When my son was about four and a half, we often took city buses and walked a LOT (we lived in downtown at the time). So he was familiar with the idea of looking at bus numbers and enjoyed reading them. While driving to somewhere once, I noticed a bus in the next lane and pointed it out to him. This conversation followed –
Me: Hey, look bus number 555!
O: Yea!
<Long pause>
O: Oh so that’s 15!
Me: No bus number 555.
O: Yea yea! So that’s bus 15!
Me: 555, O.
O: 3 fives make 15, no?
Me: <Penny finally drops for me and I’m speechless for a min>
O: <holding up all his fingers as I glimpsed quickly in my rear view mirror> Hey Mamma, remember? 2 fives make 10. Now show me your one hand with five more fingers! See, 3 fives make 15!
Multiplication learnt organically. No instructions, no worksheets, just a small child’s curiosity unfolding through endless theories and exploration.
Counting, adding, subtracting, multiplying, dividing, fractions, measuring, estimating – all these operations are incredibly intertwined into our daily lives. Everything from cooking to account keeping to buying fruits and vegetables involves math. Math is all around us – from the patterns on leaves to animal shells to designs on our bed linen and clothes to dates and time… everywhere. Try to escape from math in your daily life, it is impossible. Yet, we insist that math must be taught in preschool (or earlier!) as a stand alone subject, without context or purpose, with endless mind-numbing repetition through worksheets and testing.
Why?
“But, how will they ever learn to add and subtract if we don’t teach them the basics properly?!” Many adults ask this question in dismay, not realizing that there is, for example, math (implicit) in even a question as simple as, “Do you want one more toast?“
From a very young age, children naturally tend to sort, classify, count, observe patterns and use their fingers for all sorts of number related tasks. They often ask a million questions around these ideas, play in ways that organically break open and unfold mathematical concepts. They may not know it formally as “math” yet.
As soon as they hit preschool age though, adults tend to swoop in and “teach” math in more formal ways, nudging and coercing kids to count, add and subtract in more methodical adult ways, attempting to make numbers “fun”. Thing is, we don’t need to make it “fun”, it is already interesting to them, woven into various aspects of life. Only when we step back and observe these connections though, can we support that learning in more meaningful ways than mundanely quizzing our children, “What is 2 + 1?”
Free play is powerful. By free I mean an activity that a child chooses of his own accord and plays the way he wants. Here are just a few ways through which young children explore math ideas (which we can support by providing the materials and environment as well as being available for their curiosity driven questions):
The more obvious ones:
- Playing with blocks of various shapes, tangrams, building materials
- Math manipulatives (for free exploration, without an adult imposed agenda)
- Legos (my son figured out a heck of a lot of addition and multiplication with Legos on his own)
- Other put-together / take-apart toys
- Playing with measuring tape, tools and scales
- Books with numbers, rhyming poems
- Puzzles
- Board games
- Using money at stores
Less obvious ones:
- Climbing, running, jumping, hopping games that children naturally tend to make up (e.g. counting the number of steps between two locations, counting stairs)
- Playing with other open ended materials and loose parts: cardboard boxes, crafting with “junk” such as bottles, bottle caps, straws, paper, containers
- Building collections – rocks, shells, leaves, sticks, matchbox cars
- Playing / building with sticks outside
- Sorting laundry into categories, colors
- Cooking / baking (great for fractions and estimation especially)
- Setting the table at dinner time (a plate, a fork, a spoon and a napkin for each person)
- Water play – provide a tub of water with containers of different sizes and shapes
- Cleaning up toys at the end of the day – sorting them into their respective bins
- Arranging a bookshelf – sorting books by size
Schools tend to focus on memorization and speed during the early years, with the idea that if a child knows their times tables and can count to higher numbers, they can automatically do higher level math better. This is logical adult thinking, not necessarily how children absorb concepts. First, there are many paths to getting to the same concepts. Second, the intense emphasis on speed and memorization puts unnecessary pressure on a child to arrive at that correct answer quickly, rather than arriving at the understanding through an iterative process over time. As a result, children often stop “playing” with numbers and start to categorize it as “boring work”. I’ve known many children who start to hate the idea of math (after having loved it) simply because there is such an emphasis on arriving at the correct answer and quickly.
Right up until the time that my son started attending second grade at a regular school (until then he had attended either play-based schools or been unschooled), he used to be excited about counting and arithmetic and had a deep interest in very large numbers. Side benefit – I learnt a heck of a lot about large numbers through exploring his curiosity along with him – quintillion, nonillion, googol number and whatnot. “How many stars are there in our galaxy?” We read books and Googled some ideas when he wanted to delve deeper, and discussed them for fun.
While every child’s journey through math concepts looks different, it is nearly impossible that there is no math in their daily lives at all. In my son’s case, his interest later led him to randomly coming up with “math games” while I was cooking or doing laundry.
One example – ‘Ma, what is 2+2?” After I’d answer this, he’d ask me, “What is 4+4?” Then, “What is 8+8?” and so on and so forth until it got really hard for me. And he’d get a real kick out of reaching the number which was hard for me to do quickly. He’d do it all over again the next day or a couple of days later. He’d come up with different games every few days for a while and through this process he discovered – odd and even numbers, patterns in numbers (counting, addition, multiplication), fractions, negative numbers and so much more.
