Extracting Data from Distractors

R. James Milgram

Many Math Educators are trying to classify student errors to mechanize mathematics instructionThis has proved to be very difficult.But using the results of large scale

testing, and all the distractors, it seems to be possible to make headway.

Many Math Educators are trying to classify student errors to mechanize mathematics instructionThis has proved to be very difficult.But using the results of large scale

testing, and all the distractors, it seems to be possible to make headway.

Many Math Educators are trying to classify student errors to mechanize mathematics instructionThis has proved to be very difficult.But using the results of large scale

testing, and all the distractors, it seems to be possible to make headway.

We start by looking at the pattern of responses.

Then we look at some examples to get an idea of what these patterns represent.

We start by looking at the pattern of responses.

Then we look at some examples to get an idea of what these patterns represent.

Note the largest incorrect responses reverse the powers of 10. This is probably an artifact of inefficient teaching

Here is a first grade example

Note that response (C) actually is higher than the correct response.

Here is a first grade example

Note that response (C) actually is higher than the correct response.

The issue: Students are not taught that the

digits in the shorthand base 10 notation describe the EXPANDED FORM.

They think the shorthand notation is the name of the number.

In both cases the popular answer reflects the ORDER of the digits, not their “weights.”

Here are some examples:

The most popular wrong response represents adding or subtracting whole numbers and separately adding tops and multiplying bottoms in the fractions.

Comments I do not understand the rationale the

students used for distinguishing 8,496 from 84,960, or 4.65 from .465, but I suspect that these students actually multiplied by the conversion factors.

In the remaining cases 23.6 and 236, 2.79 and 27.9, most likely the students understood that one needed a conversion factor, but they seemed to believe it had to be a power of 10.

Comments I do not understand the rationale the

students used for distinguishing 8,496 from 84,960, or 4.65 from .465, but I suspect that these students actually multiplied by the conversion factors.

In the remaining cases 23.6 and 236, 2.79 and 27.9, most likely the students understood that one needed a conversion factor, but they seemed to believe it had to be a power of 10.