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.
In the Netherlands there is discussion about the best way to teach mathematics, especially in the case of primary school students. Being able to identify and understand pupils’ multiple problem solving strategies is one of the pillars of pedagogy. However, it is very demanding for teachers, since it requires to notice and analyze pupils’ mathematical thinking and to understanding their actions. The skill to notice and analyze a student’s mathematical thinking is usually not emphasized in Dutch primary school teacher training. It is important to find ways to help teacher-students to analyze student mathematical reasoning, and to learn to recognize the importance of such analysis. Sherin and van Es used the concept of video clubs to help teachers in US schools to notice and analyze their students’ mathematical thinking. In such video clubs, students jointly discuss their filmed lessons. This leads to the following research question:How can video clubs be used to teach students who are learning to become primary school teachers to analyze their pupils’ mathematical thinking and to learn to recognize the importance of such analysis?This paper describes a study that monitors a video club with four participants.
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The implementation of the new mathematical knowledge base in Dutch teacher education institutes for primary education raises a need for curriculum development. Teacher educators have to raise student teachers’ subject matter knowledge to a higher level. In working on this aim teacher educators experience that student teachers often feel uncertain about their mathematical skills and are not very interested in formal and abstract mathematics. Student teachers prefer to focus on mathematical pedagogical content knowledge. This paper presents two design studies that try to tackle this problem. The first one targets the development of student teachers’ specialized content knowledge (SCK) and the second one focuses on their horizon content knowledge (HCK). Both studies target developing student teachers’ mathematical subject matter knowledge in the perspective of teaching mathematics in primary school. In the studies we established student teachers’ learning environments that kept them involved and motivated, even when they found the mathematics hard to do. Primarily, this attitude supported their mathematical growth, while it also developed their pedagogical skills and insight. INTRODUCTION
