There is a great game about polynomials presented by Rachel Kaplove on the eHow YouTube channel. The rules are very simple:
- Each student gets a card with either expanded polynomial, for example $x^2-81$, or one of its factors, for example $x-9$ and $x+9$.
- If a student has a polynomial, he/she needs to find classmates with the right factors.
- If a student has a factor, he/she needs to find a classmate with the right polynomial.
You don't need computers for this game and students should work in groups to achieve the final goal. But, of course, students need to know the factorization of polynomials for this activity.
Regarding the lack of motivation, I would consider three reasons:
- Students don't find algebra useful because the tasks are not related to real-world problems.
- Students aren't excited about algebra because the tasks lack the gaming aspect.
- Students aren't good with algebra because they don't understand its basic principles.
These issues can be solved with the following approaches:
- Polynomials in economics (coming a nice example from agriculture!)
- Playing with maths using computers (there is no excuse not to use them)
- Didactic vs Project-based learning (explaining the concept of powers)
Now let's cover each point in detail:
- Polynomials are extremely important in economics to model economical behaviors. Since the author of the question teaches in the agriculture-oriented school, I found the book "Agricultural economics" and the word "polynomial" was mentioned there 21 times! For example, a short-run total cost function of modern production technologies can be realistically described by a third-degree polynomial like this: $TC = 2q^3 - 15q^2 + 50q +50$ (taken from "Maths for Economics (3rd edition)" by Geoff Renshaw, p. 141). The graph of this function shows the most efficient output range (green) where the total cost $TC$ doesn't vary much with the output $q$ as well as the least efficient output range (red) where output increase would cause significant production cost increase.
- Instead of doing boring calculations by hand, let the students play with maths using computers and programming. Check this inspiring TED talk by Conrad Wolfram about Computer-Based Maths! There are no excuses not to use computers for two reasons:
- Software for programming maths is cloud-based and free (for example, Wolfram Programming Lab).
- Computers are dirty cheap nowadays (for example, Chromebook for \$150 or Raspberry Pi for \$25).
(to be continued...)