Primary mathematics training of trainers

In March I was asked to plan and prepare for a nation-wide training on primary-level mathematics, grades 1 through 4.  This request came through my position at the Ministry of Education’s curriculum unit.  I went through the new primary curriculum we’ve created over the last 4 years, complete with lesson plans for each discipline, each day, and compiled the mathematics topics I know to be problematic.  These included place value, data analysis, rounding, fractions, decimals, geometry, weights and measures, and estimation.  I put together a plan for the week and wrote a little manual for the training.

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This is the ‘abacus cup’ activity, where each cup represents a place value. Reading the number represented by the various sticks in each cup solidifies the structure of our base 10 number system.
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After all, the 2 in 423 does not mean 2 at all, but rather 20. Everybody uses these numbers with ease, but you have to play with them to understand them deeply.

Then I called all my mathematics teacher colleagues who could get away to give a lesson or two and we trained the trainers for a week at the National Teacher Training Institute in Dili.  Our trainees, who would become trainers, consisted of top primary teachers who had been involved in previous trainings, and who were reportedly not afraid of mathematics.  (Those who were afraid of mathematics got trained next door on the new 5th and 6th grade curriculum, all disciplines.)

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As always, we made great use of leaves, stones, seeds, rubbish and local artesania. This was by necessity, since no one has any special equipment, but it’s actually even better than special equipment, since it links the concepts firmly to daily life.

It went well, with everyone having a good time doing pratika while they learned the basic concepts.  My feeling was the same as I’ve had working with the junior high teachers:  just giving them time and space and encouragement to work out exercises and solve problems was all it takes to ramp up their teaching capacity quite a bit.  Confirming that they’re on the right track is invaluable for them.

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This is our leader whom we call ‘Commandante Mena’.  She runs the National Teacher Training Institute’s primary in-service training programs. She attended the TOT to brush up on her mathematics skills. She’s measuring the width of the room using informal units: her feet.
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After using informal units, the trainers used formal units – cm – and worked out the conversion factor.

Now the fun begins.  Those ‘National Trainers’ are this week passing on what they’ve learned to directors, assistant directors and top mathematics teachers in all the municipalities of Timor-Leste.  Those attending this week’s training will then return to their own schools and pass the material off – third time now! – to every teacher there.

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Students will be shown how to measure their height with units of centimeters and also meters.

The natural question is ‘How much is lost with three pass offs?’  Or perhaps, ‘Isn’t there a better way to do this, such that teachers can be trained directly by an expert, so that at least the teacher is given correct, clear information directly?’

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If you have any sort of balance, and a syringe or measuring cup, you can use water to measure the mass of an object in grams, since one mililiter of water is 1 gram. That’s Mestre Ze from Ermera in back, of Green School fame, and Mestre Angelo from Lautem, who took us fishing last year.

Sure there is!  But it’s too expensive! This trickle down technique requires much less travel and trainer time. Experts are also few and far between, and most of them are full-time teachers, so taking them out to train deprives their students of a teacher.  This week is the single week of vacation between the first and second trimesters of the 2017 academic year, and it’s important to make full use of it.  (There are usually two weeks with kids out of class, but this year the first week was Holy Week, spent preparing for Easter.)

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This is the training of directors and assistant directors, and the scene is familiar: working together to solve the exercises. I was careful to be available, but also patient enough to let them crystallize what they did and didn’t understand.

The Ministry of Education also has a small video team, and I arranged a couple of SESIM teachers to teach nearly the entire training manual on film, which then goes by USB drives to each school, so that they can at least have a video expert on the spot.   Of course, on video one is limited to lecture and demonstration, but we always invite the viewers to grab it themselves and try it themselves.

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Mestra Joana is a mathematics teacher from Portugal and has worked with us in the primary curriculum project for 4 years. Her Tetun is great, and she speaks Portuguese so that we can all understand it!  Here she’s showing the directors how to make paper pentagons. 

This sort of ongoing training will be necessary for years to come.  I intend to continue working with the Ministry to find ways to increase the effectiveness of the trickle, and to do my best to inspire teachers with the intrinsic wonders of mathematics.

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