'Let Us Discuss Math'; Effects of Shift-Problem Lessons on Mathematical Discussions and Level Raising in Early Algebra

We investigated whether early algebra lessons that explicitly aimed to elicit mathematical discussions (shift-problem lessons) invoke more and qualitatively better mathematical discussions and raise students' mathematical levels more than conventional lessons in a small group setting. A quasi-experimental study (pre- and post-test, control group) was conducted in 6 seventh-grade classes (N = 160). An analysis of the interaction processes of five student groups showed that more mathematical discussions occurred in the shift-problem condition. The quality of the mathematical discussions in the shift-problem condition was better compared to that in the conventional textbook condition, but there is still more room for improvement. A qualitative illustration of two typical mathematical discussions in the shift-problem condition are provided. Although students' mathematical levels were raised a fair amount in both conditions, no differences between conditions were found. We concluded that shift-problem lessons are powerful for eliciting mathematical discussions in seventh-grade shift-problem early algebra lessons.