I do a lot of mathematics in my everyday life. Some of that is due to me doing a climate science PhD, which requires me to be able to handle lots of data, some of it is due to me doing programming and maths problems in my spare time, but a lot of it I think is just part of living in the modern world. Finances are an obvious example, particularly things like taxes and interest that require an understanding of percentages. Another is the constant barrage of statistics and studies that we are surrounded with. Being able to, if not carry out the statistical analysis itself, but at least understand how one would do it can help you navigate the data and hopefully avoid those trying to pull one over on you using manipulated statistical data.

Maths pops up everywhere, but I encounter a lot of adults who are either convinced they can’t do it, or are even afraid of maths. Lots of people have that one bit of mathematics, perhaps percentages or algebra or probability that they could never understand, and that is often caught up in childhood memories of feeling humiliated by not being able to do maths, or not having it explained in a way they can understand, or memories of trying to learn times tables by rote. There’s a lot of different ways that maths as taught in early years can not stick. To make matters worse, maths is cumulative, that is, more advanced concepts use and combine earlier tools and ideas, so if you struggle with those, then later concepts will be an even harder struggle.

Given this, I was thinking about how you might go about explaining basic maths in a comprehensive and non-judgemental manner, trying to take into account common issues with learning maths.

First of all, I think the most important thing to do is to remove as many of the psychological issues with learning maths as possible. A big factor here is the fear of failure, of being judged for not understanding maths, and feeling that “well, I’m not ever going to get it”. Like a video game, where a failure just results in a “Continue?” screen, this would need to be a place where you can get things wrong without feeling terrible about yourself. This also includes avoiding certain stress causers such as high speed mental maths and rote learning multiplication tables, or at least finding a way to make these less unpleasant, whether that’s by encouraging learning through repeated practice or just acknowledging that we live in the modern age and if you do understand how to do them, you can just use a calculator.

Another factor here is giving reasons for why we’d want to do this piece of mathematics, linking it into contexts that people will already understand. If a piece of maths doesn’t directly tie into a real world context, then we need to explain why we are looking at it, and what it leads into.

I think also making this connectivity between different areas of maths clear is important as well. For practical reasons, we are taught maths in discreet sections; here is algebra, here is shape and space, here are numbers. Explaining how all of these can be linked together can often be a key for understanding them, since it lets you address a confusing problem through the lens of something you might already understand.

On a practical level, there are two ways to go about a course aiming for this. One is to be extremely specific; reaching out to individuals with particular problems about maths and working with them. While this is a very good way to handle it for those individuals it would be very work intensive, and I think for an internet based course we’d want to go to the complete opposite end of the scale, at least at first. This is what I mean by comprehensive: it would need to cover as many different ways of learning and understanding maths as possible, essentially trying to solve problems that individuals have by solving every problem we can at once. Of course, the range of issues people may have is pretty wide: some people may only struggle with say, division (a common problem I’ve heard when discussing mathematics with people), while others might find the entire subject just a slippery mess, numbers jumping around the place, so it would need to be navigable enough for the first group to get to the part they need, while complete enough to cover all the ground the second group may want, and it must do this without condescending to or dropping the morale of either group.

Furthermore, particularly for the most basic parts, such as addition, subtraction, multiplication and division, we’d want to cover all the different methods. People often have one particular method of solving these, so explaining how all the different methods come to the same answer and might have different uses is important. Finally, if you are a parent of a young child learning this stuff, they might be being taught a very different method to how you were, so helping those parents understand what their children are being taught is vital.

For this project, I am picturing a systematic series of articles and/or youtube videos, explaining concepts of mathematics with an underlying structure between the articles/videos so we can show how it all links together, and with frequent real world examples of the mathematics, would fit this.

Who would the target audience be? Not young children learning this for the first time I think; the practical examples would be created with things like taxes in mind, that kids learning them for the first time wouldn’t get. I am aware that creating a series defined as being “Mathematics for adults who hate mathematics” isn’t a killer pitch, but I think there are enough people who struggle with a particular part of maths, but want to improve, that such a creation would be worth it.

Obviously there’s a lot of work to be done here. Creating curriculum for mathematics is, of course, a full time job. But I think it this is something I can do, collecting resources and creating lessons that will hopefully help at least someone with that bit of mathematics that has slipping through their fingers for years.

If you have a particular issue you’d want covered, please comment below and discuss whatever issues you may have, or if you have ideas on how to go about doing this, I’d love to hear them!

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Would something like a tree or web structure be possible as a way to organize ideas? It sounds like part of what you’re talking about are things like cross-connects, like how repeating decimals (in the arithmetic category) are a kind of limit (in the calculus category).

…now I’m imagining kind of a wiki structure, with links and suggested paths through for studying particular topics…

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