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.
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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.
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We conducted a descriptive study among first-year engineering students at the Anton de Kom University of Suriname. We analyzed students’ errors regarding necessary prior knowledge in a calculus A exam. We found that the stage of the solution in which prior knowledge is required impacts the importance of prior knowledge. We also found that many errors concerned basic algebra and trigonometry concepts and skills. We concluded that even though the required prior knowledge concerns basic algebra and trigonometry, the stage of the solution in which prior knowledge is needed is of great importance.
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