Teaching algebraic thinking without the x’s
August 2, 2010 4 Comments
Students need not wait till they meet Mr. x to learn about algebra. In fact, the best way to learn about algebra is to learn it while there aren’t x’s yet; when all the learners need to deal with are concepts that still make sense to them. Here is a list of tips and ways for developing algebraic thinking while learning about numbers and number operations.
1. Vary the “orientations” of the way you write number sentences.
For example, 5 + 20 = 25 can be written as 25 = 5 + 20. The first expression is about ‘doing math’, the second engages students about ‘thinking about the math’, the different representations of the number 25. The thinking involved in the second one is ‘algebraic’.
2. Be mindful of the meaning of equal sign
If you want to ask your learners to find, for example, the sum of 15 plus 6, do not write 15 + 6 =___. It’s a recipe for misconception of the meaning of equal sign. I recommend: What numbers is the same as (or equal to) 15 + 6? Better, What number phrases are the same as (or equal to) 15 + 6? This last one promotes algebraic thinking.
3. Encourage learners to generalize.
The task, 18 + ____ = 16 + ____ is an example of a task that has many answers. Encourage students to make a statement about the relationships between the numbers that goes to the blanks. Algebra is about relationships and making generalizations. In Year 6 or 7, you can even use this to introduce the notion of variables!
4. Encourage learners to always find other ways of solving a problem.
For example, initially, they will solve the problem ____+ 3 = 4 + 15 by adding 4 and 15 then taking away 3 to find the number that goes to the blank. Encouraged to find other ways of doing it learners will recognize that 4 is one more than 3 so to keep the balance, the number in the blank should be 1 more than 15 which is 16. This solution illustrates algebraic thinking. Algebra is about the process first, and the product second.
Here are different ways of finding solutions to the problem in #3.
5. Develop the habit of investigating number representations and number relationships.
In my example in #4, you can further challenge learners to check if this relationship works for operations other than “addition” for equations of this form. This will be a very good math investigation project for the class. Algebra is about generalizing arithmetical processes.