Problem Solving and Reasoning

When thinking of maths in primary education, we usually think about numbers and equations, however, we should be thinking about the skills behind these equations and encourage children to understand that those ‘boring’ and ‘long; problem solving questions can be used in everyday situations. It is important that those who teach children are clear in their minds that mathematics is more than just a collection of skills, concepts and principles (Haylock and Cockburn, 2013). The future of education is changing, and we need to be able to teach children the skills and abilities they need in a changing world. Education is focusing more on the child’s development and ensuring that develop the skills needed for the future. The ability to solve complex word problems will be a key skill required for the future (Donaldson, 2015).

There is a growing focus and aim to teach children skills that they will need to use in everyday life; not just for a test or exam at the end of the year. The concept of education is changing, where the focus is not on test results and defined, straight-forward answers but on the child’s holistic development and how their cognitive skills are being used. The ability to use cognitive abilities in learning is crucial for a meaningful learning to take place (Stendall, 2009). Success too often depends on pupils remembering what to do rather than having a secure understanding (Ofsted, 2008). Outside of education, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts (Mills and Kim, 2017). In order for children to be able to use these problem-solving skills and understand how to apply them they need to experience it and encounter different problem-solving situations to be able to practice and enhance their skills. “There would be no great musicians if in music sessions students could only move notes around on a page. Great musicians develop by applying the theory to practice in hands on experiences. This isn’t happening enough in classrooms across the globe when it comes to maths.” (Boaler, 2014, p. 130).

However, problem-solving is not as simple as “learning the skill”; there are several reasons why students find it challenging and therefor lose interest in the subject. Firstly, not understanding or reading the question properly. Understanding the question is a crucial aspect in problem solving. First of all, the question needs to be understood before the problem could be solved (Polya 1981; Krulick and Rudnick 1996; Zalina, 2005). Due to the long sentences and wording of the questions, students get confused about the objectives in the problem. They could not bring the meaning to the problem or might misunderstand the meaning (Tambychik and Meerah, 2010). The reason why students misunderstand the problem could vary among students. They could have difficulties understanding the language, the mathematical terms used or making connection of the problem. The longer time needed to understand questions results in longer time to solve problems. In order for students to be able to understand lengthy and worded questions could be to familiarise them with the mathematical and linguistic terms usually found in problem-solving questions. For example, a table, like below, could be displayed in the class or discussed in a numeracy lesson.

(The Literacy Loft, 2019)

Another reason could be only trying one solution. Often children will only evaluate one option to answer the question and then become frustrated and often give up. Children need to be taught trial and error and to evaluate different methods to use. Teachers need to be able to coach children to use general strategies until they find the solution. For example, making a table, drawing a diagram, searching for a pattern amongst data or thinking up a different approach and trying it out. There is no doubt mathematic skill will be required for pupils to contribute and participate in society in later life however the way some maths is presented puts pupils off (Noyes, 2007).

References

·        Boaler, J., William, D. et al., (2000) ‘Students’ experiences of Ability Grouping – disaffection, polarisation and the construction of failure. British Educational Research Journal 26(5): 631 -648.

·        Donaldson, G. (2015) Successful Futures: Independent Review of Curriculum and Assessment Arrangements in Wales. Caerdydd: Llywodraeth Cenedlaethol Cymru.

·        Haylock, D. and Cockburn, A. D. (2013) Understanding mathematics for young children: a guide for teachers of children 3-8. London: Sage

·        Krulik, S. and Rudnick, J. A. (1993) Reasoning and Problem Solving: A Handbook for Elementary School Teacher. Boston. Allyn and Bacon.

·        Mills, K. and Kim, H. (2017) Teaching Problem Solving: Let students get ‘stuck’ and ‘unstuck’. Education Plus Development. Brookings.

·        Noyes, A. (2007) Rethinking school mathematics. London: Paul Chapman Publishing.

·        Ofsted. (2008) Mathematics: Understanding the Score. London: Ofsted.

·        Polya, G. (1981) Mathematical Discovery on Understanding Learning and Teaching Problem Solving. New York: John Wiley and sons

·        Tambychik, T. and Meerah, T. (2010) Students’ Difficulties in Mathematics Problem-Solving: What Do They Say? Science Direct. Procedia. Social and Behavioural Sciences.