Approaching Maths Backwards

The other day, I made a big mistake. I uttered the word ‘maths’ in Gemma-Rose’s presence. Oh my! She instantly became stiff and prickly.“What’s wrong with maths?” I asked.

“It’s boring. It’s just a lot of numbers.”

“You don’t like numbers?”


I attempted a little nudge: “Numbers can be fun. We could play a game together… a computer game.”
Gemma-Rose flung herself down on the sofa next to me, with a huge sigh. I opened my computer and soon we were on the games page of the Manga High website. “What would you like to play?” Nothing… anything… I could choose. I clicked on the first game on the page, and waited while three other ‘players’ joined us. Then Gemma-Rose began dutifully working out problems, while a character in a hot air balloon floated across the screen. Many problems later, the game finally ended, and these words flashed up on the screen: “You finished third.”

Third? Every problem was solved correctly and Gemma-Rose finished third?  What a stupid game.

“You have to get the answers faster,” I said. Then I added, “Do you think being timed helps children learn maths?”

“No! Being timed just makes me feel like panicking.”

“Let me have a go,” I said, as I chose a different game to play. Soon I was clicking and calculating and clicking. It wasn’t long before I was sighing and saying, “This is so boring! Do people think kids are stupid or something? This isn’t a game. This is just a maths exercise in disguise. It’s trickery.”
Gemma-Rose grinned. “I told you maths is boring!”

But it’s not. And I know Gemma-Rose isn’t really bored by the subject. I’ve seen her interested in such things as the Fibonacci sequence and Pi.

I wonder if maths can be approached backwards? Could we offer the big picture, show children how fascinating and interesting maths is, and then wait for a child to wonder about the details? Maybe it’s a bit like writing. We expose a child to the big picture by introducing them to great writing, when we read to them. A lot of children are then inspired to compose their own stories. But If we spend a lot of time making a child work on her spelling and grammar, she might lose interest. The details can be learnt as a child actually writes.

I’ve been pondering something else: Can maths concepts be approached from many different directions? For example, we could just tell our children what Pi is and how to use it to calculate the area of a circle (which I am sure they’ve been impatiently waiting to do!) and then set them some problems. Or we could treat Pi as something very interesting in its own right, and return to it again and again, just a little at a time, from different directions… a video, a book, a mention in a conversation, a pie!.. Each time a child comes into contact with Pi they learn more about it.

So I have a daughter who can tell you about Pi and Fibonacci and even Pythagoras, but she’s still not 100 % accurate when it comes to times tables (though she knows how to work them out given enough time). And you’d better not ask her to do long division.

Some people might say, “Just make her sit down and get those maths facts learnt, once and for all!” I am tempted to agree. That would make life a lot easier. But I can’t do that. Why not? Because that would threaten our relationship. I’d lose Gemma-Rose’s trust, a barrier would go up, and she would stop listening to me.

“Who’s in charge here?” someone else might add. Gemma-Rose is. She knows what she needs to know right at this moment. I’ve discovered it’s impossible to force kids to learn anything they don’t want to know about. That doesn’t stop parents trying though. Or teachers.

I know if I am heavy handed my daughter will probably run a mile from maths. But letting her learn maths in her own way, in her own time, may very well lead to something very exciting.

Of course, real life is already teaching Gemma-Rose a lot of the details of maths. I’ve been thinking about this too.
“You use maths all the time,” I said to Gemma-Rose. “It’s all around us.”

It is?

And then we had a very interesting real maths moment. Perhaps I can tell you about that in my next post.

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  1. Reply

    Gemma Rose sounds exactly like my Lilah Jeanne! Like you I have endured the comments of forcing multiplication table tests upon her and like you I have refused. I am still searching for a way to spark the curiosity about math and help her not dread it, or feel that she is "bad" at it. Looking forward to your next post!

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      I have been offering my girls small tastes of maths such as a video from the Numberphile series (though some are a bit too complicated for their age), or a few paragraphs from a Murderous Maths book, or a game (a proper one!,) or I suggest we do some paper folding or other maths-related activity…. I'm always on the look out for something interesting I can share.

      I just had a look at the Moebius Noodle website (see the next comment!) and it looks packed full of wonderful ideas. I am going to enjoy exploring the site!

      My daughter Sophie used to think she was 'bad' at maths. She was using one of those attractive online maths courses at the time. It all looked good but plodding her way through all the maths problems was making her hate the subject. Since then we've been exploring maths informally and now Sophie thinks of herself as a bit of a maths magician! Her whole attitude changed.

      Thank you for stopping by. I've enjoyed chatting with you!

  2. Reply

    I unschool my daughter who's 9 and I'm convinced that maths can be learnt without pages of exercises. I get so excited as she suddenly seems to grow into each new concept when the time is right. I also started a maths circle as a place to explore adventurous maths with others. Have a look at and you'll see what I mean. They love maths and are convinced that it can and should be an exciting discovery.

