Purpose
Programming Focus: Recursion, Abstraction, Fractals
Recursion and functional programming are two programming techniques that go beyond the Framework requirements but they are fundamental to learning to program. Functional programming was introduced in Unit 3, and we'll return to it in Unit 8. Unit 7 is about recursive commands, mainly fractals. 
It starts with a teacher demonstration of the Vee project, in which a short program generates V-shapes with randomly chosen decorations at the ends (shown right).
The same program suddenly generates arbitrarily complex results if the vee procedure itself is added to the list of possible decorations (shown left). This is a teacher demonstration rather than an independent lab activity because the collective "gasp!" of the class is itself a valuable learning experience.
After the demonstration, students develop their own non-recursive fractal tree program by building up from small cases (a one-level tree is just a trunk; a two-level tree is a trunk with two branches, etc.) so that they are not confronted at first with the seeming magic of a procedure calling itself. Only after they've written several almost-identical procedures (tree 2, tree 3, tree 4, etc.) does the lab suggest combining them into one recursive procedure, tree. The students then discover why recursive procedures need a base case to terminate the recursion (comparable to their tree 1 block in the non-recursive scheme that draws just one line without calling for any branches).
Once the tree fractal is thoroughly understood, students go on to construct other common fractals (Koch snowflake, Sierpinski gasket, etc.) in Lab 2.
The elegance of the programs themselves helps students see computer programs—and not just the effects they produce—as things of beauty. A key moment in developing that sense is when students understand how a short recursive procedure can generate a deeply complex computational process.
BJC Videos from UC Berkeley
There are a number of BJC videos from the edX version of the curriculum that are relevant to Unit 7. These are available on the Teacher Resources page.
Teacher Guides for Student Labs
- Lab 1: Trees
- 2–4 days (70–140 minutes)
- Lab 2: Recursion Projects
- 3–5 days (95–190 minutes) for required pages
Assessments and Solutions
Optional Teaching Resources
- Vocabulary Activities for Units 7 and 8 are combined in Unit 8
Old Recursion TG
U7 Student Labs