We’re in the second round of the B session trainings. One group of 5 SESIM trainers went back to Oecusse, the enclave down the coast of West Timor. I’m in Ermera municipality, again with Mestra Mimi and Mestre Fin on science, while Mestre Berbardino and Mestre Julio take care of mathematics. We are also joined some days by another SESIM part timer, Mestre Hortencio, who has worked with me developing locally based mathematics activities since before SESIM was formed in 2009.
The pratika line-up was the same as in Lautem, and of course we get better at it each time we do it. The topics we do this week are all from the first trimester, so the teachers will begin teaching them in January. Here I’ll present a few representative pratika sets we do in both science and mathematics, to give a broader perspective on how our training links to the curriculum.
With good support by KOICA and UNESCO Jakarta, SESIM carried out the revision for Timor-Leste’s junior high science and mathematics curriculum in four steps:
- Review the syllabus and textbooks with two primary objectives:
- Reduce the total content to be taught by determining which sections are less important and can be deemed optional, that is, not to appear on the national exam.
- Select and develop a set of pratika (simple hands-on and inquiry activities linked to local culture and experience) representing each of the priority concept areas from the syllabus.
- Write a Pratika Manuals for teachers that include, for each pratika:
- Clear simple directions on how to do it.
- Basic theory of the concepts involved.
- Link to life in Timor-Leste.
- Write teacher guides with four primary objectives:
- Designate which syllabus sections are priority and which are optional.
- Offer additional information for unclear sections of the textbooks.
- Link the syllabus concepts to daily life in Timor-Leste.
- Present calendars for teachers to follow as they teach each year’s contents.
- Write student exercise books, offering sample exercises and test questions representing every section of the curriculum.
With several steps of piloting, reviewing, and feedback from teachers and Ministry of Education officials, the process took over a year and finished early 2015. SESIM took advantage of many of the pratika we had been developing for years, including in our Encyclopedia of Science and Mathematics of Everyday Life, published in 2009 in Tetun.
My experience with this project matches my experience with other curriculum work I’ve done here, including the massive k-6 national curriculum reform project just wrapping up now. There is a constant concern that the piloting was not complete, the feedback not thorough enough, and the time for editing not sufficient. It is no surprise then that we routinely find small kinks in the fabric as we carry out these nationwide trainings. Our errata list has gone to two pages.
Nonetheless, we continue to be quite satisfied and confident with the overall quality and utility of the revision work, which is now part of the official curriculum. Teachers we are training give overwhelmingly positive evaluation responses in terms of content, pedagogy, and the written materials we’ve produced. We’ve got a good thing going.
Curriculum content decisions often come down to agonizing trade-offs. We couldn’t find space for Archimedes’ principle, even in this land of fishers. We designated as optional the mathematics section on quartiles and stem and leaf diagrams even though they can clearly be useful. And we decided to allot two precious weeks of review to the front end of the 7th grade mathematics calendar, because so few students are prepared for the content level in the 7th grade syllabus. (Calling this section ‘review’ is a bit of a rosy perspective; many students will be encountering these concepts for the first time, because their 5th and 6th grade teachers skipped over them.)
The existing curriculum is ‘spiral’ in structure, meaning each year students are taught many of the same topics, supposedly at a higher level and with new information and applications. In astronomy, a small yet high interest part of the current syllabus, we narrowed the pratika to three. In 7th grade a longer pratika is carried out to show the relationship between the sun, moon, and earth.
Here is Mestre Fin, at right, doing the introductory ‘dance,’ in which the sun is represented by a broom (in order to be around 100 times larger than the earth), the earth as a lime, and the moon as a peanut. The earth and moon then begin walking around to mimic actual orbits. All rotate on their axes.
Then night and day and eclipses are demonstrated with a flashlight representing the sun in the front of the classroom, a demo which is poorly viewed by most of the class. But then everyone is given a lime and a peanut (a wad of chewed gum also works), each on a bamboo skewer, and sent out into the tropical sun to do it themselves.
After everyone has tried it, we do it all together, like a line dance. Here they are rotating their lime, into which has been stabbed a tiny nail at approximately 9 degrees south latitude to represent Timor-Leste. As they turn it, their nail goes in and out of the light, thus, day and night.
Then they’ll put their peanut into the lime’s shadow to show a lunar eclipse and the lime into the peanut’s shadow to show a solar eclipse.
