# Writing analogy: calligraphy copybooks, applications and books

blog, en, enrich, enriquir, activities, activitats, analogy

## The analogy

Recently, I discovered a analogy about mathematical activities: what kind of writing task do you do?

• You just complete the calligraphy copybooks: follow the marked line with pencil. So you are not able to write free content nop form.

• You could write a formal application to Government for example [2]. With this kind of document, you are restricted with a lot of format constraints but you could freely write the content.

• And finally, you could write a book [3]. You are not restricted to form or content.

Following 5 Practices for Orchestrating Productive Task-Based Discussions in Science [1] these categories rise up the demanding of knowledge. And I think that students really “write a book” if they do Project-based learning.

## An example of this analogy

I give you an example of this analogy for practicing fractions as operator. I want students to calculate $$\frac{3}{4}$$ of $$16$$.

### Calligraphy copybooks

• Activity: “Calculate $$\frac{3}{4}$$ of $$16$$
• Students possible response: “$$\frac{3}{4} \text{ of } 16 = \frac{3 \cdot 16}{4} = 12$$

### Aplication

• Activity: “Two farmers want to divide a 4 x 4 plot but the first should have three times surface than the second.

Divide this plot to verify this requeriment"

• Students response:
• understand what is “three times”
• calculate somehow1 that one farmer has 12 squares and other 4 squares.
• draw

### Book

• Activity: “Two farmers want to divide a 4 x 4 plot but the first should have three times surface than the second. What’s the best way to do it? Consider costs like fencing, buying seeds, irrigation, etc. and crop benefits.”2
• Students responses: ?

Update: I change the book analogy from this:

Can you find three different ways to divide this plot verifying this requeriment?

What is the division which has the minimum cost? (each fencing side has a cost of \$10)?

Can you compare yours with your neighbours’?

Can you find out what is the minimum cost division among all possible divisions?"

to above.

# References

[1] Cartier, J.L., Smith, M.S., Stein, M.K., and Ross, D.K. 5 practices for orchestrating productive task-based discussions in science. National Council of Teachers of Mathematics, 2013.

[2] Govern de les Illes Balears. Llibre d’estil. amadip.esment, 2006.

1. Try and failure, $$\frac{3}{4} \cdot 16$$, equations ($$3x+x = 16$$), etc.

2. Does the cost vary if we choose joined (arc-connex) regions than disjoint areas?