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A Question Revisited

Written by Wendy B. Sanchez and Nicole F. Ice
(News Bulletin, April 2005)

The multiple-choice Question 3, as it was described in the November column, was intended for use with an electronic student response system during instruction. This informal assessment is a way for teachers to gather information about their students’ thinking and to give teachers “a nice starting point for an investigation into the effect of multiplication by rational numbers.” We believe that Question 3 has great potential to promote students’ thinking, talking, and debating about mathematics in a variety of classrooms. It is important to remember that NCTM members who read the NCTM News Bulletin vary from elementary through university-level teachers of mathematics. Thus, we intentionally left the question vague so that readers teaching at all levels could use it in some form with their students.

One focus of the reader comments was on our use of the terminology “larger” and “smaller” in Question 3. We certainly agree that the terms “greater” and “less” would have been more appropriate for the question. Our intent was to use wording that would make it clear how all teachers could use such a question, adapting it as needed, to promote mathematical discussion among students.

We also agree that choice C should have read “is sometimes greater than, sometimes less than, and sometimes the same as the original number.” Of course, we would use the word “equal” instead of “the same” if we restated the question as suggested by readers. We appreciate the comments of the readers who pointed out this oversight.

Readers also noted that the answer to the question depends on the set of numbers from which a student takes the number to be multiplied by 4/5 . If the number chosen is zero, then the result is equal to the original number. If the number chosen is positive, then the result is less than the original number, though if the chosen number is negative, the result is greater than the original number. Again, we intentionally did not provide the given set of numbers for the students to consider in answering this multiple-choice question so that teachers would be able to use the question in a variety of classrooms.

We appreciate your comments and are glad to have an opportunity to respond to you. We hope that our word choices did not impede any teacher’s use of the question or some variation of it. Please continue to send us your comments. We value your input.