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Dynamic Programming (DP) is commonly regarded as one of the most difficult topics in the upper-level algorithms curriculum. The teaching of metacognitive strategies may prove effective in helping students learn to design DP algorithms. To explore both whether students learn and use these strategies on their own and the effect of guidance about using these strategies, we conducted think-aloud interviews with structured guidance at two points in a college algorithms course: once immediately after students learned the concept and once at the end of the course. We explore 1) what metacognitive strategies are commonly employed by students, 2) how effectively they help students solve problems, and 3) to what extent structured guidance about using metacognitive strategies is effective. We find that these strategies generally help students make progress in solving DP problems, but that they can mislead students as well. We also find that the adoption of these strategies is an individualized process and that structured strategy guidance is often insufficient in allowing students to solve individual DP problems, indicating the need for more extensive strategy instruction. 

According to an ecological affordances perspective, any static curriculum has a set of affordances, and differences in teachers, students, and the teaching environment change how those affordances are viewed and used. Therefore, teaching is a relationship between the curriculum, the teacher, and the students. As such, it is not only possible but expected that a teacher will diverge from the details of a lesson plan to better accommodate the needs of themselves as a teacher and their students as learners. In this study, we report on a mixed-methods investigation that explores the different ways upper-elementary and middle-school (7- 13 y.o. students) teachers implement the Scratch-based TIPP&SEE learning strategy and the reasoning for their approaches. As expected, we find that teachers across grade levels often deviate from lesson plan details to cater to their own classrooms. For example, teachers serving younger grades were far more likely to keep scaffolds that lesson plans suggest removing. The varied degree of deviation suggests that the repeated use of a learning strategy, alongside lesson plans that present a variety of scaffolded implementations, is beneficial in enabling teachers to adapt lesson content to serve the needs of their specific classroom.