After that we all come back into the classroom and demo moon phases with a flashlight in front, emphasizing that these have little to do with eclipses, that is, no occulting is happening. This demo is even less effective than the eclipse one, since angle of view is everything when trying to understand moon phases. However, it gets them pointed in the right direction, and they head outside again to try it themselves. Now the lime represents the moon, their head represents the earth, and the sun continues to represent the sun.
Here they’re turning through the month of lunar orbit, watching the phases change on their limes. This photo shows them viewing the new moon (or should we say, the new lime?). On lucky days, such as happened in the Lautem training, the moon is visible in the sky, and the phase of their lime matches the phase of the moon. It is a key realization in the process of understanding celestial observations: any spheroid under the sun, whether planet or peanut, gets illuminated from only one side, leaving the other side dark.
For 8th grade, they do a short demo modeling the structure of the solar system using various spheres. Here the sun is at left, represented by a flashlight, though the height of the room (approximately 3 meters) is pointed out to be the true scaled size of the sun in this model. (Finding 3 meter diameter spheres has proven to be a bit of a challenge.) Then planets step out in order:
- Mercury: marble
- Earth and Venus: large shallots
- Moon: pepper corn
- Mars: coffee berry (bigger than the marble)
- Jupiter: basket ball
- Saturn: soccer ball
- Neptune and Uranus: onions
Asteroids, comets, and dwarf planets are also indicated. It is then mentioned that while the size of the planets in this model are approximately to scale, the distance between them is unrealistically close. To be true to this scale, Neptune would be 9 km away!
(We have in the past led teachers on the Planet Walk, the only reasonably doable and observable model that can be kept true to both planets’ sizes and distances. This is an awesome activity, but you need a ½ km straight stretch of ground and a class ready to walk it, two conditions we realized many Timorese teachers don’t have at their schools. So we settle for this lesser pratika.)
In 9th grade, we do a similar scale model activity, with two balls as the earth and the moon, one 4 times the diameter of the other. Now we can make the distance to scale as well, without even bothering to chase up a measuring tape. The moon ball is placed on one side of the classroom, and then earth ball is set down 30 times in a line to find its position. Here the earth is a soccer ball and they are about halfway through counting out its diameters. Note the largish lime near the wall in the distance; that’s the moon.
In addition to these pratika, we set up our good telescope, donated to us by the Korean National Commission for UNESCO, and saw several nice sunspots, daily making their way across the face of the sun, thus proving its rotation, a fact not made clear in the textbooks. Some students leaked out of their classrooms to join us.
In the mathematics group, we run through the ‘review’ pratika of 7th grade. One is called ‘Place value cups’ and is basically an abacus made from sticks in cups. This system allows for more than 10 units to go into a given place value, 10 of which can then be traded in and ‘carried’ to the next cup in the form of a single stick. We do addition and subtraction, even dealing with negative numbers.
This simple pratika is always a perspective raiser, because even mathematics teachers forget that the meaning of numbers we use regularly are entirely dependent on the Indo-Arabic number system, in which meaning depends on numbers’ relative positions. Basically, the 3 in 538 no longer means just 3, due to the implicit assumption of the system we’re using.
After addition and subtraction are solidified, we work on multiplication and division by having teachers find the factors of each number up to 30. We use beans and actually put the beans in little piles to see if they come out even or if there are left overs. It may seem simplistic, but again, many teachers are not actually qualified for their current position, and many don’t have a history of having done this sort of foundation hands-on work for themselves, so doing it now can be transformative, even for the older ones.
Fractions and operations on fractions are reviewed with strips of paper, folded to divide them equally into sections, and then manipulated again to make an operation on them. Many teachers have been teaching the algorithms for these operations for years without ever understanding it the way this pratika clearly shows.
Finally, the operation of raising to powers is reviewed in two ways. First, each plots their own parent pairs back several generations using toothpicks glued on paper. Everyone’s family tree is different, but the shape of all parent pairs’ plots are the same. To count the number of parents at each generation, the power of 2 is used.
And then, with the same operation, they figure the number of branches after a given number of branchings on a certain local plant that always branches by twos.
Exams begin in two weeks and will, together with the locally important All Souls holiday, stop most educational action altogether. Thus it may be a month or so before I have more to present on this blog. Our annual Science and Mathematics days celebration will be on November 10 and 11th, and the end November and December will bring more B session trainings, each of which I’m sure will raise more insights to share.