    1. Reply

      Oh yes! I agree with you: maths can certainly be learnt without pages of exercises. We gave up doing those some time ago. I also get excited when I see my girls involved with real maths experiences. I find the subject fascinating and I love it when they do too.

      I guess what I was trying to say in this post was that even computer games aren't real maths. They look like a great alternative to formal exercises but I know they are really no better. Occasionally I do get tempted to offer one of these games to my daughter. Having to register as a homeschooler means having to tick off all the boxes…It would be easier if Gemma-Rose knew all her maths facts so I could do this. But like you, I want my girls to view maths as an exciting discovery. And I think they do, despite Gemma-Rose telling me maths is boring. She means rote learning is boring.

      Thank you so much for the link to the Moebius Noodles site. Wow! That looks good. I am going to enjoy exploring it. Maths circles? I shall have to find out more about those!

      I really appreciate your comment. Thank you so much for stopping by!

    2. Reply

      Thank you for your kind words, juggling_ginny – and for your reports and photos. Math Lexicon hilarity made my day!

      We at Moebius Noodles working on "Mathematical Circles 101" shorter course, for people who are just starting – with more emphasis on how to start, how to get into the spirit of things, how to invite anxious or bored kids to try, etc. One thing we need to change, compared to this multiplication adventures course, is how participants reflect on their adventures – something, well, more adventurous than writing reports! However fun they are to read, it's a bit too much for most people to write.

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  4. Reply

    I had trouble posting, so I did the "test" above, before writing a paragraph again. Here goes… Math makes my daughter turn all stiff and prickly too. You might recall that I am homeschooling her this year. I had to get a tutor to teach her geometry in order to save our relationship. It was dreadful and painful! I love your post, and your approach to teaching. I think that I would love living and learning in your house!

    1. Reply


      I hope you and your daughter are enjoying homeschooling despite the pain of geometry. It sounds like you found a solution to that problem. I wonder if you find it different homeschooling to teaching at school. btw, I love your 25 years of teaching recollection post. Some wonderful memories! Congratulations on reaching this milestone. I'm sure you have left your special touch on the lives of so many children. And more to come.

      It's such a pity we are unable to meet in real life and chat about daughters and homeschooling and all the other interesting things we have in common.

      Thank you for stopping by!

  5. Reply

    The world needs your thoughts, Sue. Please keep sharing them. God has blessed you with a great mind and a huge heart.


    1. Reply


      What the world really needs is more people who encourage and bring joy to others. Thank you so much for your kind words!

    • San
    • June 2, 2014

    Hi Sue,

    Thanks for this post. I will check out some of the links mentioned. Benedict really struggles with any number work, I think he has dyscalulia which is not the best thing to have when you are diabetic and your whole life revolves around carb ratios, percentages and blood readings!

    Anything we can do to help him understand concepts and to rely on technology such as a calculator can only be a good thing. I also agree with Genma Rose timing children is just mean!

    San x

    1. Reply


      I haven't heard about dyscalulia. I just Googled it. Oh yes, Benedict will need to work out all that maths to keep himself healthy. An added challenge for both of you.

      Yes, timing kids is definitely mean! I get panicky too when I'm timed. My brain freezes up!

      Lovely to chat with you as always.

  6. Reply

    I share your thoughts on striking a balance between practising the basics (i.e. the four operations) and gaining a big picture so that the child sees the relevance of maths in his/her life. It can feel quite pointless when the child doesn't see the beauty or relevance of maths in their lives. I try to do a balance of both by making sure that Tiger has a strong foundation of the basics and then mixing it in with non-drill activities like games or puzzles. The exercises are done once in a while, which keeps his interest and builds his skills; the rest of the time we play games and do puzzles. You might want to check out this list to see whether their styles of math are suitable for Gemma-Rose:
    1) books by Edward Zaccaro
    2) The Warlord series
    3) NRICH maths website
    4) Can you believe this is maths website (
    5) Math Art books
    6) Math Games and Activities Around the World by Zasalvsky

    As you've rightly pointed out, your relationship with your child is paramount. Sometimes a temporary change of 'scenery', i.e. the child doing maths somewhere else or with someone else, may be helpful. You might find that group activities such as an informal maths club in your area may be useful as a different approach.

    1. Reply


      I really appreciate the list of resources. Thank you so much. I will enjoy exploring them. I hope Gemma-Rose will too!

      Maths clubs sound like a great idea. I will look into that too though I doubt if we have something like that locally because we live in a rather quiet place.

      I remember your very fairly recent interesting maths posts. Despite our own ideas, we have to listen to our children and accept the way they learn and respond to that.

      Thank you so much for taking the time to share your thoughts. They are helpful!

  7. Reply

    What a great post Sue! It makes total sense to me.

    Why not approach maths from whole to parts? After all, that's the way we approach most everything else in our homeschool lifestyle too. It does make a bit of a mess in the beginning but then little by little this approach begins to make sense.

