The activity: connect each construction summary to a comic strip showing that construction.
I made this Connecting Representations activity today. Some things I thought about while making it:
- Some mathematical objects roll out over time. Procedures or algorithms are like this: first this, then this, finally that. Constructions are like this. Proofs are also like this.
- To represent something that rolls out over time you can’t use a single static image.
- The most sturdy representation we have for things that roll out over time is language.
- At an abstract level, there are two ways to help make a complex thing more understandable. One is to break it down into parts, and the other is to compare the whole thing to some other whole thing it resembles. (Are there more?)
- If you ask students to connect SOMETHING to a subset of that SOMETHING, their attention will likely focused on that subset in the SOMETHING. In other words, this gives students the experience of focusing on a very specific part of that complex SOMETHING.
- If you want students to compare SOMETHING to another thing it resembles, you need to compare a representation of SOMETHING with a simpler representation of that whole SOMETHING.
- While I don’t think the above task is amazing or anything, to the extent it succeeds it’s because you’re comparing a whole representation of a construction (in the comic form) to a simpler representation of that comic (the summaries).