Forming the jumble of facts into a web of knowledge

Having finished up the trainings of more than 1000 Timorese junior high mathematics and science teachers over the last two years, we’re still full of hope and optimism, but also want to bravely face the realities we’ve seen in our trainings. Continuing this blog in a somewhat negative vein, I’ve noticed during these two final trainings teachers’ lack of common analytical and reasoning skills, a non-ideal situation that compromises their classroom teaching.

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Series and parallel circuits are not hard to create with cheap light bulbs and batteries, but it immediately becomes obvious how much more complicated they can become than the quaint diagrams in the textbook. It’s a fine opportunity to embrace the complexity of reality and figure out how things really work.

For example, to wrap up our pratika with polygons, I drew a common representation of the types of quadrilateral as a Venn diagram, largest category ‘polygon’, then ‘quadrilateral’, then ‘trapezoid’, under which huddled the three interrelated categories of rhombus, rectangle and square.  I may as well have written in a different language, and in a sense I had, because I had mistakenly assumed they understood the structure and meaning of a Venn diagram.  After all, it’s in their 7th grade textbook.

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The Venn diagram Mestre Tito and I put up to analyze types of quadrilaterals. The chalk board was not optimal; it seemed to be made of plywood painted with normal black paint.

I ended up spending a half hour or so explaining Venn diagrams and the great utility of describing things within this structure.  I drew other diagrams as examples: life, containing animals, containing mammals, containing pigs, containing that one rooting out under the tree;  Timorese citizens, containing functionaries, containing teachers, containing those in this training, containing Mestre Gaspar here.  And then I returned to the quadrilateral example, specifically emphasizing the definition of each level in the diagram.

This is elemental mathematical structuring and a basic skill in general science, yet it was new to nearly every one of these teachers.  At the same time, they knew by heart the names of each of the polygons in question.  But these names had been stored away in their brains in a random heap, with only tenuous connection to the other info up there.

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With either trigonometry or similar triangles, and these handy little inclinometers, you can hone your analytical skills by measuring the height of the school flag pole.
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The other measurement you need is the distance from the spot of your inclinometer measurement to the base of the flag pole.

Similarly, we led a pratika related to the genetics section of the 9th grade curriculum, modelling the passing on of dominant and recessive genes using white and yellow corn kernels. It was the standard activity of crossing of homozygote (BB and bb) and heterozygote (Bb) parents, and showed the probability of various results, and how an offspring could be born with a visible recessive trait that is not seen in either parent.

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Teachers counting up the results of the last round of breeding between white and yellow corn.

There are only a few possibilities in these crossings, and after we did some of them I had to urge them quite vehemently that each possibility had to be worked out to see the whole picture.  They appeared far too satisfied to get only a few random bits.

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Mestra Sandra collects and analyzes results from the ten groups in the corn breeding genetics pratika.  The results were pretty close to the probability calculations. Later we realized we should be using the symbols K and k, because they represent the gene for a single trait.

In another instance, the mathematics group worked out the formulae that give the total number of sticks necessary to construct a series of linked figures, such as squares, hexagons, or three dimensional figures like cubes or little houses.  Each one has its one special sequence formula, and I noticed some of the teachers were already at work memorizing the formulae from the manual before they knew, #1 where they came from and, #2 the significance of the variables in the formulae (T for the total sticks and n for the number of figures).  Alas, if you don’t know those things, the formulae are entirely worthless, whether or not you’ve got them memorized.

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Extracting equations from sequences. These teachers have got two linked cubes on the right, and are working on the hexagon next.

It seems clear that structuring one’s web of knowledge and learning to apply it to the world around, as opposed to collecting a bucket of facts, is something new and radical for most of these teachers.  The SESIM trainers have come to understand this, and if we can get other teachers to see the value of it, it will pay great dividends for them and for their students.  We do our best to present this value by means of doing simple pratika related to daily life.  In reading the final feedback sheets from our training participants, it’s clear that we do have a lot of converts.

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Mestre Caetano, right, accompanies teachers of the science section to observe and systematically categorize characteristics of the local rocks they’ve been building with and farming around all their lives.

Next week we’ll be back visiting schools and I plan to pen the final pages of this blog from the mountainous sub-districts of Ainaro and Baucau, after accompanying teachers who have attended our trainings deliver pratika to their students.

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Despite the low priority on teaching analytical skills in schools, plenty of professional and lay Timorese use these skills regularly, such as these youths we found driving their fully steerable cars down the sidewalk in Viqueque.
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Schools would do well to make use of what these kids already know, that is, to link into their web of knowledge.
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Talking on the string telephone: no contract required, unlimited minutes, and always good network, until the string goes limp.
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Our host school in Viqueque had set up and painted a nice set of tire stools and wood benches under their young banyan tree, which also doubled as shade for the teacher’s motorcycles.
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Each morning we found local community members getting water from the school’s ailing water system: a pipe flowing weakly into a basin. By 9:00 the flow stopped, so locals had to be sure and get their day’s worth early.
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