Background: Context personalization, the practice of adapting learning materials to students’ personal interests, has been shown to increase student learning and engagement. Within computer science education, research has found that LLMs can generate high-quality contextualized introductory programming exercises. Objective: In this paper, we evaluate the capability of LLMs to generate technically correct and thematically integrated contextualized algorithm design problems. Methods: In a series of three iterative studies, we use LLMs to generate contextualized algorithm design problems from a given base problem and theme, evaluating over 500 generated problems for technical and thematic alignment. Results: We find that LLM-generated algorithm design problems exhibit significantly more issues than prior work has found for introductory programming problems. We identify issues specific to the algorithm design context and then mitigate these issues with prompt engineering techniques and model choice. With these adjustments, we produce LLM-generated contextualized algorithm design problems that are technically strong, deeply themed, and largely realistic, though realism drops with more culturally and locally specific themes. Implications: We demonstrate a viable workflow for generating contextualized algorithm design problems using LLMs, including prompt design, model selection, and identification of specific issues to review for.

The ability to identify the important takeaways from a previously-seen solution and apply them in different contexts is an important problem-solving skill. However, this skill, known as analogical reasoning, is traditionally left implicit in algorithms courses. Students are expected to develop the skill naturally as they progress through the course. In this study, we aim to conduct a more thorough investigation of analogical reasoning in algorithms. We integrate explicit metacognitive scaffolds for reflection and schema development into an undergraduate algorithms course. Then, on course exams, we insert an additional task alongside select algorithm design questions, in which students are asked to describe how a previously-seen problem influenced their design. We analyzed both the previously-seen problem selected by the student and the stated similarity. Within the 142 comparisons analyzed, we find that 37% provide insight about the underlying solution structure, and these comparisons were significantly associated with higher scores on the problem. Furthermore, about one-third of the comparisons were with a problem that course staff also selected, and these comparisons were not only much more likely to be structural but were also correlated with higher performance on the question. Our results indicate that the analogical reasoning skills are closely tied to success in the algorithms course, and encourage instructors to integrate explicit demonstrations into their curriculum.

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.

Dynamic programming (DP) is one of the most challenging topics in algorithms courses. Although there exist animation tools that assist with the understanding of DP algorithms, few existing tools are aimed at scaffolding the process of solving DP algorithm design problems. To help create a learning tool able to provide the affordances learners need when attempting DP problems, we analyzed learners' scratch paper to understand how learners approach DP problems. Based on scratch paper from 18 learners solving DP problems during a think-aloud study, we created a codebook that characterized different elements and methods used by the learners on their scratch paper. We found that learners had distinct preferences when attempting DP problems. Some learners preferred using example input with specific values to simulate ideal program executions, while some used math representations of example inputs to help derive formulas. Learners interacted with their example input in multiple ways, including filling in hand-drawn tables to organize the calculation process and dynamically interacting with the inputs by crossing, circling, or using arrows to visualize the relationships between inputs. These findings suggest potential interactions that need to be taken into consideration when designing tools to support learners in solving DP problems.