How my autodidactic 9 year old is learning maths without a curriculum

Maths with an autodidactic 9 year old

In my last post I described J(9) as fiercely autodidactic, which makes me giggle because it’s so literally true. J(9) is bright, funny, creative – and very independent. When you add in the emotional regulation challenges that come with Sensory Processing Disorder, you have a child who keeps homeschooling life very interesting.

Like his sister, J(9) didn’t get on with any maths curriculum. We stopped looking for one that worked a long time ago. He happily joins C(10) and me for maths stories and hands-on activities, but until recently it was impossible to do one-to-one maths with J(9).

I’ve heard enough stories about unschooled kids and maths to know that he’ll get there in the end. J(9) has a natural aptitude for numbers – he knows most of the multiplication tables without ever having consciously learned them, for example. So I didn’t worry about his long-term future. But maths is fun, and I didn’t want him to miss out.

An obvious solution for someone who doesn’t like to be taught is to use a self-teaching curriculum. Unfortunately, J(9) finds these boring. I sympathise. It’s difficult to bring out the joy of real-world maths in a self-teaching curriculum aimed at 9-year-olds.

I thought, briefly, that Khan Academy might be an exception. I liked how its maths curriculum is laid out, and  the sophisticated way coaches can monitor pupils’  work. Unfortunately, Khan Academy didn’t work out for J(9). I’ll share more about that in my next post.

What to try next?

One of my favourite homeschool mum roles is detective. I love quietly observing my children, gathering clues about how I can support their learning.

I considered what I knew about J(9) and maths. He has strong spatial skills and likes playing with numbers. He’s easily bored, and to focus his mind he often needs to move his body. He loves puzzles and games – but if there’s one thing even more likely to trigger a meltdown than making a mistake, it’s losing at a game. We’re working on these challenges. I know about the importance of a growth mindset, and one day I hope that J(9) will see the value of mistakes, too.

In the meantime, I relied on my own growth mindset. I took everything I’d learned from each of our maths “failures” and just kept on trying new ways to work with J(9). It only occurred to me recently, looking back over the last few months, that we seem finally to have found our groove.

maths with an autodidact

The solution (for now)

What has evolved for us is an extremely relaxed version of the buddy maths I do with C(10). Maybe “relaxed” isn’t right word. “Mindful” might be a better description of my role in the process. Here’s how it looks in detail.

The book we use – J(9) chooses a book to work from (e.g. a maths story, or a source of problems). Every day for the last month he’s chosen Becoming a Problem Solving Genius: A Handbook of Math Strategies. (I’ll say more about why we love this book in my next post.)

Where we do maths – We take our book, together with whiteboards and markers, to the sofa.

Topic of the day – J(9) picks a chapter. We rarely follow books sequentially, though we often continue with the next level of problems in a topic we left off last time.

Time of think – One of us reads out a problem. Then I stay quiet and give J(9) time to think. I only offer hints  when he asks for them (I’ve learned this the hard way). Instead, I take deep breaths and remind myself that crawling under the sofa being a snake, or jumping on top of it like a monkey, helps him concentrate.

Writing things down – If I don’t instantly know the answer to a problem, I use a whiteboard to figure it out. J(9), ever independent, doesn’t look at my workings. His brain works differently from mine and he often mentally calculates things I can’t.

I don’t force him to write anything down, but he sees me doing so, and recently he’s started to make his own notes and diagrams when he solves more complex problems. I do my secret happy-dance when he does this, because representing problems in different ways is an important mathematical strategy. It also allows him to retrace his steps when he goes wrong. (And – less importantly – one day he’ll need to show his workings in exams.)

Dealing with mistakes – J(9) tells me his answer when he’s done. Whether I agree or disagree, I set my voice to neutral and ask, “How did you get that?” If he’s made an error, he often spots it as he explains his process. He can then change his answer, so he doesn’t feel like he’s got it “wrong”.

Occasionally, when we get different answers, I realise I’ve made a mistake. J(9) likes it when that happens.

