Essential Ingredients

Published in Mathematics Teaching September 2005

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The NNS provides a good grounding in basic number skills, with some sorties into problem solving, but these are not the key features of mathematics. We are missing the investigative aspects of mathematical thinking and practice, as well as opportunities for our pupils to apply their skills in a creative way. Mathematics provides a unique system of thought which develops skills such as analysis, synthesis and evaluation; skills that are high in Bloom’s Taxonomy of Educational Objectives [2].

In addition, I think it is important that children see the value of other ways of learning and take responsibility for what they are doing.

Mathematics as a way of thinking

An essential ingredient of children’s mathematical experience should be investigative activities. By investigative activities, I mean presenting the children with an open-ended situation where they have to mathematically explore a problem or a puzzle and demonstrate understanding of its mathematical aspects. They may be required to present the work to others. I consider this to be the higher-level skill of synthesis, which is the ability to creatively apply learned skills to produce a new or original outcome.

My own background in mathematics is worth mentioning. I was awakened to the essence of mathematics in 2000, when I attended a course entitled ‘Mathematics as a way of thinking.’ I had successfully completed the DfEE course ‘Responsible teachers’ and was embarking on providing mathematics seminars for gifted and talented children. I had also attended a course for teaching mathematically able pupils at Brunel University. I suddenly realised what not only mathematics was about, but what any subject is about and began to think about mathematics in a completely different way - as a way of thinking. At the heart of any subject is the ability to really understand and learn concepts, and that you should be able to apply it to any situation, and to do so in a creative way.

My investigation

I looked closely at a year 6 class of children. They are of mixed ability, judged by their assessment results through the school. I worked with the whole range of children in the class, working around the class, with the different groups, to get a clear understanding of what each could achieve. I tried to compare how the different groups of children coped with the different types of activities provided for them.

I chose this year 6 class because I worked with them every day and know their abilities thoroughly. In the past I have worked with able children, leading mathematics seminars and master classes. I have been struck by what effect providing a variety of activities has on the able children and wanted to apply these types of activities to the wider class groups to see if they also would benefit from these experiences. The open-ended activities gave confidence and independence to the children and gave clarity of thought to how they went about solving the problems. I had noticed the lack of focus on such activities in the NNS. The question in my mind was: “Do I have to teach a three-part lesson every day and all the time? Could I find space for prolonged activity with a looser brief to the children, and provide a more inquiring atmosphere?”

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[2] Bloom, B.S: Taxonomy of Educational Objectives: The Cognitive Domain; New York, 1956

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