Using Elm to Introduce Algebraic Thinking to K-8 Students
Bibliographic record
Abstract
In recent years, there has been increasing interest in developing a Computer Science curriculum for K-8 students. However, there have been significant barriers to creating and deploying a Computer Science curriculum in many areas, including teacher time and the prioritization of other 21st-century skills. At McMaster University, we have developed both general computer literacy activities and specific programming activities. Integration of these activities is made easy as they each support existing curricular goals. In this paper, we focus on programming in the functional language Elm and the graphics library GraphicSVG. Elm is in the ML (Meta Language) family, with a lean syntax and easy inclusion of Domain Specific Languages. This allows children to start experimenting with GraphicSVG as a language for describing shape, and pick up the core Elm language as they grow in sophistication. Teachers see children making connections between computer graphics and mathematics within the first hour. Graphics are defined declaratively, and support aggregation and transformation, i.e., Algebra. Variables are not needed initially, but are introduced as a time-saving feature, which is immediately accepted. Since variables are declarative, they match students' expectations. Advanced students are also exposed to State by making programs that react to user taps or clicks. The syntax required to do so closely follows the theoretical concepts, making it easy for them to grasp. For each of these concepts, we explain how they fit into the presentations we make to students, like the 5200 children taught in 2016. Finally, we describe ongoing work on a touch-based Elm editor for iPad, which features (1) type highlighting (as opposed to syntax highlighting), (2) preservation of correct syntax and typing across transformations, (3) context information (e.g. displaying parameter names for GraphicSVG functions), and (4) immediate feedback (e.g. restarting animations after every program change).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".