Experiments on Mathematics at Udavi School – Sanjeev Ranganathan
I have a PhD in electronics and am a practicing engineer. I am passionate about cultivating and critical thinking and self-awareness in children and have been volunteered at Udavi School in Auroville from June 2013.
I spent a month with the Xth graders in the June being part of their mathematics classes observing and towards the end of each class linking different concepts they learnt, e.g. similar triangles with trigonometry and coordinate geometry, geometry with algebra. I realized that many children struggled with abstract concepts they were introduced in 6th and 7th grade e.g. fractions and algebra.
I set up an electronics laboratory at Udavi to provide children an ‘exciting’ context to learn mathematics and as an exposure to a different discipline. I maintained connection with the Xth grade through a slot allocated for an electronics class, but focussed on addressing the source of their discomfort and worked with 6th and 7th grades in mathematics. I was fortunate to find teachers who not only let me take over the classes, but also support the initiative and fill gaps that I left.
I addressed fractions and number systems with use of hands on tools and games like pizza party and Denzel blocks. Together with the children we invented many games beyond the ones prescribed with the tools. We even looked at many abstract ideas like p^2-1 = (p+1)x(p-1) and hot to visualize these through blocks.
Strategy games that are short yet intense like those made by the European company Gigamic were a huge hit and so were disentanglement puzzles. The 6th graders put up a stall at the school fair with these games to provide a challenge for children, teachers and visitors a challenge to play a game with them. The interest in development of strategy was high enough that each child spent over 2 hrs holding their stall before taking turns to go and participate in the fair. They even developed an idea of rewarding younger children who played well, even if they could not better them in the contest.
Children spent a lot more time with questions without being overly concerned with the right answers. Children spent time articulating questions and going between abstract and concrete. To take an example we talked about multiplication story (of 3x4: 3 bags with each 4 apples) and the fact that there are two corresponding division stories (12 apples in 3 bags and 12 apples in some bags such that each bag has 4 apples). We noticed how the first story came easily while we struggled with the other and learnt how to notice the quantities being asked and those missing to understand what kind of story was being told. This skill is fundamental to understanding algebra. We created a process of peer learning and children listened to each other. We started with simple exercises in repeating at random what the other said and later to processing what was said and converting one kind of story into another (multiplication into its division, etc). These listening exercises had an incredible impact on classroom participation, retention and being able to build on concepts of complexity.
This also led us to scientific phenomenon like speed, distance and time that have such a relationship. We also looked at density beyond a keyword and looked how we can make abstract ideas like mass and volume into more concrete seeing (volume) and lifting (weight).
I encouraged children to look at examinations as an opportunity to understand and grow. They were were allowed to bring one sheet with any information they felt needed to be learnt by rote, allowing for exploration of understanding and application in the examinations. I also placed a score on meta- cognition of knowing if they got something right or wrong (and you would get a score if you were sure you got something wrong and it was). They even wrote the examinations again to see if they had a better understanding after a few weeks.
We spent a fair bit of time talking about being able think of whether a result makes sense and catching common errors. We worked on EBD (Education By Design) and the 7th graders presentations on fractions, decimals, algebra, etc to highlight where they commonly made errors. The process of EBD of creating quality criteria before starting the project and using a new process (increase/decrease/retain) of feedback made inputs less personal and more constructive.
Being able to talk about algebraic expressions as stories and write stories into algebraic expressions was good, but it took a whole new perspective when we worked with geogebra that linked geometry with algebra.
In the first term I also worked on English stories the children wrote to see it they were logical or were flowing from one context to the next.
The 10th graders made many small circuits on bread boards including LED oscillators, 555 timer circuits (which they also used for make musical notes), seven segment displays, counters, taking things apart and trying to repair them and programming micro-controllers. While in action I also received support from AIAT and IITM who leant us oscilloscopes to help ‘see’ electronic waveforms and cultivate intuition of what AC/DC signals look like. The electronics lab was also utilized by some children from Deepanam school and a couple of children from TLC.