Problem Solving in Eritrea Aaron Peeters Somewhere in the world Aaron has taken leave from teaching at Kingsbury Primary School, Victoria, to spend a couple of years doing volunteer work overseas. His first few months were spent in Eritrea and he sent a couple of news items from there: February 2009 March 2009 These short items provide background for the article below which Aaron wrote on his return to Australia, while waiting to take up his next position in Ghana. In the current article Aaron offers insight into education in impoverished Africa and through his experiences discovers much about teaching in the Western World.

Context

This was a voluntary club. Students came in the morning from 8:00 - 11:30. They then had their lunch and attended school in the afternoon. Usually students either attended the morning school or the afternoon school. Basically, the classroom infrastructure didn't exist to have students attending school 'full-time'. However Matthewos, the teacher who had set this up and was the sole operator, requested that the 300 or so students attend school the whole day, as well as weekends, Saturday and Sunday mornings.

So, given these students were active, enthusiastic and eager to learn, they probably were at a bit of an advantage compared to other students. Below are some of my observations when I introduced problem solving type lessons based on tasks.

Click the photo to reveal its Task Cameo.

Crosses This task can be relatively easily started as a whole class lesson using few resources. Basically, grab a piece of paper and tear it up into 9 sections. Then write the numbers 1 to 9 ... or, so I thought. Firstly, the language barrier proved an obstacle. Demonstrating what to do helped to get the point across, but I got the feeling that these students had never used hands-on materials before, and as such, just didn't get the point as to what they were doing. This proved to be somewhat true later on in the lesson, when they reverted to using pens and chalk.

Secondly, the students had never faced a problem like this before. The aim of the puzzle is to arrange the numbers from 1-9 in a cross shape, so that both arms add up to the same total. We had to take a bit of time, illustrate some examples, and ask some of the brighter students to help translate and get the meaning across.

After playing around with the numbers, and achieving some success, I used a method I had seen Matthewos using with the students. He had them arranged into mixed ability groups, in order to get them working together and communicating, and they had all made 'mini-blackboards' out of cardboard with a wooden backing and blackboard paint on them, which they used to write up a group answer. I loved this method, because it supported what I knew about learning. The students were able to learn from each other, challenge each other and support each other. One of the things I observed was that they had never had experience looking for 'all the possible answers'. While some groups were able to find more than one, this concept was too new for them.

Also, when I asked them if there were any patterns they could recognise, in particular, with the middle number, this concept was a novel one too. In addition to this, trying to get these concepts across in a medium (english) that they weren't entirely comfortable, or confident, with provided some challenges.

It really made me think that there is a lot more we can do to help students understand than just 'tell them'. We can show them by demonstrating, using pictures, acting it out and moving our bodies. We can get them to show each other, get them to explain to each other and listen to each other.

I looked back on my time teaching in Australia, and I felt that my own students had also struggled with these types of problems when they were newly introduced. How did I support them to adapt and think differently? After more and more exposure though, my Australian students became quite good at these types of problems. However, I am pretty sure that if I had provided more opportunities for rich discussion, and group work using a strategy like the 'mini-blackboards', I would have had more students understanding what we were doing and why.

Heads & Legs Another lesson I did with the students was 'Heads and Legs'. This lesson sets up a story about someone visiting a farm which has a pen full of 'cows and chickens.' The visitor counted all of the legs and there were 50. The visitor counted all of the heads and there were 17. But what the visitor couldn't remember was how many of those heads and legs belonged to 'cows' and how many belonged to 'chickens?' In Eritrea 'cows' weren't that common, so it became 'donkeys and chickens'. I had learnt from the last lesson, that this setting up stage of the problem was crucial to the students having a clear understanding and taking the problem on.

Click the photo to reveal its Task Cameo.

I invited some students to come up and act as donkeys and chickens, introduced the story using people that they know, and drew up some pictures on the board. I was confident that they had understood most of the language. However, had they understood the problem?

It turned out, that none of the students had understood the requirements of the problem. Some of them had some kind of an idea, but they launched straight into dividing the heads and legs by 4 or 2. They could work out how many chicken legs there were, but forgot to take into account that there were donkey legs too and that the heads had to add up to 17 also. However, after some more time explaining, and starting the students off with a 'trial, record, improve' method, most got the hang of it, and were pretty happy with themselves when they had found an answer.

I waited until a fair few students had solved it and then handed out the mini-blackboards. I emphasised that 'groups work together,' and I would go around checking that all students in the group could explain the solution. If someone couldn't, I told the group I would be back in 5 minutes to check that student could explain it to me, so they best help explain it to him or her.

Generally, I found that one of the great successes of Matthewos's Science Club, is the confidence this peer tutoring and group work instills in the students. It is so uplifting and valued by the students that it really improves their attitude to learning.

I discussed the lessons I had run with another volunteer who was formerly a maths teacher in England. He was very supportive, commenting that these were 'real maths questions', not just the skill and drill type most commonly found in Eritrean classrooms.

Although too short a time, this was a great experience. I observed that these students definitely have the capacity to solve complex mathematical problems - all they lacked was the experience. The curriculum in Eritrea is somewhat a remnant of the colonial era, resembling the 'chalk and talk' textbook based learning we had in Australia last century. Introducing these types of problems to the students was fun for me, and fun for them. It presented a big shift in what mathematics was for them. I would have liked time to try some more because they seemed to be getting the hang of it. The student-centred learning already in place was great for me to slip into as a new teacher, because the students were being responsible. Their groups and routines were already set and familiar, so by changing the course work I wasn't changing too many things at once. They were able to support each other. They could check each other's work and question it. I discussed the lessons I had run with another volunteer who was formerly a maths teacher in England. He was very supportive that these were 'real maths questions', not just the skill and drill type most commonly found in Eritrean classrooms. I found that students had trouble understanding what the question was asking and applying their knowledge of maths to find a solution. However, they were very good at working together and trying new things, so with more practise I'm sure they would have improved further. Unfortunately, the curriculum doesn't offer any space for these types of problems, so there won't be any opportunities for them to practise. However, I'm sure Matthewos will encourage them to develop these skills further when he has the time.

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