Problem Solving


Mathematics does not come easy to all of us and in fact was referred to as the “Marmite subject." (Tiley-Nunn, 2014, p.1) and referred to as a social stigma, although less pronounced than literacy. This problem is believed to be a factor of bad experiences early in education (Marshall et. Al. 2016, p.66).
Is numeracy really that important to us in problem solving?

“developing a good, lasting understanding of mathematical concepts and the confidence to use and apply numerical skills in everyday life. It includes experiences that enable children and young people to develop their broader numeracy and financial skills by exploring relationships in quantities, space and data, and to apply them to real-life situations. Mathematics helps children and young people to make sense of the world around them and to manage their lives. It gives them skills they need to interpret and analyse information, solve problems and make informed decisions” (Donaldson, 2015, p.49).

Regardless of each person’s individual mathematical ability, it is hard to argue that we all need a basic, core mathematical knowledge to get by in everyday life for basic problem solving. So how do we ensure that these core skills are obtained by all children?

“The key to enthusing pupils about problem-solving is removing the main barrier that prevents independent thought, and that is fear: fear of not understanding, fear of being wrong and fear of being embarrassed. The first step to creating young problem-solvers is to reduce these fears for them.” (Tiley-Nunn, 2014, p.10). Therefore, a way of addressing these fears would be an important step in overcoming this issue. Tiley-Nunn propose a method with which “you can’t go far wrong”. They propose the following formula for a positive outcome:
(Interesting + Accessible) x Challenging = Excellent


That means:
1)    Interesting - the idea or concept must be interesting to keep children’s attention;
2)    Accessibility - the children must understand what they are dealing with; and
3)    Challenging – it must present a challenge for the whole classroom.

This seems like a sensible approach but in my view can suffer from an inconsistent response in classes with students of varying abilities. Whilst the first two parts of the formula can probably be applied to any classroom, the third might be a stumbling block for those children with less natural ability. I therefore think that this will work best in classrooms where children’s abilities are reasonably balanced.

Resnick proposes a similar idea based on classroom engagement which in my view would still require a classroom with children of similarly balanced abilities. “If we are to engage students in contextualised mathematics problem solving, we must find ways to create in the classroom situations of sufficient complexity and engagement that they become mathematically engaging contexts in their own right . . . They should also permit students to develop questions, not only solve problems posed by others” (Resnick, 1988, p.38)

Donaldson, emphasizes the need to teaching well as a vital component of learning mathematics. “Taught well through relevant contexts, mathematics can engage and fascinate children and young people of all interests and abilities. It provides strong support for the development of wider skills, particularly critical thinking and problem solving, planning and organisation, and creativity and innovation. It enables people to communicate ideas in a concise, unambiguous and rigorous way, using numbers and symbols. A high level of numeracy and mathematical competence is important for the prosperity of the country.”(Donaldson, 2015, p.49).

Despite much development in teaching methods and theory, it is still a fact that basic understanding of mathematics remains a daunting prospect for many who fail to realize its importance in our daily lives. Far too often, you also see many children thinking of mathematics as a useless subject that they have to do simply because it is in the school curriculum. So perhaps the most important issue to tackle is that from an early age a different approach is required, whereby the basic concepts are put across in a more practical manner with emphasis on basic problem solving – using play as a method has been shown to produce very good results. This kind of approach would ensure that the concepts of problem solving are instilled into children’s minds from a very young age such that it becomes a normal everyday tool that they use without giving it much thought.

Pratt advocates this kind of practical approach: “mathematics affects not how much knowledge they ‘acquire’, but the kind of knowledge they develop. Children taught through problem solving and mathematical thinking simply develop a different kind of mathematical knowledge than those taught through explanation and routine practice”. (Pratt, 2006, p.62)

If we were to analyse any particular day in our lives, we could come up with quite a few instances where we have used mathematics to solve an everyday problem. How much money do I need to buy the items I need from the shop today ? How far do I need to walk to get to a particular location ? Did I get the right change at the shop? How much of each ingredient do I need to make 100 cupcakes ? These are but a few examples of everyday problems that we solve without giving much thought to but are possible thanks to our basic understanding of mathematical concepts. In my view it is therefore very hard to argue that numeracy is not important in problem solving, I would in fact state that it is absolutely essential and we therefore need to make sure that our teaching methods and approach are able to deliver the best possible foundation for our young children.









References

Donaldson, G. (2015). Successful futures: Independent review of curriculum and assessment arrangements in Wales. Welsh Government.
Marshall, E.M., Wilson, D.A & Mann, V. (2016) Attitudes and Anxiousness bout maths. In Brave New World: Proceedings of the CETL MSOConference (pp. 66-74). Chicago
Pratt, N. (2006) Interactive Maths Teaching in the Primary School. London: Sage.
Resnick, L. B. (1988) ‘Treating mathematics as an ill-structured discipline’, in R. I. Charles and E. A. Silver (eds) The Teaching and Assessing of Mathematical Problem Solving. New Jersey: Lawrence Erlbaum Associates.
Tiley-Nunn, N. and Beadle, P. (2014) Primary Maths: Anyone can feed skittles to sharks. London: Independent Thinking Press.




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