    Have you seen this TED Talk:

    I would love to hear how you are approaching maths from this whole to parts method. My ten year old daughter, a self professed math lover, loves to play chess and mancala. I will be on the hunt for more strategy/brain games to incorporate into our days. Not that we're winding down our outside activities, we'll have lots of time to explore!

    We also have the elementary and middle school Zaccaro book, Family Math I &II, and the Danca McKellar books as well a few others. I just need to bring these down from our shelves, offer my girls to go through these together and see what sparks an interest.


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      I'm glad you understood what I was trying to say about working backwards with maths! Sometimes I think kids get bogged down with the details. They never get to the big picture, which is sad because they might find it very interesting and even exciting!

      I've been offering my girls videos, and books etc that most people would think too difficult for them. And yes, sometimes they don't understand everything, but most times they understand enough. For example we were watching a Numberphile video about Fibonacci and music. I explained what the Fibonacci sequence is. The girls then wanted to try writing a piece of music based on this sequence.

      Another time, we watched a video about measuring Pi using pies. I explained what Pi is. The girls then understood the video and enjoyed it. The fact that Pi is used to measure areas and circumferences of circles was irrelevant. The girls just found the constant relationship between circumference and diameter of a circle fascinating in its own right.

      I want to offer my kids more hands on maths. We've done some paper folding etc. using this website:

      I think puzzles and strategy games are good too. I was very interested to hear that the math teacher in the TED talk recommended these. Thanks for the link!

      I am reading a book called 'Alex's Adventures in Numberland'. I think it is a bit too difficult for my girls at the moment, but I'm enjoying it. I keep sharing snippets of what I'm reading with them.

      I haven't seen any of the books you mentioned but I shall have a look!

      Thank you so much for chatting!

  8. Reply

    I've been thinking a lot about this post. And just now I read this article: Number 3 on the list is like what you are talking about here. I really do think this "backwards" approach is really not backwards at all, but quite an important way to learn many things!! 🙂 I always try to have my "end" in mind as I do what I do, so I may get to where I want to. Hope that makes sense.. Words are not –>my<– thing, but they surely are yours, Sue.

    1. Reply


      Your words worked fine! Thank you for the link. The article happened to be just what I need at the moment. I have so many creative ideas but I'm not very productive. i waste so much time because I'm not organised and don't get down to work. I related so well to the point about setting deadlines. I don't do thta because I know I won't meet them. I cheat! I should make myself work harder.

      Working backwards… yes, I see what you mean. Unless that end goal is firmly in sight, we don't really know what we are striving towards. It motivates us when we are lost in the details. It applies to maths. It also applies to my novel writing. It was appropriate the example was about writing! I shall have to start a notebook. First note: the end result! Thank you so much for returning and leaving the link!

  9. Sue, I loved this post so much. It is exactly how we do maths. My children can't tolerate doing things any other way! I am so glad, because otherwise we would probably all be slogging through a deathly dull age-appropriate curriculum and missing out on so much exciting learning.

    Today, just doing a few questions from our current favourite maths book (Becoming a Problem-Solving Genius by Edward Zaccarro) we talked about negative numbers, dividing and multiplying fractions, pi, powers, long division and long multiplication with decimals, among other topics.

    When I was working with Cordie, I had a mental block on how to multiply decimals and we ended up working out that a 4/5 lb piece of cheese cost £476! We laughed so much – I don't think either of us will ever forget again where to put the decimal points. She even took a photo of our whiteboard workings to look back on and laugh!

    I have been enjoying all your posts lately, and your videos. Thank you for all the time you put into your blog!

    1. Reply


      I enjoyed your own maths post earlier today. I was in a rush so didn't stop to comment, but I'll be back. (There were a couple of things you said in particular that really resonated with me.)

      I have been surprised at how many people understood what I was trying to say in this post, despite me finding it hard to put it into words. It could be there are a lot of children who work better using a backwards approach. I actually googled the words 'learning maths backwards' (after I'd written this post) and came across someone else who said this way suited her children. There were some negative comments on that post saying maths needs to be learnt sequentially, from those that don't believe it can be learnt in any other way. Such people have very set opinions. Observing our own children can teach us so much. That's one of the things you were writing about. What does it matter what the 'right' way is? All that matters is how our own children learn best.

      I laughed about the cheese. That was a fortunate mistake. You will remember that forever!

      Thank you so much for reading my posts. I do enjoy mulling over ideas with you!

  10. Reply

    I just came to your site through a link on Navigating By Joy – I'm so pleased I did! My 7 year old is convinced she doesn't like maths – or anything 'educational' for that matter – and I never thought of approaching it backwards before! Am feeling rather excited that this might open something up for us – thank you so much!

    1. Reply


      Lucinda's post was excellent, wasn't it? She was very kind linking to my own maths post. Thank you for hopping over to read it. For some children it seems it's not maths which is the problem, but the way it is presented. I love how Lucinda described herself as a detective, observing what works best with her children. You'll have to share your own maths experiences if you try the backward approach. Let us know if it appealed to the sausages!

      Thank you so much for stopping by to comment!

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