The following section comes from the assessor’s manual in an oral mathematics test of 15-year-olds, involving the ideas of perimeter, area, and circumference:

1. Ask: “What is the perimeter of a rectangle?” [Write student answer.]

2. Present sheet with rectangle ABCD. Ask: “Could you show me the perimeter of this rectangle?” (If necessary, teach.)

3. Ask, “How would you measure the perimeter of the rectangle?” If necessary, prompt for full procedure. (If necessary, teach.) …

10. “Estimate the length of the circumference of this circle.”

11. “What would you do to check your estimate?” (String is on the table. If no response, prompt for string.) …

13. “Is there any other method?” (If student does not suggest using C=pd, prompt with, “Would it help to measure the diameter of the circle?”)

The scoring system works as follows:

1. 1. unaided success
   2. success following one prompt from the teacher
   3. success following a series of prompts
   4. teaching by the tester; prompts unsuccessful
   5. an unsuccessful response; tester did not prompt or teach
   6. an unsuccessful response despite prompting and teaching
   7. question not given
   8. unaided success where student corrected an unsuccessful attempt without help

Successful responses are combined into two larger categories called “unaided success” and “unaided plus aided success,” with percentages given for each.

[From Mathematical Development, Secondary Survey Report #1, Assessment of Performance Unit (APU), Department of Education and Science, Great Britain (1980)].