As a mathematics consultant I often get to work with children who are deemed to be “having learning problems” or who are “making slow progress” in the subject.
The last two days I have seen such children at a local secondary school (Year 7’s, Grade 6) and today with Year 6’s (Grade 5) at a local primary school. What struck me in these two days was just how bright and incisive these children can be when we catch them “off guard” and they are able to show their real talents.
Yesterday was an example of this. I attended a joint observation of a lesson that I had helped to plan with the class teacher. It was a data lesson linked to work that the children had been doing on “The Great Plague of London” (1665/66). Theywere asked to make sense of the following information:
Weekly records of deaths from the Plague in London 1665:
Week beginning June 6th: 43 deaths
Week beginning June 13th: 112 deaths
Week beginning June 20th: 168 deaths
Week beginning June 27th: 267 deaths
Week beginning July 4th: 470 deaths
Week beginning July 11th: 715 deaths
Week beginning July 18th: 1089 deaths
Week beginning July 25th: 1843 deaths
Week beginning August 1st: 2010 deaths
Week beginning August 8th: 3880 deaths
Week beginning August 15th: no record
Week beginning August 22nd: 4237 deaths
Week beginning August 29th: 6102 deaths
Week beginning September 5th: 6978 deaths
Week beginning September 12th: 6544 deaths
Week beginning September 19th: 7165 deaths
Week beginning September 26th: 5532 deaths
Week beginning October 3rd: 4929 deaths
Week beginning October 10th 4327 deaths
Week beginning October 17th: 2665 deaths
Week beginning October 24th: 1421 deaths
Week beginning October 31st: 1031 deaths
Week beginning November 7th: 1414 deaths
Week beginning November 14th: 1050 deaths
Week beginning November 21st: 657 deaths
Week beginning November 28th: 333 deaths
Week beginning December 5th: 210 deaths
Week beginning December 12th: 243 deaths
Week beginning December 19th: 281 deaths
Week beginning December 26th: 152 deaths
The teacher asked the children to explain what the Plague was and how it spread. These children then engaged in a sensible and interesting discussion about boats coming from overseas where they had gone for exploration and trade returning with rats who had managed to get into the food supplies kept in the ship’s hold. They talked about fleas living in the rat’s fur and how this became a process of transmitting germs which was to cause widespread death and misery.
The teacher then asked the children to discuss what they made of the data. They talked about a rising trend in deaths, of e peak being in September when it reached 7165. They posited ideas about the heat of the summer period helping the disease to spread more widely and the fact that there was no immediate idea about isolating people or introducing remedies to combat the worst effects of the illness.
This was a group of children that were deemed to be “slow learners”. They were able to think about averages, the range, the possible shape of a graph to represent the data, of a possible reason and explanation for no data appearing on the week beginning August 15th (based on the trend of the last few weeks they agreed that the figure must be about 3900 to 4000 and agreed that it could be plotted on a graph to show the likely number).
Both of us observing were frankly open-mouthed in amazement by what the children were showing us. This was not a page from a textbook and was related to something they were studying and were deeply interested in. If it would have been a textbook then they would have seen the exercise as “maths” and known that they are no good at it. They “can’t do” averages, ranges or hypothesise about trends. They are just not “good enough” to do that.
It made me see all over again what I have also believed that we label and compartmentalise children. They begin to believe our labels and they pass it back to us. “I’m no good at maths, my mum and dad were never any good at it.”
Today, in the primary school I worked with a group of children who have had difficulty in learning their tables. I told them to tell me what they knew. They showed me the 2 times table, the 3 times table, the 5 times table and the 10 times table. Then one of them said that he knew a pattern for the 9’s.
I told them that we can work out times tables they don’t know from the ones that they do. We started with an investigation of the 12 times table. They quickly discovered that they could add the 10 and 2 tables to get a result. They were pleased with this and two of the boys wanted to carry on beyond 12 X 12. They stopped at something like 23 X 12 and then I asked them to tackle the dreaded 7 times table.
They could do this as 5 times and 2 times added together. The group was away and making up a 7 times table well beyond 25 times 7! I asked them to see of they could notice a pattern and they came back with some really interesting ideas. Odd number tables are in a pattern odd then even.. so we can’t be right if we have two odd numbers in a row or two even. One of the girls wanted to explore the 8’s and one of the boys wanted to explore the 13 times table.
Now today is a special day here in the U.K. This evening (as I write) we are having a huge telethon called “Children In Need”. The school had allowed children to come out of uniform for the day as long as they contributed to the “Children In Need” appeal. There were photographs being taken and the children were collected half-way through our lesson to go and buy home-made cakes for the appeal (I have to admit that I purchased one myself). They all wanted to rush back to carry on their investigations into times tables!
Just like the lesson the day before I could see so-called “slower” or “less able” children forgetting their label and indulging in the fun that mathematics can (I would say should) be. This was not because it was being marked or assessed but because it was enjoyable!
I wonder if this is not proof of what we have all been saying as we try and answer the “back to basics” brigade and their big guns in government and the media. It is enjoyment, engagement and involvement that will bring about learning. The return to an age of boring rote mathematics from boring textbooks will just switch them off and they will return to the model that we have labelled them… “the slow children” the “ones with learning problems”.