Teaching Maths Another Way

I was watching a mathemagic show the other day (that's a magic show in which the magician does multiplications in his head faster than you can do them on the calculator). Right at the end, the performer revealed to the audience the trick he used to square 57683 (i.e., to multiply 57683 by itself). It's not a trick in the magical sense of the word, it's a formula for calculating (x+y) to the power of 2, which we all learned in high school, except he figured a way to make it useful beyond the final exam.

So many of us learn to ace the test without thinking of everyday applications for the things we learn. Isn't it a sign that we should change the way we teach? Remove the notion that math is the same as learning to do sample problems or calculating answers. Maths should be about solving problems, turning an unknown problem into a known one, thinking what data you need instead of having it supplied on a plate. Maths should be about tricks like the ones the "mathemagician" used to break down the problem into manageable chunks.


Not many Western schools teach the Vedic Maths of simplifying calculations, for example, and yet there is something inherently beautiful about the fact that the square of a two-digit number that end in 5 is always the product of the first digit and one more than the first digit, followed by 25. For example, the square of 75 is (7x8) followed by 25, or 5625.

Or the trick for multiplying by 11 (see tutorial 6). This is not calculating - this is playing with patterns.

In another excellent video clip, Dan Meyer suggests how to make maths problems more challenging and more fun for our students. TV has trained us that any problem can be solved  “in 22 minutes, with three commercial breaks and a laugh track”, and his dream is to teach a patient way of solving problems.

For sure, not every learning style is suited to patient problem solving. Not every student will have a natural ability to perform complex calculations in their heads. But if these ideas improve the school experience for even one student, they are worth trying.

iPads and Learning Styles

In the last ten years, computers have become the answer to the complex issue of lifting education standards. Students dropping out of school? Give them computers in the classroom. Numeracy outcomes deteriorating? Here is a website where you can do sums and compete with people in other countries. Too few teachers? No problem: replace them with computers that work 24/7 and never get sick.

This year, a new sub-trend has emerged, with iPads as the latest panacea. Apparently, all you need to keep students motivated and interested in schoolwork is to get iPads.

iPads are cool, no argument there. The education programs available impress with variety and ingenuity: from spelling through division to scientific reasoning and creative writing, you can download an app to suit every student's needs.

Too simple to be true? You bet.

While almost every child (and grownup) will enjoy playing with an iPad, not everybody's Learning Style is suited to this method of learning, iPads are mainly tactile and visual, with a limited auditory output that's not sufficient to satisfy an auditory person. Kinesthetic learners, dreamers and people who learn in social groups are left behind in the iPad revolution. True, they're also left behind in traditional methods of teaching, but what's the point of replacing one inadequate regime with another?

Learning Style Analysis (LSA) is a tool designed to determine a student's learning strengths and needs. Before you go to the expense of buying an iPad for every student in every classroom, spend 5% of that budget analysing their learning styles. You may discover they don't need an iPad nearly as much as they need a quiet place to concentrate or an electric fan on a hot afternoon.

Parent-Teacher Interview Tips

To a teacher in the first year on the job, few things are as scary as speaking to The Parents. Some will tell you their child is not stimulated enough in class. Some will say the work is too hard. There should be less homework. More homework. Some want to know whether Johnny behaves at school, others whether he's made friends, surprisingly few ask about the actual learning.

It all depends on the type of parents you're dealing with. Here are some useful definitions to help you make sense of it all:

• Helicopter Parents are over-involved parents who hover over their children offering to help you with every aspect of teaching their offspring.
• Lawnmower Parents run ahead of the children, smoothing away obstacles in their path and sometimes even doing their homework.
• Tiger Parents pressure their children into overachieving, sometimes at the expense of social and physical development.
• Grasshopper Parents think there are things more important than working hard at school: sports, parties, holidays, family reunions, watching TV....
• Vacation Parents steer away from the responsibility of parenting trusting somebody else will do it for them.
• Groupie Parents treat their children like rock stars.
• iParents try too hard to be cool.

