Even if home educators follow a child-led approach in many areas, maths seems to be one subject where it is thought children ought to be receiving some form of daily instruction. Many parents seem to be afraid of maths, perhaps because their own experience of maths at school was negative and they are afraid of failing their children in this area. Many people seem to think they are no good at maths, and I think this itself is reflective of our schooling and the disservice being done to mathematics in classrooms. We seem to equate maths with arithmetic or calculation ... SUMS! But, wouldn't it be great to take maths out of the box? What if we can think of it, as Arthur Benjamin describes it, as "the science of pattern"? (His 6-minute TED talk here is worth a watch!
In recent weeks, the boys and I have been following a programme called Multiplication Explorers from Natural Math. I have found these activities to be really useful in reshaping my own ideas about mathematics, and we have had fun together exploring patterns. My second son, after just 4 terms in school, thinks he is no good at maths. Let's face it, kids know which table they're on and where they are within their class. This was one of the reasons why I took the boys out of school. In fact, he is not bad at maths. He just doesn't much like numbers! Just because he struggled to perform the tasks set by the curriculum for his age when he was in school, it doesn't mean he wouldn't be able to grasp the concepts given a little more time. In fact, he is brilliantly techy these days and uses mathematical thinking in coding and problem solving. Through the Multiplication Explorers we have seen that he is a visual learner, and able to see patterns where he might not be able to see numbers. It has been very interesting.
As I am not very mathematically minded myself, I have been a little frustrated by my own limitations. Sometimes I haven't felt able to make the most astute observations or to ask the most pertinent questions to move the boys forward. Fortunately my husband (who is a maths teacher) and eldest son are very mathematically minded and so we have seen our activities and discussions develop in ways which are beyond my capability, and this has been helpful in stretching my understanding and in helping the younger boys. What has been so great is watching the boys themselves see mathematical truths in patterns. For example, today we learned about prime numbers without looking at a number. Noticing that these numbers stood alone, different, in a pattern of circles, we considered why ... Because they are only divisible by themselves and by one. Lightbulb moment!
On another occasion, we were building multiplication towers and started with Lego bricks. The boys pretty soon moved over to Minecraft, and it wasn't long before I discovered myself short of the right size and colour Lego bricks. I had discovered for myself the wonder of Minecraft - Unlimited bricks! Beautiful multiplication towers!
One of the scariest things about school mathematics is the importance of getting the right answer. One of the most beautiful and liberating things about this course has been the realisation that you don't have to be 'right' or 'wrong'. rather you can explore and experiment or bring your own ideas to the table. Rather than leaping in because we perceive 'a mistake', try observing and reflecting, "Hmm, interesting ... What next?" or "Why did you put that one there?" Given the same task, we might all produce a very different response. And that is OK. 2 examples of our very different factorization diagrams:
And a selection of pictures from our experience of taking mathematics out of the box in recent weeks:
And here is our favourite youtube video from this project: Nature by Numbers.
We also recommend Vi Hart's youtube channel, Doodling in Maths Class! (Example: Infinity Elephants)Transform your view of mathematics. Enjoy!