Wednesday, February 8, 2017

Maths is the Science of Pattern

From the earliest experiences we have with maths the role of pattern plays a key role in how we learn and remember maths facts, concepts and relationships. The pattern of the number names as well as the numerals must be learned so that we can label and communicate our mathematical ideas in the same way that letter recognition and pronunciation is a prerequisite for literacy.

Even the idea of rational counting is a pattern where one more is added to get the next number or quantity. This can be extended to tens, hundreds, thousands and so on just by changing the referent being counted.

Counting by 2s and 5s is another  pattern that helps us learn and remember numerical relationships. Try counting by 5s starting at 3, instead of 0, and see what happens. The further you go the easier it gets because you very quickly see the pattern of 3s and 8s. The same can be done with fractions although it is clearly more difficult. Visualize half of a half of something. You should be seeing a quarter. Procedurally you have double the denominator to make one half into one quarter. So what is half of a third? A sixth? You double the 3 to get 6. Now you can find a half of any fraction without having to do the desperately miserable fraction multiplication algorithm. Try one third of a quarter. A twelfth, right?  You multiplied the denominator by 3. Now you can find a third of any fraction, even a third of three quarters; three twelfths. But that one is easier to do by dividing the numerator, 3, by 3 to get 1. A third of three quarters is one quarter. A third of 3 horses is 1 horse.

All of which brings us to the picture of the Sierpinski triangle fractal. Fractals are wonderful examples of patterns in maths. This triangle will go on for ever like all fractals. Look at the three pennies at the top. This group of three pennies is repeated over and over again to make bigger triangles. Here's a link to the wonderful Fractal Foundation site where pattern reigns supreme.       

Wednesday, January 18, 2017

DeVos and Special Education

In Canada, all the ministers are experts on the fields they are in charge of. The Education Minister has teaching experience and the Minister of Immigration is an immigrant. In the US we seem to adopt the opposite policy where people are put in charge of thing sabot which they know very little.

This is wonderfully illustrated this week were Betsy DeVos, the president elect's pick for Education Secretary apparently has no idea what IDEA is. IDEA is the remarkably successful federal act that was adopted many yeaers ago to provide students with special needs access to a regular education. As a parent of a son with Down Syndrome i can attest to the success of this program. Now 24, he has many neuro-typical friends, has a wonderful social life, attends college and works several jobs. Without IDEA he would have gone to a special school like such students do ini Singapore, Russia, and many other countries where his disability would have been stigmatized and he never would have become a productive, integrated member of society.

When asked about IDEA in the confirmation hearing DeVos said it should be up to individual States whether to include children with special needs in public schools. Clearly she is totally unaware of the requirements of the public law.  This is the same as the Secretary for Foreign affairs not knowing where Russia and China are.

Devos, a billionaire,  has clearly never set foot in a public school and has no idea what special education is all about. Private schools, where her children attended,  are not required to provide special education services in most States and so her goal or privatizing education is going to have a profound effect upon the education of these most vulnerable members of society.

On a personal ;level, I am so glad that my son is no longer in public schools and that I am retired but my heart goes out to all those parents with children with special needs worried about what is going to happen. Heaven forbid we return to the pre-1975 special school situation,