In principle, you can play chess without a chessboard and chess pieces. You simply sit in a bus with your colleague and your conversation goes: e4 - c5 - Knight to f3 - d6 - d4 - I take d4 by my c pawn... But people prefer to use chessboard and chess pieces, because it allows them to unload a significant mental burden and focus.
When teaching complex subjects, we can use a similar principle to help students unload a significant mental burden and focus: we can create our own pieces and chessboard, change positions of the pieces on the board, and so on.
Imagine a biology lesson, where your aim is to teach students a classification of insects. It is neatly written in the book, but you can do better: you start by giving students 12 pictures of distinct species of insect and ask the students to divide them into four groups based on similarities. This way you make students observe the details of pictures. They need to clarify for themselves that color is not a relevant characteristic. (Green beatle and blue beatle go together, green beatle and green dragonfly don't.) Then you ask them why they formed the groups the way they did, and you make them verbalize arguments.
The information content might be very similar to that of a book, but by creating tokens and giving a task with tokens, you made students think much more. To build on previous activity, you can give students characteristic of different insect types that correspond to previously formed groups and let the students decide which goes by which.
More examples of what you can do:
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Classify into predefined categories
- Tokens = graphs of functions
- Task = assign properties - (dis)continuous, periodic, monotonic, with upper bound, ...
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Order according to some characteristic
- Tokens = complexity classes, e.g.,
n log n,n^2,2^n, ... - Task = order according to rising complexity
- Tokens = complexity classes, e.g.,
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Find a meaningful ordering
- Tokens = pieces of a printed story (e.g., parts of a fairy tale)
- Task = put the pieces together according to the flow of the story
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Pair A with B
- Tokens A: data structures
- Tokens B: use cases
- Task: pair data structures with corresponding use cases