From 2006 we started a programme to gradually improve the total quality of ~ 20 govt secondary schools in and around Baduria block of N.24 Parganas district in West Bengal. . To start with, this means getting the teachers motivated and excited to learn and do things differently . To some extent this has taken off . In June 2008 we were able to form a network of Work Education teachers and they are doing all kinds of new and different things and also having fun.
The Maths teachers had been pestering us for a year to start something with them as everywhere Maths is the most scary subject with most failures . But it has not been very easy to get Maths Resource persons. In May – June 2009 two resource persons became available : Swati Sircar ( taught Maths in Seattle , USA for many years ) who is a part timer at Shikshamitra and Sabyasachi Mitra , who has returned to West Bengal after being associated with Jodo Gyan Delhi and has conducted various workshops in many parts of India. And so finally the Maths “network” is starting.
Here is a report by Swati of two workshops held at Swanirvar
First Maths teachers wshop on 23rd June , 2009
There were around 30 teachers from 20+ different schools, some of the KKB staff, Gopal Mondol (the key math person in Swanirvar primary dept ) & Sabyasachi & I as resource people.
We started around 11:00am with a round of intro followed by what the teachers perceive as problem areas while teaching math in high schools. There were mainly 2 kinds of problems:
(i) the type coming from common practices in the society like going to a tutor & then conflicting ways of the tutor & the teacher. & (ii) problems on how to explain things to the children so that they get a clear concept.
We mentioned (& do need to be very clear about this in upcoming meetings as well) that we can't help them much with the type (i) problems other than telling them what's correct. Somehow these teachers will have to ensure that the children have more faith in them than the tutors.
Among the type (ii) problems the teachers mentioned the following as most problematic areas:
1. Use of inverse proportion in Class V as part of unitary method - we suggested that the children write one sentence using their common sense whether the concerned quantities will increase or decrease. After that they will be able to figure it out. They shouldn't be blindly applying an algorithm without using common sense.
2. There was some conflicting definitions in different editions of textbooks. We cleared those up.
3. Transformation geometry in general - We showed them a glimpse of how this can be taught in class. But decided to go deeper into this in a later meeting.
4. Some application type problem of mensuration.
5. How to correctly say a fraction in Bengali.
6. Some more language related issues.
While the teachers were mentioning these areas we often started discussing what we can do about it & spread into other related areas.
In the 2nd part after lunch, we specifically took on some concrete things that can be done immediately in class. Those included -
1. Introducing & dealing with negative numbers using very simple TLMs (e.g. 2 different colored but same size & shape buttons). It was interesting that the teachers weren't impressed while we did it on the board, but really liked it when we used concrete material.
2. How to show translation by folding a paper. This also led to a very interesting activity led by Sabyasachi on why transformation geometry & how it can be a very useful tool. The teachers were given a couple of problems. They all attacked them with conventional methods - mensuration & could hardly get the correct answer to the 2nd one. However when Sabya used transformation the answer became obvious to everyone without any calculation.
After that we decided on the format of how the teachers wanted to take things forward. It was decided to go topic by topic & spread across different classes - thus giving us the opportunity to do justice to it. Though it was originally thought of as Class VI-VIII, the teachers have stretched it to Class V-X.
For the next meeting on 14 Jul, they decided that we will work on "ratio-proportion". Part of the reason is that this topic comes earlier in the school year, so whatever they learn with us, they can apply in class immediately.
Second Maths teachers wshop on 14th July , 2009
We had planned to discuss ratio & proportion specifically. We started the discussion with why we need ratios even though it is so similar to fractions. We discussed situations where ration is more appropriate than fractions & where fractions won't help. Several examples came from the teachers. Then we discussed ratio-proportion vs unitary method - i.e. which method should be used while doing problems. Some activities were suggested that can be done by the students in class. Teachers commented on which can be done by class V & which is more appropriate for class VII. Then as a follow up to one of the activities I asked 2 puzzles to the teachers, one leading to the Golden Ratio. One of teachers solved & got the Golden Ratio during the session. Many were interested to know more about it. So in the next session I will show them more material on it.
We also digressed with every one's consent to some geometry as well. & for the next session we have decided to look at fractions & geometry and also make some simple geometry teaching kit consisting of various shapes.
We plan to gradually expose the teachers to various resources including good textbooks, math booklets on interesting topics, magazines & online math groups.
Third Maths Teachers Workhop 18th August , 2009 :
The main focus of this meeting was to make simple TLM's for geometry. We had also brought some books that discussed Fibonacci numbers & golden ratio & other things. Some of the teachers wanted to buy those books & placed order. We discussed some general questions the teachers raised on fractions & ratio-proportions. These included some confusion that the teachers had on various methods their students are using as well as some simple steps that make solving equation easier.
Then we got immersed in making various geometry shapes out of mount board. We 1st made a list of common shapes of various triangles & quadrilaterals the teachers should make. We also showed how the left out pieces can also be used to check whether the students have understood the concept of say, what a triangle or a polygon. Many teachers collected a lot of such "left-overs" at the end. We demonstrated how this cut-out shapes can help the teachers in the classroom. These included - (i) to show a shape, (ii) to quickly draw a shape on the board, (iii) to show a shape in different orientation (e.g. the top angle of a right angled triangle can be the right angle).
