Number Patterns and Representations

This is the fifth lesson in Jo Boaler’s “How to Learn Math (for Students)”.

It is up to us to make sense of math.  One way is by using intuition, which is a general sense or feeling about what works. According to Sebastian Thrun, founder of Udacity, “Every time you see a math problem it is useful to stop and think intuitively, what do I think is going on here?”

A great aid to intuitive thinking is visual representations through drawing.  That takes the math out of the realm of formulas and algorithms and puts in into a concrete context.

There are “Big Ideas” in math that the formulas and algorithms are about exploring and using.  However, sometimes in math class, those big ideas get lost, and consequently, students get confused.  For example, the Big Idea of Pi:  In every circle and every sphere the circumference is always a little bit more than three times the diameter. If students can learn the big ideas and hold onto them, they will find math really clear and easy to use.

In other words, formulas are only useful if you understand the big idea that they are illustrating, so students should always start by trying to understand the big idea.  Drawing a picture helps a lot.  Keeping in mind that math is about relationships between quantities helps too.  So asking questions about how the quantities relate (like diameter and circumference) can help facilitate understanding of the big idea (pi is the same for all circles).



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