Determine the parents' priorities and address their concerns according to the type of parents they represent. Even if you're a holistic thinker, add a few details to demonstrate how well you know the child. If you're an analytic, it may help your confidence to compose a list of salient points about each child, something the parents can take away with them from the interview.

Best of all, you can impress the parents - as well as help the student - by mentioning their learning style. "Annie benefits from doing her homework in the lounge on the floor," or "Ben needs to chew on something, physically, in order to chew on a complex homework problem" is exactly the type of thing most parents need to hear.

Teaching Love By Hand

(Today's guest post is by Tracy Lockley, an Australian writer, school teacher and mum. As she teachers her toddler daughter to cook, Tracy's words remind us of the value of love, family traditions, working as a team and learning by doing... or, if you're too small to do, then at least learning by watching.)

This afternoon, Mckenzie and I made a steamed pudding together. It was the perfect day for it – cold, grey, rainy with wind howling in off the Southern Ocean – the perfect time for a mother and daughter to engage in the time-honoured transfer of knowledge that isn’t in a book or on the internet.

I know she’s only two and a bit, but I also know that I never really cooked until after I left home. The kitchen was my mother’s domain. Although my father cooked from time to time and I baked endless chocolate cakes to avoid having to write lines for forgetting to take my books to class, my mother cooked most efficiently alone.

I would sit on the kitchen counter and read poetry to her while she cooked and she would narrate what she was doing, only occasionally requiring me to hold a pan while she scooped the contents into a bowl, or stir the gravy while she added stock. The rest of the time, I watched, and read, and learned. In this way I learned not recipes, but what food looks like, smells like, what the texture feels like as it progresses from raw ingredients towards the table.

This afternoon, as I worked around Mckenzie’s fluffy little head, helping her hold the beater, showing her how to cup the egg in her hand and how to time that sharp little blow with the back of the knife, I realised how much knowledge is contained in the simple act of making a steamed pudding.

Yes, there was a good description on the internet of how to tie the foil over the bowl, and that the bowl should be greased, but nothing about making a pleat in the foil to conduct the moisture away, how to make two straps of foil that intersect at the bottom of the bowl to ease the finished pudding out onto the plate, nothing about lining the bottom of the bowl with paper-thin slices of lemon, or dipping them in sugar so that they taste like marmalade or how to overlay them in a beautiful pattern like scales on a fish.

All this knowledge is contained in me. It exists, dormant, while I am driving on the freeway, teaching, sleeping, skydiving, but it is always there. It was planted there over a hundred chilly evenings, watching the smile on my mother’s face as she lifted the bowl off the pudding and said “Dad loves this” and many Christmases when either my mother or my grandmother would call on me to supply the pressure of one finger (oh hallowed moment!) as they secured the string on the pudding bowl before committing it to the water, followed by the patient tending of the pudding, topping up the water until it was done.

Over the years I have added my own variations and discoveries and of course, none of it is written down. I wouldn’t know where to begin. I will have to wait a few years before Mckenzie is old enough to supply that finger pressure on the string. It takes two women to do it. The string came off today when time came to lift the pudding from the pot. On your own, you just can’t do it.

In an age when many women’s cooking skills go as far as heating microwave dinners, I wonder whether Mckenzie will grow to love food in this way, not just as nourishment for the body, not just as a list of
ingredients and instructions, but as communal enterprise, and the communication of love from the cook to those she (or he) cooks for, and from generation to generation. Her apprenticeship has started. She touches and tastes freely at every stage of the process (“Mmm… taste like egg”) and delights in her handiwork when the finished product appears, but still asks “Where come from?”

In part, she’s right. A cake is more than its ingredients. There’s a kind of magic that happens and there are spells that bind generations together. I would like to think that one day, in another kitchen, far, far from now, another woman, maybe Mckenzie, or maybe her daughter will work patiently around a little head, teaching things that aren’t written down, but written on the heart.