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 this chapter, I look back at the implementation of W12-16, a major reform of mathematics education in the lower grades of general secondary education and pre-vocational secondary education in the Netherlands including all students aged 12–16. The nationwide implementation of W12-16 started in 1990 and envisioned a major change in what and how mathematics was taught and learned. The content was broadened from algebra and geometry to algebra, geometry and measurement, numeracy, and data processing and statistics. The learning trajectories and the instruction theory were based on the ideas of Realistic Mathematics Education (RME): the primary processes used in the classroom were to be guided re-invention and problem solving. ‘Ensuring usability’ in the title of this chapter refers to the aim of the content being useful and understandable for all students, but also to the involvement of all relevant stakeholders in the implementation project, including teachers, students, parents, editors, curriculum and assessment developers, teacher educators, publishers, media and policy makers. Finally, I reflect on the current state of affairs more than 20 years after the nationwide introduction. The main questions to be asked are: Have the goals been reached? Was the implementation successful?
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In bepaalde single-core configuraties met één processor, b.v. embedded control systems zoals robotic applications die uit vele korte processen bestaan, kunnen de context switches van een proces een aanzienlijke hoeveelheid van de beschikbare processing power verbruiken. Het verminderen van het aantal context switches vermindert de executietijd en verhoogt daardoor de prestaties van de toepassing. Bovendien is de end-to-end executietijd van de processen langer dan strict noodzakelijk, b.v. omdat de processen moeten wachten op controllers die een taak uitvoeren. Door de regels voor synchrone communicatie via kanalen in de procesalgebraïsche specificatietaal Communicating Sequential Processes te versoepelen, kunnen we de end-to-end executietijd verkorten. In ons onderzoek definiëren we verschillende graafproducten, bewijzen we dat deze producten een prestatiewinst opleveren (onder bepaalde voorwaarden) en we werken de numerieke en combinatorische aspecten van deze graafproducten uit.
