One of my favourite quotes is from the Pirates of the Caribbean movie. When he & his crew are in a bit of a fix Captain Jack Sparrow tells them “the problem isn’t the problem, the problem is your attitude to the problem”.
I often think of that quote when parents talk to me about the difficulties their child is having with problem solving in maths. I dislike the phrase ‘problem solving’ because using the word ‘Problem’ is part of the problem with understanding maths. The purpose of this type of maths question is to develop conceptual understanding, adaptive reasoning and strategic competence but all the student hears is the word ‘problem’.
That word brings with it negative feelings and the student immediately thinks that this question is going to be hard. I prefer to use the words brain teaser, a maths puzzle or just a plain maths question. It switches the focus onto solving the question.
In school, we are taught HOW to do our maths. The assumption being that if we know how to do it, then we also understand why we are doing it that way. This isn’t always the case and that is why some students, who are good at maths, struggle when the question is presented in a different way.
The biggest challenge with sentence based maths questions is clearing away the unnecessary words and focusing on the actual question. I explain it as translating from English into Maths or maths into English. When the student sees maths as a language then the transition becomes easier, because they are familiar with the concept of translating when doing Irish.
After that I ask them to consider this question; what specifically am I being asked? The maths question will always be based on something that they have just learned or have already learned. This helps them to focus. Another good question to ask is ‘Why? Why are they asking me this question? Again it brings to focus back onto the maths element of the question rather than the words around it.
I always recommend having and using a rough work column in the maths copybook. It is also important to write out your thought process line by line, mathematically. In secondary school, Project Maths embraces the concept of multiple solutions. Writing out your reasoning allows the teacher to follow your train of thought, allowing them to correct where necessary and to give marks on work done. Remember in maths having the correct answer is not always the main objective.
Often the need to do maths at all, beyond the basics, is questioned. In the UK‘s new national curriculum, the purpose of the study of maths is to provide ‘a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics and a sense of enjoyment and curiosity about the subject.
In Ireland, the objectives of the Leaving Cert Maths Syllabus, at foundation, ordinary and higher level, are that learners develop mathematical proficiency. These are characterised as; conceptual understanding—comprehension of mathematical concepts, operations, and relations; procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately; strategic competence—ability to formulate, represent, and solve mathematical problems in both familiar and unfamiliar contexts; adaptive reasoning—capacity for logical thought, reflection, explanation, justification and communication; productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence, perseverance and one’s own efficacy.
So maths is way more than just doing the sums, it empowers us to understand the world around us and to help us to solve problems when we encounter them in life.