Math: Developing a Mindset

You keep hearing about Mathematical thinking. What is it? How do you develop a Mindset for Math?

Khalid has a nice post on How to Develop the Math Mindset.

Math uses made-up rules to create models and derive relationships. When learning, I ask:

• What relationship does this model represent?
• What real-world items share this relationship?
• Does that relationship make sense to me?

I will add a couple of more:

• How does one develop a mind-set for thinking beyond mere numbers, formulas and low level concepts.
• How can we take these insights that come out of that mindset and apply to real problems

One of the slides I used to have on my “Thinking About Thinking” talks was to ask the audience (mostly CS students) to do a few of the following multiplications, mentally.

19 X 21

25 X 15

Very few actually find the simple algebraic patterns, till you point them out.

That brings us to one more insight (not my own):

• A lot of problems can be solved by looking for patterns and applying some existing knowledge

The more mental models we build, the easier it is to apply them.