### Appendix 1: An Outline for an Interview on Prospective Teachers' Algorithmic and Intuitive Knowledge of Rational Numbers

1. Solve (or explain why it is impossible to solve)

1. 4 : 0.25

2. 0.2 : 0.8

3. 0.8 : 0.2

4. 0.25 : 0.6

5. 8.25 : 4.5

6. 3 x 5

7. 8. : 4

2. A student used the following procedure to multiply 0.25 x 5.25 Do you think that the student's answer is correct? Yes/No.

Explain why lines 4, 5, and 6 were written in the way they were?

Explain the position of the decimal point in line 6.

3. A student solves the expression 5 : 0.8 in the following manner:

1st step 2nd step 3rd step Explain steps 1 and 2.

What is the answer to the original division problem (5 : 0.8)?

4. A student used the following procedure to solve : 3.

Stage 1 Stage 2 Stage 3 Stage 4 Do you think that the student's answer is correct? Yes/No

Explain Stages 1 and 2.

5. A student used the following procedure to compare the fractions .

He wrote : 14 x 13 < 11 x 17

Hence Do you think that the student's answer is correct? Yes/No

Do you think that the method he uses for comparing fractions is adequate? Yes/No

6. In the division problem a : b = c, a is the dividend, b is the divisor and c is the quotient.

In the multiplication problem a x b = c, a and b are factors and c is the product.

In a division problem, the dividend can be smaller than 1.

Yes / No. Why?

In an addition problem, the sum can be smaller than one of the addends.

Yes / No. Why?

In a multiplication problem, the product is always greater than 1.

Yes / No. Why?

In a multiplication problem, the product is always greater or equal to each factor.

Yes / No. Why?

In a division problem, the dividend must be greater than the divisor.

Yes / No. Why?

In a division problem, the dividend must be greater than the quotient.

Yes / No. Why?

In a division problem, the quotient must be a whole number.

Yes / No. Why?

In a division problem, the divisor must be a whole number.

Yes / No. Why?

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