It would have been much more convenient for me to not see the value in these games and either dismiss him quickly because I was busy, or, turn the problem right over to him, “You tell me, what is 2+2? That’s a simple one, isn’t it?” Side note – that’s the quickest way to get a 5 or 6 year old to turn and run as fast as possible the other way! Ha. I do speak from experience, after which followed very quick learning for me to ditch ALL of my adult agendas and simply enjoy the game for fun, the way kids do. Learning happens more effortlessly when it feels genuinely fun and an adult doesn’t have to put glitter on it by constantly asking, “Isn’t this fun children?”
Over time, he started asking me to give him written addition and multiplication problems, harder and harder ones (I’ve heard/read stories such as these from other unschoolers as well, so I know my son is not an anomaly). He didn’t mind that he couldn’t do half of them on his own, he came up with his own strategies to simplify them. E.g. he came up with breaking apart two digit odd numbers into tens and ones and called it “chop addition”. He was particularly proud of that (he hadn’t formally been introduced to place values yet either!). Sure, he couldn’t add two numbers as “fast” as your typical first or second grader who was taught “methods” from the start, but he could do it and sure as heck explain it at a conceptual level and often, with real world examples IF you allowed him the time to do it.
Half way through second grade at school though, that spark started to die. He started being very hard on himself in order to arrive at the “correct” answer and with expediency. It was heart-breaking to for me to realize that a child who was so excited and curious about numbers was now afraid to try for the fear of being wrong to please his teachers. Somewhere around then, one of his teachers had mentioned to my husband and I that we should do mental math at home for speed, so we put two and two together and figured out why this was happening. This is not just my son’s story, mind you, it is many many children, so much, that people consider it “normal” and something to “get past” or “push through” without ever questioning how they got there. The same child who used to enthusiastically ask me to write up hard problems now “hated math”, let alone do ANY of the math worksheets sent home from school.
Even though teachers can be incredibly well-intentioned and invested in the well-being of every child, having to adhere to and deliver a standardized curriculum within a set period of time to a bunch of assorted kids with different learning styles often leads to killing curiosity, intrinsic motivation and natural learning in many. The focus shifts from meeting children where they are to fitting them into the curriculum somehow. I cannot tell you how many adults I’ve heard utter these words: “Ugh! I hate math so much!” or “I can’t do math!”, yet, balance their check books, buy things at stores, do all kinds of calculations to support daily life. Have to wonder how they got there.
How did math become so detached as an idea, separated from daily life and treated with special gloves? I’m not even talking about mathematics involved in learning quantum physics, just regular stuff. How many people actually have a need to use anything more than basic math in their daily lives? And when they do choose careers that involve higher level mathematics (finance, astrophysics, anything), they learn it along the way, with context and purpose in their chosen path. Yet, so many adults impose so much math upon their children earlier and earlier, assuming that if the kids didn’t learn everything and quickly, they will fail at life. There’s a fear that people often associate with math, which unfortunately gets translated into rigid curricula and rote work for young children.
Play is the natural way that young children learn best – everything from math to language to emotions and social ideas emerge through play. What play looks like at every age changes, but it is still play. Adults play too, in fact – ask any scientist they will say things like, “I was playing with this data…” Young children explore, hypothesize, test and investigate ideas iteratively to understand the world in which they live. Adults can enhance these experiences instead of interfering by observing and understanding play and then supporting in meaningful ways. Creating a learning environment for ideas to unfold is different from teaching them through direct instruction. It’s the difference between enabling children to think creatively about problems vs. giving them the steps to solve the problem.
Children who have been in rich learning environments, given the space and freedom to experiment, play with ideas, and think for themselves, naturally start to seek teachers and lessons and structure as they grow up. They are able to identify what they need in a way that suits them best. If schools focussed more on the providing a rich learning environment, rather than direct instruction in the early years, there’d be a lot less “learning issues”.
Schools must lead the way on fundamental changes such an these – since they are in the business of educating children full time. For better or worse, schooling is the norm now for children given that parents often work long hours outside the home. It is not possible for every parent to have the time or mental space to think deeply about the best learning environments for their children. So they have come to trust schools deeply. I see it as schools’ responsibility to invest in providing learning opportunities for their teachers on how children learn by (a) encouraging them to step back and observe the children in front of them, (b) valuing community over competition (that’s a post for another time!) and (c) learning to create an environment for every kind of child to thrive.
Work sheets exist for adults to “confirm” that children are learning, to be able to quantify learning in simplistic demonstrable terms, to calm our own fears, rather than working from a place of trust. Children have no such need to *know* whether they are learning, until adults infuse them with doubt by separating learning from life. Until we continue to use curricula set in stone, age driven guidelines and expect standardization of children by a certain ages, we cannot open up our minds to the infinite possibilities of creating rich learning environments.
As Sir Ken Robinson rightly said, “If you can light the spark of curiosity in a child, they will learn without further assistance, very often. Children are natural learners”.
Additional reading:
https://www.psychologytoday.com/us/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-school
https://www.psychologytoday.com/us/blog/freedom-learn/201004/kids-learn-math-easily-when-they-control-their-own-learning