If student is stuck, ask him/her to draw a picture.
Some students may say that two-fourths covers the same area as one-half but two-fourths is still bigger. Ask the students what it means for two fractions to be the “same”. One way to explain that two fractions have the same value is that they have the same area or that they describe the same length.
3. Show from the last page and read the following problem to the student:
Kate went for a walk. She walked mile and then stopped to take a break. Then she walked mile more. How far did Kate walk altogether?
a)Say: Without working out the exact answer, give me an estimate that is reasonable. (If needed, provide clues: Is this an addition problem or subtraction problem? Is the answer more than or less than mile? More than 1 mile or less than 1 mile?)
b)Say: Tell me what you were thinking to reach this estimate.
Goal: Students should be able to reason that since and.
c)Say: Show me how you would find the exact answer. Talk aloud as you solve the problem. (If you have fraction circles, you could ask the student to show you how they would find the answer using the fraction circles. Students may also use their pictures drawn in question 1 to aid in solving the problem).
Goal: To determine if students recognize the need for common denominators when solving fraction addition problems. Also to determine if students can use knowledge of fraction equivalence, , to help solve the problem. Students should be able to reason that or .
If a student answers but estimated that the answer would be MORE than 1, ask him/her to draw a picture of and then point out estimate from part b and ask if that is a reasonable answer based on the estimate.
***IF STUDENT CANNOT CORRECTLY FIND THE EXACT SUM, END INTERVIEW HERE.***
4.IF STUDENT CORRECTLY ANSWERS 3C ABOVE:
Take out the printed number line on the last page of this document.
Say:Show where is exactly on the number line.
If a student just estimates the location, ask:
Can you find the exact location on the number line?
If a student struggles to make fourths, help him/her make halves, then split the halves in half.
Goal:To determine if students can
  • partition a number line in fourths;
  • locate equivalent fractions on the number line;
  • apply knowledge of equivalent fractions and fraction addition to find sums on a number line.
Note how student partitions the number line.
Does he/she notice that is the same as ? /

Question 3.

Kate went for a walk. She walked mile and then stopped to take a break. Then she walked mile more. How far did Kate walk altogether?

Question 4.

Show whereis exactly on the number line.