New Zealand Graduating Teacher Standard 1.b

Graduating teachers have pedagogical content knowledge appropriate to the learners and learning areas of their programme.

Maths has changed a lot since I left school. When I was in primary school maths generally revolved around teachers modelling an equation and then the students were given a whole bunch of problems to solve using the equation. There was also a lot of ‘skill and drill’ which must have been effective because many decades later I find myself transported back to my primary school maths class reciting the timetables. I loved the subject, but I knew a lot of kids had an unhappy experience and that numbers were just a mystery.

Nearly two decades later I’m back in primary school where the emphasis is more on teaching numeracy. Despite many people’s hatred of the subject, maths is used all over the place. When we go shopping and see 20% of a shirt, what happens if we buy two shirts, is it 40% off? In baking people often double or half a recipe depending on their needs. Sports uses all sorts of fractions all over the place and the old adage those who don’t understand compound interest are destined to pay it, partly explains the prevalence of loan sharks in areas of low education and consequently low income.

So I get the importance of making the connection between ‘every day maths’ and what happens inside the classroom.

Getting kids to use materials and images to explore the principles taught BEFORE getting them to writing out the equations. There’s also a lot more emphasis on being able to use different strategies and formulas to find formulas,

The group I have been working with in a maths class have been learning about fractions. Last week they were working on ordering fraction and this week they are using fractions of a set using addition. eg. 2/3 of 18 = 6+6= 12. I’ve been using the Hungry birds which we decided were jelly babies, but the point was the same. The kids took to the lesson where we were using materials and imaging quite quickly and in fact were complaining that it was too easy. “Woohoo!” I thought to myself. Time to move on to using number properties in the afternoon session.

Now the students at the school scamper off to other classes before coming back to see me in math in the afternoon

The group and I met again in the afternoon and I was keen to get started on using number properties. By the end of the lesson I was despondent to find over the space of a few hours, that for a few students the bottom fell out and were back to square one. Worse than that, one of them had forgotten what the numerator and denominator’s role in fractions.

Things I will do differently next time.

Done more of a recap of the previous lesson, especially jogging the memory of some students about the parts of fraction.

Getting kids to practice writing down what they see when they are in the using materials section.

Any other suggestions?

Hmmm…. I am not a teacher BUT when I work with my children on something, I tend to do the practical hands on thing several times, then add the overlay of theory / explanation, and only after that move to the theoretical only.

With my students, I go exactly the other way – theoretical framework first, then move into the practical, but constantly relate it back to the framework.

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Thanks for your comment. Maths, or numeracy as it seems to be known as, is all about teaching the hands on stuff before the theory. The teaching of algorithms before understanding of concepts is frowned upon. I’ve still been plugging away, but the other problem is the students lack of basic facts knowledge.

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I agree- hands on stuff before theory.

I have been taking part in a maths project between ACU and a number of primary schools recently. Some interesting ideas that I have got from this project and may (or may not!) be useful are:

Get students to JUSTIFY their answers. This means they need to put into words why the answer they have given is correct. It tends to highlight any misconceptions or ‘shallow’ understanding students might have.

Another observation I have made is that it is useful to ask another student to RETELL in their own words how another student got an answer.

These ideas worked really well to develop students mathematical thinking. I’m looking forward to giving these ideas a go over a longer period of time during my next placement.

Hope these ideas were useful,

Jessica

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Thanks for your comments. That post was done early in my Teaching Experience and so I’ve learned a lot (and made a whole bunch of mistakes) since then!

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