If I’ve got the same answer via a different process, I ask J(9) if he’d like to hear how I did it. Then  I try to respect his answer! He’s gradually learning that one tends to make fewer mistakes using simpler processes, but if I’ve learned not try to foist a method on him.

And, I admit, there are still times when J(9) can’t see where he went wrong, doesn’t want to talk about it, and he ends the session early, frustrated. I’m learning not to get upset when that happens – it doesn’t negate the learning that’s gone before. We’ll come back to the topic another time, when he’s ready.

When are we done? – There’s no minimum time for our sessions or number of problems we do. We might do one question or thirty. J(9) is in control of his learning.

maths with my autodidact

The results (so far)

One-to-one maths with J(9) has transformed from something we both dreaded into an absolute pleasure (mostly).

I’m hopeful that our buddy maths routine will continue after we’ve exhausted the questions in Becoming a Problem-Solving Genius. Perhaps we’ll move on to Murderous Maths or try out one of the many great sources of maths videos.  I’ll let you know.

Perhaps the best outcome of our new way of doing maths is that J(9) is beginning to trust me as his learning mentor. I know he will always want to learn as independently as possible. As he gets older that’s not necessarily a bad thing. But I want him to know he can always come to me for help and support.


I’m appreciatively linking up here:

Weekly Wrap-Up at Weird Unsocialized Homeschoolers

The Hip Homeschool Hop at Hip Homeschool Moms

The Home Ed Link Up week 4 at Adventures in Home Schooling

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24 thoughts on “How my autodidactic 9 year old is learning maths without a curriculum

  1. I’m so pleased you have found something which works so well! I just wish I could do the same for the girls. We have started having very relaxed fraction maths, complete with biscuits which we cut up to demonstrate. Funnily enough I never hear a complaint about that! I can’t always fall back on food to teach a mathematical concept else we’ll all be the size of houses!
    I think the white board might just be one of your best ideas. I like the idea of the girls working one problem at a time, without the fear of lots more to come.
    Thanks for sharing, it’s always interesting to see how others work!

    1. I think whiteboards are our favourite homeschool tool. The postman delivered a pack of new dry wipe markers and a couple of magnetic board rubbers today, and I have been ridiculously happy all day every time I look at them. Is that very sad?

      Biscuit maths sounds like a splendid idea. I bet you could go right through to calculus and trig with your creativity! Small biscuits?

  2. I find myself reading this post with knowing nods and smiles. You’re not alone! 🙂 I know exactly what the scenes look like when they happen because I happen to be a veteran to such scenarios, especially your points in “Time to think” and “Dealing with mistakes”. 🙂

    The natural process of maturation in children, both physically and emotionally, will bring about much positive changes that will enable them to be more academically ready (in the traditional sense). It appears that you’re doing a great job with J(9) by honouring his learning style. 🙂

    1. Thanks, Hwee – it’s always a relief to know I’m not the only one!

      You’re so right about natural maturation. Seeing how much C has changed over the last year has helped me to be much more relaxed about J. In fact C was telling me all about it today, after watching a load of psychology videos stemming from her current obsession with author/YouTuber/genius John Green. 🙂

  3. Another idea I will have to keep in mind. I really like seeing the way you individualize learning to keep your students engages.

    1. Thanks Carol. Considering they are only 16 months apart, my kids learn in such different ways. It’s a real pleasure zoning into what makes each of them tick.

  4. A book you might want to look into for your autodidact is _A Beginner’s Guide to Constructing the Universe_ subtitled “The Mathematical Archetypes of Nature, Art and Science” by Michael S. Schneider. It’s an everything book that explores the numbers 1 through 10 and their significance from about every possible angle. Although not specifically a curriculum, more like a museum, it could be a year-long study by itself.

    1. Thank you so much, Nancy. I’ve just downloaded a copy. I’ve never come across the idea of “sacred geometry” before but it looks fascinating, and right up our street.

