Construction of mathematical knowledge through whole-class discussion

A word problem that requires addition of fractions with different denominators was presented to 11 classes of 4th- or 5th-graders, 10 years of age. It had three answer alternatives: adding the denominators and numerators separately, transforming fractions into decimals before adding them, and the standard, most appropriate solution. Students in each class were required to choose an alternative themselves, state their reason for the choice, and discuss which alternative would be right. After whole-class discussion, they were asked to choose an alternative again and nominate the student who had offered the most plausible idea. Then students in six classes were informed which alternative was the most appropriate, whereas those in five classes were not. Finally, the students, irrespective of the presence/absence of feedback, were required to solve the initial problem without the alternatives as the post-test, and two new problems as the transfer test. The results showed that (a) the students could offer more or less plausible arguments for or against each alternative, which in most classes included the correct explanation; (b) both vocal and silent students could write a mathematical expression for the post-test problem and manipulated it correctly, incorporating other studentsʹ ideas presented during the discussion, with or without the teacherʹs feedback, though their generalization was rather limited; and (c) the students could recognize and memorize reasonable explanations offered by other students in the discussion.