Math was my favorite subject in school. And thankfully it never even struck me that that is odd. And now it is my daughter’s favorite subject. Yet I hear all the time now about how math is not fun. So I decided to put some thought into what makes math fun, and what to do to so that learning math is fun !

**The first and most important thing to do is to approach it conceptually** : Math is based on concepts that can be applied to many many situations and form the foundation. A lot of parts of math are then just logical derivations of the basic rules. Eg multiplication is a basic concept – when you add the same number several times, you are multiplying the number. Practice and quick recall of math facts is useful, but not as important as being able to understand the concept, and derive any multiplication answer from that concept. The same is true for all basic math operations. Once you know the concept, then anytime you are stuck, you can derive the answer from the concepts. And the concepts apply to different situations e.g multiplication as repeated addition for integers can then be applied to multiplying fractions by integers. It’s the same concept.

The question then arises of how to do this. We may all agree that this is important, but to teach, we need the tools and lessons that can help us do this. Below are a few examples and links to tools below that hopefully provide a more concrete approach. The key to teaching several math concepts is to visualize it. And once that visualization is used a few times, the mathematical concept can settle down in the mind of the person/child learning it.

Here’s a wonderful article by Stanford Professor Jo Boaler on the value of teaching math visually

https://www.youcubed.org/think-it-up/visual-math-improves-math-performance/

Specific tools that help in teaching maths through concepts :

- A set of tools that teaches math concepts really well through visual and physical manipulatives is the Montessori materials – which are fabulous at teaching math with manipulatives that do a good job of illustrating the concept through physical materials. I once went a Montessori teacher training and there were trainee teachers there who were in tears because suddenly math operations made simple sense, instead of being this long list of numbers and operations (math facts) requiring rote memorization.

Below are links to a couple of videos that illustrate a few of the materials and approaches used in Montessori math training.

For teaching multiplication via skip counting :

https://www.youtube.com/watch?v=eKuVCeg7zCc

Here’s a wonderful example of visualizing algebra – the binomial cube which is a visual illustration of (a+b)^{3 }= a^{3 }+ b^{3 }+ 3a^{2}b + 3ab^{2}

https://www.youtube.com/watch?v=crjItXrt43Q

I once did the Montessori teacher training for mathematics, and it was amazing to see some teachers in tears because math finally made sense to them as they saw it conceptually through the Montessori math materials.

- Another great source of visual math lessons is Stanford professor Jo Boaler’s site youcubed.org.
- Last but not least, it’s not hard to make up your own. A wonderful exercise I once saw on introducing fractions was to ask students to cut a square piece of paper into 4 equal pieces in as many ways as they can think of. Below are some creative examples. This is a lot of fun, and the kids can compete on who has the most creative shapes that are equal. It also helps understand the concept of fractions as each of these methods leads to pieces that are a 4
^{th}of the whole.

And of course you can continue. Eg what happens when you cut another one of these into 2 pieces – it then becomes 1/8^{th}. A student went on to explore and did the series shown in the picture below.

Doing math conceptually is a lot of fun, and the approaches often allow for further discovery with the tools as we saw above in the fractions example. We hope you agree. If you have additional examples or tool sets, please do email them to us.

We will continue this blog post with several other approaches and examples of how learning and teaching math can be a lot of fun.