Different Strokes for Different Folks - Differentiated Instruction in Math

In class this week we learned about Differentiated Instruction as it pertains to teaching math.  Differentiated instruction does not refer to my all time favourite Calculus unit, but rather to a method of teaching by which you try to tailor the class to the varying needs and learning styles of the student.

Some people (like me!) learn math best the traditional way: when a teacher stands at the front and explains the concept on the board with examples, then gives problems for students to solve independently.  Other people learn best by discovering concepts themselves through manipulatives (see my last post) and then connecting that visual to a formula and maybe practicing that formula in a group.  Still others would prefer to look at diagrams representing the concepts as they learn.  There are many different styles of learning, and, although it I don't believe it is possible to cater to all styles all the time, there are some excellent ways to incorporate different learning styles into a math classroom.

As we went through the class activities today, I didn't really feel as if they were methods of instruction so much as they were absolutely excellent, elegant ways to check understanding of concepts and help to further knowledge and understanding.

One activity we did involved 16 squares of paper.  Some had rules on them (like # of tiles = 2p+1), some had graphs, some had a table of values, and some had diagrams. We were told that among these 16 squares there were only 4 equations represented.  So, we had to match the squares together and group these squares into 4 groups of 4.  The clever thing about this is that by representing an equation four different ways, it challenges everyone to think about equations in those four different ways.  BUT, it allows people to start wherever they are most comfortable (be it a rule, graph, table, or diagram).  Genius!

Another activity we did was something called Open Questions.  Every student gets a small whiteboard and a marker, and, when the teacher puts a question up on the board, they answer it on their whiteboards  Then they may hold their whiteboards up for the teacher to see, or maybe exchange it with a neighbour to see what each other got.  But what is an open question you might ask?  Well, the best way to describe it is with an example:

Draw a line with a negative slope that passes through the point (2,4).

This question actually has an infinite number of possible answers!  As long as the students draw a graph that has a line with negative slope going through (2,4), then their answer is correct, but the steepness of the slope will vary from student to student.  Can a student get an incorrect answer?  Yes, of course, but then the teacher will be able to see instantly what part of the question the student didn't understand.  If the graph has a positive slope instead of negative, but does pass through (2,4), then the teacher knows that student understands coordinates but is a bit hazy with slope.  Or, if a student has made the line pass instead through (4,2), the teacher will know to review coordinates.

It's a really elegant way of seeing how much students understand without putting too much pressure on them - students generally find this sort of thing really fun and again, it caters to all different learning styles!

One last activity that I want to highlight is a website called Which One Doesn't Belong created by a Canadian math teacher by the name of Mary Bourassa.  The URL is www.wodb.ca. There's also a book full of these puzzles available written by another math teacher called Christopher Danielson. Here is an example of one of these puzzles (it's actually the logo from the WODB website):

This activity is awesome.  The general idea is that each of the quadrants doesn't belong, but for a completely different reason!  For example, the top left one doesn't belong because it has a different font than the others.  This is an amazing activity for differentiation because the students will likely approach the puzzle different ways depending on their learning style, and what they are already comfortable with.  But, by having a class discussion, everyone gets to see why each quadrant doesn't belong and there will likely be many "Aha!" moments as students begin to understand the other answers. There are loads and loads of these on the WODB website and more are added all the time because they encourage people to submit their own ideas.   Many of them are quite difficult - I encourage you to check them out!

I really had a good time in class this week.  I thought that using differentiated instruction in a math classroom was going to be quite challenging, but these activities are wonderful ways of incorporating different learning styles into the classroom and actually getting students (especially those who may not be as keen on math) to (dare I say it) enjoy math class.