Thoughts on Learning Maths



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“…it is not an imposition on children or an artificial exercise to work with numbers, quantity, classification, dimensions, forms, measurement, transformation, orientation, conservation, and change, or speed and space, because these explorations belong spontaneously to the everyday experiences of living, playing, negotiating, thinking and speaking by children.”  ~ Loris Malaguzzi

What do you think Malaguzzi was saying in this quote?

“…it is not an imposition on children or an artificial exercise to work with numbers…”  

I’ve been thinking about this a lot lately; artificial exercises in learning. I am not sure whether I am an incredibly indecisive homeschool mama or an incredibly reflective one. I do know though that how we flow through our days is something which is continually on my mind.

These last few weeks, as I have been trying to find a working balance between unschooling and learning which aligns with our Australian Curriculum, I keep coming back to maths.

Much like reading (which I’ll share some thoughts on next week), I am becoming more and more convinced that targeted explorations (ones which focus on specific skills) can be both engaging and beneficial to Jack and Sarah while still allowing them to learn at their own pace and in their own way.

I think Malaguzzi is saying a couple of things in this quote. Firstly that working with numbers; exploring numbers and mathematical concepts outside of a child’s independent play, is a valid and worthwhile experience for children as these same concepts occur naturally during play and so an authentic connection can be made between the two.

Spielgaben Spielgaben Spielgaben So an invitation which encourages children to explore counting or classifying, computational strategies,  shapes and patterning, measurement and volume, addition and subtraction or other mathematical concepts is not an ‘artificial exercise‘ for children as they will interact with the materials, make discoveries, test theories and practice new skills in much the same way they would during spontaneous play.

Secondly, what would be your understanding of an artificial exercise? I think these two words are the cornerstone of the Reggio Emilia Approach. Are the experiences we are providing authentic?

  • Are they based on our observations of our children?
  • Do they represent a deep respect for children as capable, intelligent and with an extraordinary inner drive to explore and discover?
  • Do they ignite a child’s curiosity? Does the experience make the child want to learn more?
  • Are the materials beautiful or interesting to look at? touch?
  • Can the child hold, move and explore all the materials?

So while so much of Jack and Sarah’s understanding of mathematical concepts has come from engaging with different materials during play, we also work together on specific skills.

Spielgaben Spielgaben I think in order to make sure we are responding to our child’s interests and not our own, we really need to watch and listen to our children so we can identify their questions or any misconceptions they may have.

If we jump the gun, if we have a sequence of skills we plan to introduce, we are creating experiences which are external to the child; artificial exercises. However when we watch their play and notice their wonderings, we can create an experience which meets their needs at that moment.

For us this means me referring to our Australian Curriculum and being mindful of the scope and sequence of concepts and then watching Jack and Sarah for opportunities to explore these concepts as their interests develop.

I am feeling more confident now that we can move forward with maths in an authentic way and I am looking forward to sharing more of our explorations with you all.


Jack and Sarah are working with our Spielgaben set. You can read my Spielgaben review here.

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To take advantage of this discount, simply send an email to mentioning An Everyday Story and Spielgaben will reply with a discount coupon. 

22 Replies to “Thoughts on Learning Maths”

  1. Hello Kate. I’m just wondering we’re you access your Australian curriculum from? We are still deciding if I am going to homeschool but I would love to have a look at the curriculum.

      1. Thank you Naamah

    1. Yes, sorry Carla. How did you go? Have you had a chance to look at it yet? It is really great because the whole scope and sequence is there for each of the different subject areas. I use it as a guide rather than as a curriculum; just to keep in my mind the different concepts and topics and then since it is in my mind I am able to create different explorations or put out different materials which will allow Jack to work on those concepts.

  2. * where

  3. Beautiful reflective post, Kate! I think it’s wise to assess and evaluate along the way, no matter what schooling path is chosen! Sounds like you have found a balance that works for you and for your kids… although Im not homeschooling, my philosophy is similar in that I am generally child-led but where I see need or opportunity, I feel happy to introduce more intentional teaching/activity. Hm, maybe I will just send my kids to your place 😉

    1. Thanks Kate 🙂 Well they can come over any time! I think I am getting more comfortable with teaching specifics. I really want to protect Jack and Sarah’s enthusiasm for learning and I want to make sure that when I’m teaching specific skills that it fits naturally into something we are learning rather than as an separate out-of-context style of learning. I’m am gaining confidence though, I figure we have a little while to work on it together 🙂

  4. Im new Reggio Emilia but find it so fascinating. I appreciate your insights and recently Ive been thinking a lot about “artifical activities” myself. I have a two year old where would you suggest I begin with this approach? What books should I read? Thanks so much for the beautiful blog!

    1. Hi Sarah. I think with a two year old, the best place to start is with a lot of sensory exploration. A lot of exploring in nature, exploring authentic art materials like paint (watercolours and washable), pastels (chalk and oil), charcoal, clay that sort of thing. Lots of open-ended exploration. Many of the books are intended for preschoolers/kindergarteners. I would recommend Learning Together with Children and The Language of Art. These are the books that I refer to most often. Your local library might have them otherwise I have linked to them on Amazon so you can have a bit more of a look.

  5. Flo - from Uruguay says:

    The other day I was taking the plates and glases form the washing machine, with the help of my daughter, she is five, and she started putting all the cups and glases in the table. And suddenly out of random, she recognized that there was a pattern: cup, glass, cup, glass, so she continued the serie….till there were no more glasses or cups available. I was astonish and happy to encourage that simple work….it came from her…I hadn´t notice it before!

