What Could Be Different
So math is actually easy but we are convinced (or we convince ourselves) that it is hard. What can we do about it? There is a LOT that is wrong with the typical approach to teaching math, but I’ll try to keep this positive and reasonably short. Here are just a few guiding suggestions:
Think Creatively As Well As Critically
Math is known for having only one right answer and thus not thought to be a creative endeavor. However, while there may be only one right answer, there are usually multiple or even unlimited ways to arrive at that answer, which is where divergent thinking has a role to play. Instead of (or at least in addition to) teaching algorithms we can be teaching concepts and principles, throwing them out like legos and letting students decide how to assemble them. Different groups can be given the same objective, and then if they don’t arrive at the same answer they can figure out through discussion where the discrepancy is (this is where critical thinking comes in).
An example of how solutions can be arrived at in different ways is in the order of arithmetic operations. Look at the following numbers and try to add them in your head:
12 + 15 + 11 + 3 + 19
Now try to add them in this order:
19 + 11 + 12 + 3 + 15
It’s easier to do in the second case because of the way they are grouped: 19 + 11 = 30, 12 + 3 = 15, 15 + 15 = 30, 30 + 30 = 60. These steps are all easy to do in your head, making the answer easier to arrive at than if you tried to add them in a different order. Here’s another example, with multiplication:
2 x 7 x 3 x 5
Now multiply them in this order:
7 x 3 x 2 x 5
It’s easy to do 7 x 3 = 21, 2 x 5 = 10, and 21 x 10 = 210 in your head. Many basic arithmetic calculations can be simplified this way (including subtracting and dividing), and done more quickly and easily in your head than by writing them down and following the standard algorithmic approach, or even using a calculator.
Make Things Easier, Not Harder
You can’t blame math teachers for wanting to dazzle and stun their students by making things look more complicated than they are, but everything in math is actually simple if presented in the right way. Different students will take better to different explanations, but because math is based on logic, there is nothing about it that is not self evident if viewed from the right perspective.
Be Like Socrates
In fact, because math is so internally consistent, it is the ideal arena to apply the Socratic method. When I tutor clients in math, I do my best to avoid ever telling them anything, but rather lead them through the process of discovery by asking them the right questions at the right times in the right way to allow them to arrive at conclusions themselves. What I am teaching them is not a set of facts, but rather a method of directing their thinking in productive ways, so that eventually they come to be able to automatically ask themselves the right sorts of questions in a variety of situations.
Follow Interest, Not A Curriculum
The prerequisite for any type of learning is a thirst for knowledge, which can only come from creating and pursuing questions a student is actually interested in, and it just might not line up exactly with any pre-determined curriculum – in fact, it probably won’t. Learning does not take place on a pre-set schedule, but then neither does life. By identifying and supporting the interests of students, instead of trying to standardize them, we empower them to develop their own greatest strengths, which are, of course, unique – and thank goodness for it.
Nurture The Joy Of Discovery
There is a widespread myth that kids have to be forced to learn, but it’s simply not true; kids are, in fact, eager to learn, just not necessarily whatever happens to be put in front of them. Often in math we focus on teaching certain techniques to the exclusion of all of the interesting diversions that appear at every turn. The irony is that all we really have to do is nurture the joy of discovery, and kids will discover more for themselves than we could ever teach them. By allowing kids to ask and answer the questions that are important, meaningful, or just plain interesting to them, we empower them with the ability and the confidence to develop their own gifts, which is what will actually enable them to lead happy, meaningful, and fulfilling lives.