Mental Arithmetic and Natural Learning

© Beverley Paine, Nov 2008

I'd like to put in a good word about mental arithmetic. Although it was one of the things I least liked when I was in primary school my children learned maths largely by working sums out in their heads, without using pencil and paper. I learned the value of children working things out mentally when Thomas, at the age of four, asked 'Is half of a quarter an eighth mum?' We stuck to teaching him maths mentally from that point, only letting him use paper once we knew he fully understood the concepts he was working with.

Our eldest child was mathematically capable very young and we introduced workbooks at age five. She raced through the Rigby Module graded books and at age seven began to do the same with the Mortensen system, which uses coloured 'bricks' similar to Maths-U-See. By nine she had begun to lose the plot and had started to believe she wasn't any good at maths, even though she could do the exercises in the maths book with over 90% accuracy. She hated doing the 'working out' on paper as she could often 'see' the answer in head and didn't understand why all the steps, which she didn't understand, had to be written down. We backed off and she didn't do any maths bookwork for two years, instead using maths to solve problems every day but in her head.

At the age of eleven we gave her a maths test for her grade level - which was two years ahead of where she'd left off doing maths bookwork. She achieved 95%, with long division to four decimal places the only sums she got wrong. She had correctly worked out the multiplication to four decimal places, even though we'd never taught her how to do large multiplication sums. She'd never done or seen long division before. As with her younger brother, this was a powerful demonstration of our children's natural ability to calculate and problem solve in their heads. It made me even more determined to allow Thomas to learn in this most efficient and obviously effective manner.

We didn't use a mental arithmetic book or short tests the way I learned at school decades before. I made the mental arithmetic problems as real as possible, keeping them in context with their everyday lives. I trained myself to see and use any opportunity to gently weave a mathematical calculating or problem solving question in here and there, trying to keep it natural rather than making it sound like a test or lesson.

In this way I built a 'hidden' structure to our unschooling, learning naturally lifestyle. Most people think of natural learning as the children simply doing what they want when they want and haphazardly learning what they need to - the criticism I hear most often is that this produces gaps in the young person's knowledge and skills. That's not what we did at home: the structure was there, but it wasn't overt or obvious. By keeping homeschooling records I could see what my children were learning and when, what they needed - or I wanted them - to learn next. I could tweak our learning environment to produce the desired results. Nothing was haphazard or unstructured about it. And once I understood the power of learning in this way, instead of abandoning text and workbooks altogether, we used them they were most appropriate and useful.

I believe that mental arithmetic skills are one of the best tools we have in our brain's 'tool box'. Like spelling and grammar, mental arithmetic is a foundation 'tool' - it's like my husband's favourite and trusty hammer, an owner builder it is something he'd be lost without. It is quick, comfortable, does the job and does it well. Without the hammer we wouldn't have the lovely house we have today. Teaching our children how to use these foundation tools - mental arithmetic, spelling and grammar - in whatever way works best for our young learners and ourselves, is an essential part of our homeschooling lives.

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