Traditional Math Just Doesn't Work Anymore

I recently fell into an illuminating conversation with an old friend about math and math education. He was telling me how his daughter is homeschooling his grand-daughter and how much his grand daughter loves math and science. As the conversation continued he told me how his daughter was teaching her child traditional math and "how well" it was working out. He went on to say how he didn't think these new methods of math instruction helped at all and wondered why schools were not using the same methods to teach math his daughter was using and that he had learned 50 years ago..

I then shared with my old friend how I had had an unusual experience in my undergraduate math education course yesterday when one of the students had asked me why young children need to know why there are 180 degrees in a straight line. "Can't you just tell them?" the undergraduate student had asked. "I know there are 180 degrees in a straight line and that's been fine for me", she continued.

A little taken aback I then asked the student how she would explain to a young child how there were 180 degrees in a straight line when there was no angle to measure. She didn't say anything.

So, with my old friend watching I then tore the three corners off a paper triangle and lined them up so that they made a straight line by putting the three points together. There, I said, 180 degrees in the three corners of a triangle and a straight line. Seeing  a somewhat disbelieving glint in his eye I then took a 360 degree rotating protractor and rotated it through 180 degrees saying that degrees are a measure of rotation about a point; in this case the point where the three corners of the triangle come together. Here's a nice demonstration of the concept that angles are measures of rotation.

After a few seconds of thought he said "Hmmmm, why wasn't I taught math this way?" I wonder if he will say anything to his daughter.

The persistent  perception of math as a process of telling and memorization seems such an enigma in this day and age.

Why a Rigorous Math Curriculum?

Why oh why did the maths education community have to choose the word "rigorous"? The greatest problem about choosing a word like this is that "rigorous" has so many different meanings. In an incredibly informative NCTM Summing Up statement, Linda Gojak, NCTM president describes how many different ways there are of defining the word rigorous. The problem with having such a loose word is that it can be interpreted in so many ways depending on a particular individual's agenda. For example, there are myopic people like Angela Lee Duckworth who have taken the word to mean "grit" and are advocating that all children develop the type of rigor that is all consuming and totally at odds with theories of child development. Clearly some people will do anything to make a name for themselves and get to deliver a TED talk, even if it is the worst one I have ever watched.

How much better it would have been to use a word like "interesting' or "relevant" or "meaningful" or even "inspiring" to describe a math curriculum. Why does maths have to be rigorous for kindergarten children? It's like requiring them to engage in rigorous play, or rigorous reading. It's like asking fifth graders to engage in rigorous creative writing, or rigorous music or P.E. lessons.

Why can learning not be a natural process through which we hold children to achievable standards through activities they find rich in interest, relevance and motivation.  Why can maths not be inspiring, wonderful, relevant, meaningful, and simply interesting?

How many adults would classify the pursuit of their adult lives as rigorous?