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.
Ask to explain work "How did you do that?" Criticize work "That is in the wrong order" Key activities Example Tell/show work "Look what I have done" Explain work "I have 6, because you have to double it" Justify work "I am right, because 5 times 5 = 25" Reconstruct work "I'll better do it like this" Correction to: "Let us discuss math"; Effects of shift-problem...
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