    1. I notice these things too. Math concepts that Jack and Sarah have picked up along the way. The other morning Sarah was spreading butter on her breakfast toast. She asked Jack if he wanted her to cut it. He said, yes in half, then you’ll have 2 pieces or half again and them you’ll have 4 pieces. In that simple conversation I learnt that Sarah understood cutting a whole into pieces and Jack understood that two parts are halves and half of a halve made 4 pieces. I was astonished too 🙂

  6. where are those images on the ipad in the background from?

    1. They are part of the digital learning resources which come with the Spielgaben set. Jack is really enjoying the challenges at the moment.

  7. Hi Kate. I’m a fellow reflective homeschooling mama and I really appreciate your reflective posts 🙂 I love what you’ve come up with with keeping math authentic. My kids actually ask to work on math (ages 4&5) and that’s when we do more of the specific, targeted exercises. I’m not sure they would be as interested if they didn’t get lots of opportunity to “play” with math while exploring their interests. It’s all child-led and as unschooling moms we do have to be one step ahead, all the time, it seems!

    1. Hi Amy, my Jack asks to work on different projects – a lot of science, social studies, experiments, that sort of thing but has never really asked to work on maths which is why I think I am thinking about it so much. I often think, well if he were at school he’d be doing this and that and then I start to overthink things and worry that we should be doing more which I know is just me still unlearning how to be a teacher.

      You are so right, children are never enthusiastic about learning (in an authentic and meaningful way) when they are forced. I hear from a lot of frustrated homeschool parents who want to know how to get their children to love learning and it is often that case that their routine is too parent-initiated/directed/controlled. As child-led homeschoolers we do always have to be one step ahead…but only one otherwise I find I start to take over too much 🙂 It’s a difficult balance 🙂

  8. Great thoughtful post. I see maths skills as a tool for learning, just as reading is a tool for learning. I remember one of the first things I learned about Reggio was that they would directly teach some skills – such as wiping a paint brush against the pot. I have also directly taught my daughter some skills – for example, I’ve told her explicitly what the letter sounds are. Equally, I’ll tell her that the fern is an example of a fractal, or that the number after 39 is 40. I won’t drill and I will follow interests – in this case, she has an interest in plants and loves pointing out the house numbers when we walk down the street.

    I’ve found this effective for her – at 3, she can sound out CVCs and has a good bank of sightwords – I don’t even know where she’s picked up most of them. She can also count beyond 100, knows shapes in 2d and 3d, and has just begun adding simple numbers in her head. It’ll be interesting to see if my son follows a different path or not.

    There are a couple of good books which have helped me learn more about embedding maths (such as maths art, maths vocab and maths concepts) into everyday play and life. Moebius Noodles is one and Let’s Play Math is another – both of which have good blogs. There is a good glossary at the end of Moebius Noodles which, if you’re like me and barely remember anything of maths at school, is a must read!

    1. Thanks Cara. You are so right, I won’t drill and I will follow interests 🙂 I think I am still learning to trust; still learning that I don’t have to provide all the learning for them, and that they will give me the cues and learn from the environment I create for them. Until three years ago, I had been in school (teaching and learning) for 25 years! It’s a long time and a lot of learned ideas of what is learning. We are getting there though.

      I have heard of Moebius Noodles, but I had forgotten about it so will look it up again 🙂 Thanks for that 🙂 And you are so right, I have had to review even the most basic of concepts – I just couldn’t remember what counting on or subitising meant. My husband thought it was really funny. What hope would I have for future years if I was looking up kindergarten maths!!

  9. maru arana says:

    For me Malaguzzi’s quote means that children will encounter and work with math naturally in their play. It isn’t something we have to insert into their day- it is already there. Our focus is to pay attention so we can ask questions, give them the vocabulary, & yes sometimes make things explicit. Reading, like math, can happen naturally and easily but sometimes we need a little explicit instruction to move forward. Cathy Richardson has some fantastic books about building number sense. “Building Number Concepts Book 1 & 2” They are structured in way that builds children’s knowledge along a natural continuum in very playful ways- using story mats & small objects to counts and sort. The key for me is thinking about math and building number sense, building geometric sense, it just arithmetic.

  10. Thank you Kate, this is really lovely and thoughtful post, it made me think.

    As a Unschool family I do occasionally have moments of concern about leading the children’s experiences. Both sides of it. How much is too much, it is natural learning if I am leading the experiences. As well as am I doing enough, is it being lazy not to push certain concepts…

    I like your thoughts about artificial exercises, it gives me a reference to answer this for myself. If I am preparing experiences that I feel are engaging a natural wondering than I am not forcing and interfering (which as Unschoolers we don’t want to do) Also if I am not pushing concepts they are not ready for I am not simply being lazy 🙂
    Thank you for your lovely blog, I feel lucky to have found it 🙂

    Sarzy x

    1. **** is it natural learning. Not it is…

  11. I finally sat down tonight and worked out how to get the spielgaben inspiration cards on my iPad. I think these will be a good place for our 4yr old to start with our spielgaben set until I have our third baby (4 weeks) and can do a little more thinking about other ways to use it. Thanks for the inspiration.

    1. You’re welcome Naamah. Jack really likes the inspiration cards. I’ve found that they have been a really good jumping off point for him. He’ll build a few and then take it from there building his own.

      And the very best for the next few weeks! How truly exciting for you all.

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