It has been argued that teachers need practical principled knowledge and that design research can help develop such knowledge. What has been underestimated, however, is how to make such know-how and know-why useful for teachers. To illustrate how principled knowledge can be “practicalized”, we draw on a design study in which we developed a professional development program for primary school teachers (N = 5) who learned to design language-oriented mathematics lessons. The principled knowledge we used in the program stemmed from the literature on genre pedagogy, scaffolding, and hypothetical learning trajectories. We show how shifting to a simple template focusing on “domain text” rather than genre, and “reasoning steps” rather than genre features made the principled knowledge more practical for the teachers.
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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.