We also demonstrated some simple geometry models made by straws & staplers. Some teachers made some straw models also. Some took some straws home to make their models.
They wanted to know how to tackle the transformation geometry section (in class VII & VIII) - a major head-ache for most teachers. We showed reflection. But since we didn't have enough time, we decided to devote the next meeting on a workshop for geometry using paper folding & paper cutting. This would include the rest of transformation geometry.
Due to puja & Id holidays + unit tests etc we decided to skip Sep & have our next meeting on 26 Oct.
4th Maths Teachers Workshop 26 Oct , 2009 :
The main agenda on 26 Oct meeting was geometry. We started with some folding activities & the geometry theorems / corollaries behind them. We explored many theorems by folding or cutting papers. For the teachers it was like doing a practical in Math - something they had never done. We discussed how they can & should use this in classroom to engage the students & give them a feel for geometry. Then we did some activity on transformation geometry (class VII & VIII). We explained how these activities can cover this part of the syllabus in 3 periods. The teachers were visibly very engaged in & excited by these active way of dealing with geometry.
We asked the teachers for feedback on what they have learned so far & on their experience in trying those things out in class. Most are going to write & give it to the KKB in-charge. Some mentioned that children are understanding & remembering better, One even said that earlier it used to take him few minutes to settle the class down. Now as soon as he takes out a TLM the class immediately gets in order to see that!
The teachers had also ordered some books which were distributed. The author is going to join us for the next meeting in 7 Dec with his innovative algebra.
We are going to visit 3 schools on 16 Nov.
5th Maths Teachers Workshop : Dec 7, 2009:
Due to some travel arrangement mishaps, I reached Swanirvar around 1 pm. As per my suggestion, the teachers wrote brief reports on the impact of these monthly meetings in their classes. When I reached they were finishing up. We had 30 min before lunch & 1.5 hours after.
Main presentation / activity was around doing algebra using Subir da's techniques. We covered
1. 4 operations of integers with algebra pieces
2. + / - on integers with integer scales
3. + / - of quadratics with algebra pieces
before lunch.
After lunch we covered
1. multiplication of linear polynomials resulting in quadratics
2. factoring quadratics
3. division of a quadratic by a linear polynomial (with remainder)
all with algebra pieces.
Algebra pieces are essentially 3 types of rectangles / squares in 2 colors - 1 color for positive, 1 for negative
1. 1 unit x 1 unit = +1 or -1
2. y unit x 1 unit = +y or -y
3. y unit x y unit = y2 or -y2
We didn't have time to cut out the pieces from the EVA sheets. We plan to do that at the next meeting on Mar 9. So I showed it on the board. I showed them the integer scales. The teachers felt they are 2 small to use in a class of 60-100+ children. But they got the basic idea & hopefully will create their own. One teacher mentioned how he will create a bigger one from class demonstration.
We also created class-wise subgroups from the teachers present - 3-4 teachers per class. The job for these teachers will be to make a list of problem they face while teaching in that class (remedial or otherwise) & give it in writing at the next meeting. Then we take it from there.
We won't be meeting in Jan or Feb as all the schools will be busy with the remaining unit tests, remedial ones, annual exams & reports.
I also thanked the teachers because their experience helped me as trainer at the Nadia DIET workshop with high school math teachers just like them.
6th Maths Teachers Workshop : Mar 9, 2010:
1st part of the meeting included a brief sharing of my experience on teaching integer multiplication (negative x negative = positive - in particular) at the Learning Network Conference & through emails in ActiveMaths yahoogroup.
After that the 21 teachers got in 4 groups & started working with the EVA sheets to make the algebra pieces (mentioned in last report). Each group had one white & one colored sheet. The process was as followed:
1. paste one sheet over another with some non-soluble glue like Dendrite
2. draw a proper rectangle on the joined sheets - this was a challenge as none of the edges of the sheets were straight + there were no long enough scales
3. draw a grid in the rectangle - this grid on cutting gave 2 inch x 2 inch, 2 inch x 2 cm & 2 cm x 2 cm pieces
4. cut out the grid
5. do damage control - checking if the 2 layers of the pieces are stuck together or need some further glue & fixing as necessary
6. distributing the finished pieces equally among the group members
The process was neatly streamlined & in 2 hrs every teacher has a goody bag of TLM. We also demonstrated that these algebra pieces when dipped in water do remain stuck to the black board. Therefore these pieces can be straight away used for classroom demonstration as well.
In the 2nd half, we discussed & finalized some logistical details regarding next meeting & next visit to some schools. The teachers got in to class-wise groups - Class V, VII, VIII & IX-X to discuss & write down the following based on their past experience:
1. What are the children, who are in this class, capable of doing?
2. You will be happy, if the children achieve the following in during this class:
There were no teacher who had experience of teaching class VI. It seemed many teachers didn't have a clear idea of what their students really knew / can do & this exercise got them to think about that. I intend to send a more detailed questionnaire to them for need analysis.
At the next meeting we have planned to do a syllabus analysis & choose which are things we should focus on more in depth & which should be covered lightly. This is all the more important because this session is for only 11 months & not the usual 12 months. The teachers agreed that this analysis will be helpful at the beginning of the session.
Reported By,
Swati Sircar
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