Tuesday, June 11, 2013

Maths and Diversity

Every time I teach a new course I go through the same process. It doesn't happen very often so I can never remember what the process is. Perhaps I don't need to remember; perhaps i will always go through the same process whether I remember it or not.  I first look at all the materials the person who used to teach the course used. I then panic for several days thinking i cannot possibly assimilate all this material and then I realize that I always develop my own set of materials base don the course description, the goals of the course and the skills, knowledge and dispositions it is designed to address in the big scheme of things. Last time it was an intro to teaching and education undergraduate course; this time it's a graduate level math course; Math and Diversity.

I developed the course with several colleagues from the fields of mathematics ed., special education and TESOL about five years ago but I have never taught the course by myself. The course is designed to help graduate students and practicing teachers  teach math to students who are English learners, have special needs, have a math disability or are from poverty. 

I have always believed that the essence of being a good math teaher is understanding the intricacies of the math we teach. It's important of course to understand child development and pedagogical theory but even the most exemplary of these are less effective if the teacher does not understand the math. Imagine teaching french without understanding the structure of the language or knowing vocabulary? So, I've decided to make math numeracy the focus of the course and then illustrate the application of this through differentiated instruction in the four areas described above. For each element of diversity the math is the same; it just needs to be presented or thought about in a different way for each one. I'm going to use Bob Wright's book Developing Number Knowledge  because it does such a great job of breaking the ideas associated with number down into it their component parts so that when we assess children's mathematical knowledge and understanding we know where to go in the instructional process. The book is one of a series of 4 in the very effective Math Recovery program.

By the way, it's time we eliminated the r word from our language unless you are referring to the timing on an engine.

Thursday, June 6, 2013

Sweet Sixteen

The Richmond Round Church that I wrote about in one of my recent posts has 16 sides to it, one built by each of the original settlement families. 16 turns out to be quite an interesting number when you stop to think about it.

We have all been, or will be, sweet 16 at some point and Tennessee Ernie Ford and Johnny Cash both sang about "16 Tons". It's a square number and was the 16 Gun Salute at the Jubliee celebrations in York, UK.  It's also the number of ounces in a pound which must be quite mystifying to anyone brought up with the metric system, and it's the number of pieces on a chess team, black or white. It's also the almost incomprehensible:
        The 16-cell beta_4 is the finite regular four-dimensional cross polytope with Schläfli symbol {3,3,4}.
         It is also known as the hyperoctahedron (Buekenhout and Parker 1998) or hexadecachoron, and
         its composed of 16 tetrahedra, with 4 to an edge. It has 8 vertices, 24 edges, and 32 faces. It is
         one of the six regular polychora.

Sixteen is the age at which you can drive a car on the highway in most States and, under British Law, the age at which you can do all sorts of wonderful things as outlined on this really neat  web-site at Today's Date.

Wednesday, June 5, 2013

Number Patterns in Problem Solving.

This appeared on my Facebook page today. I get lots of these with the invitation to solve it. I'm not very good at FB so I never like to click on anything I think is going to get me into trouble. Who knows what is lurking the other side of a smple mouse click?

Anyway this is a really neat little problem that very eloquently demonstrates the power of pattern in learning math. As I have said many times before the identification of a numercial pattern changes everything in terms of trying to remember facts as well as more higher order thinking activities such as genuine problem solving. Most algebraic problems require the application of a pattern of some sort.

So what does the idea of pattern have to do with this little FB treat? First there is a pattern to each of the descending series of numbers; at least until the 3 is reached. They descend by 1 eachg time. The numbers on the right also descend but by different amounts, 14, 12, 10. extending these patterns, if there was a 4 on the left the number on the right would be 12 ( 8 less than 20), then would come 3 on the left and 6 on the right (6 less than 12). Now look at th relationship between each of the pairs of numbers and you get 8x7=56. 7x6 = 42, 6x5=30, 5x4=20, 4x3=12, and 3x2=6. Each number descends by 1. I could be wrong, of course, and completely missed the trick, if there is one, to get a differerent answer.

I'm not sure if one needs to be a genius to solve this. I would expect any 4th grade student to be able to solve this if they have been taught that math is the science of pattern and not a random collection of facts and ideas.

Tuesday, June 4, 2013

Richmond Round Church Bicentennial

This year will mark the 200th anniversary of the iconic Round Church in the village of Richmond where I live about 15 miles from St. Michael's College.

To be mathematically accurate, or linguistically correct, the church is not actually round but has 16 sides, so for all intents and purposes it is pretty round. I think each side of the church was constructed by one of the local families in the village at that time.

We kicked off the year of celebrations with a Scottish music concert on New years Eve, Hogmanay, and then have celebrated the musical heritage of the church with a concert each month featuring a different genre of music. We  have sold T-shirts and other mementos of the occasion including a beautiful Christmas tree ornament in the shape of the Round Church. The celebrations will climax the weekend of August 9,10 and 11th with more music, a farmer's market, an art exhibition  and visits, and probably speeches, by local and State politician.

The monthly concerts have been a wonderful way of bringing the community together to have a good time dancing and/or listening to some great music. Students from the local schools have been involved through class visits to the Round Church in which they write about their experiences, draw pictures of the church and imagine what it must have been like in 1813. It really is so neat to see so many teachers from local schools getting their students involved in the appreciation of their local heritage.