      1. There is also an “old” PBS series called Life by the Numbers (narrated by Danny Glover) that could be too advanced for your children right now but approaches math from fascinating perspectives. It’s pricey but so good. You might want to check out the book first or the review on
        I love the big picture of mathematics, not just the computation~

        1. I love the big picture, too, Nancy (definitely a Myers-Briggs intuitor).

          I see that Keith Devlin consulted on the series – I’ve got his Introduction to Mathematical Thinking (not that I’ve got very far with it so far). I’ll definitely check out the book and YouTube clips of the series.

          Thanks again – I love hearing about these kind of resources.

  5. This was such a lovely post to read and one of the many reasons I love homeschooling. We can really observe our kids and recognize what works and what doesn’t work. No public school teacher will ever have the time to do that. Math is not a favorite around here either. I am going to check out a couple of your resources and some of the resources your commenters mentioned.

    1. We are so lucky, aren’t we Karen? I love seeing your photos of Keilee engrossed in one of her passions. You are both such an inspiration.

  6. Lucinda,

    I can relate so much to your words about being a detective. I am doing that all the time, trying to help Gemma-Rose, especially, enjoy and learn maths. Sometimes I have to step very carefully. Like J, she can get very frustrated. The barrier goes up and then she won’t listen.

    Trust… you have hit the nail on the head! Unless they trust us, they won’t even listen. That trust can be so easy to damage. That’s why I don’t insist Gemma-Rose does things the conventional way even though that would be far simpler for me. She wouldn’t learn anything and the trust between us would disappear.

    Funny how we are both pondering maths at the moment!

    1. Sue

      Being a detective is fun, isn’t it? Especially when the rewards are so great.

      Yes, it would be simpler in many ways if my children both learned in more conventional ways. But then my life wouldn’t be nearly as interesting. I am reminded of one of the characteristics of what psychologists call “flow” – something about the level of challenge being enough to engage us but not so great as to put us off. (Mihaly Csikszezentmihalyi puts it much better.)

      I am always glad to be pondering the same subject as you. It’s so interesting chatting with a kindred spirt, especially one with so much unschooling experience!

  7. Gosh, it’s been a long, long time since I have visited. Without a computer for 6 months, my blogging mostly stopped…but I have a laptop again! LOL Does this all sound familiar! Sam (9) and his SPD…and Math…and games. I’m going to try video instruction (Saxon) next year and see how that goes. He needs structure and rules…and LOTS of repetition. I considered Khan too. Maybe that will be next? or simply books and games? His spatial reasoning is crazy good. Odd how it works out, huh?

    1. Jessy,
      I’m so pleased you’re back!
      I can completely relate to all the things you’ve tried with Sam. And it sounds like you now know a lot more about his learning style than you once did. I keep telling myself that’s a good thing with J(9)!
      I have terrible spatial reasoning so I find these boys amazing. 🙂

  8. Whiteboards – brilliant:) I’ve been using a little blackboard with my youngest (4) to help explain various things and it works really well. After reading this I’m wondering why I haven’t used it ( or bought a whiteboard) with my 9 year old? It is a perfect tool for maths – thank you for helping me:)
    The buddy system looks like it is really working for you both. My 9 year old really enjoys maths when I attempt the same exercise as him and he loves it when I get something wrong. You have made me reflect on this and I’m now going to make my involvement a constant part of his maths session.

    Thanks so much for linking up to this weeks #homeedlinkup

    1. Whiteboards are my absolute favourite homeschooling tool, Prudence! We bought ours in the US (I so wish we had Target and Dollar Tree over here) but I’ve noticed they seem finally to be available at a reasonable price over here.
      Buddy maths is probably all of our favourite parts of the day (most days, anyway!).
      Thank you so much for hosting the link up. I have already connected with a heap of fantastic bloggers thanks to you. 🙂

  9. What a great post! I have a 7 year old who is extremely suspicious of anything educational – particularly maths. I love your approach and will be looking at the books you’ve been using!

  10. It’s been too long since I visited your blog. (So much reading to do! So little time!!) I always love when you write about math because it’s such a sore spot in our home, and I think I must have the most stubbornly independent children in the world!! I’m going to be checking out some of these resources to strew on my bookshelf for them 🙂

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