A Circle Is...
Consider this set of twenty words: sum, quotient, remainder, fraction, factor, perimeter, measure, product, digit, angle, difference, equal, diameter, meter, denominator, average, circle, whole, divide, and subtract.
Suppose your students were asked to first define them using only words, and then to define them using words, symbols, diagrams, and/or examples. Could they do it?
A recent study in Western Australia involving 646 eighth graders discovered that the average number of acceptable responses using only words was 4 and when using symbols, etc. the average number increased to 11 words.
Sherrie Serros, University of Wisconsin in Eau Claire, tried the same experiment with her preservice elementary students. She discovered that her adult students could define only six words (sum, quotient, product, difference, divide, and subtract) using only words. The students considered all of the words to be "challenging, frustrating, difficult."
Try the experiment with your students......but be sure you can do it yourself first!