Mathematics and Problem-Solving

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February 9, 2017 by Sarah Gillie

Where learners’ EF (Executive Function) is underdeveloped and/or working memory is overloaded, mathematics can pose real challenges that go beyond understanding numbers or carrying our calculations. It’s common for EF to impact maths, not least because of the importance of sequencing, and EF difficulties can co-occur with dyscalculia as with dyslexia. Although EF techniques may also help students with dyscalculia, it will take longer and it is unlikely to be enough. (I will write more on this important and under-resourced need another time)

EF-supportive techniques should, on the other hand, show benefits in the short to medium term for students whose maths difficulty is a result of their EF weakness, rather than a co-occurrence. Such students may have a sound grasp of number concepts and straightforward calculations, and might be able to work well orally, or maybe complete a whole page of the same type of sum or calculation à la Kumon. Their difficulties tend to manifest when they are faced with problems involving more than one type of mathematical operation (+, -, x, ÷), or multiple steps, or written in words, or a combination of these. Unfortunately, by the time children are only 7 years old they are most likely already encountering such mathematical challenges both in the classroom and at home.

Bear in mind that the brain’s executive functions, which among other things enable the processing of instructions, are still very much in the developmental stages while students are at primary (elementary) school. At home, in nursery and pre-school, children learn to follow simple commands, consisting of words and gestures. Gradually they begin to interpret more complex instructions, with perhaps two or three steps, sometimes reading cues such as facial expressions. EF weaknesses can mean that these skills are underdeveloped and it is likely that the demands of a written comprehension task or multiple step maths problem will be exhausting, frustrating and demoralising.


As with many recommendations to support learning needs, they may seem obvious once written down, but they are often forgotten. When implemented these are strategies that can benefit all learners. If these strategies are well embedded in your classroom or homework routines, they will promote independence in learners who are ready, and leave you more time to focus on those who still need help.

mathsymbols

Three strategies I have found worked really well both in the whole class setting and 1:1 are:

  • Be REALLY explicit when teaching mathematical language, introduce new words with care and have clear displays grouping words, symbols and diagrams. Revisit the language and refer to the displays as often as is appropriate
  • Talk through each example you model explicitly, no matter how often you have done it before
    • Encourage your learners to talk themselves through their problem-solving tasks – if they repeatedly self-talk themselves through a mathematical task, the steps can become embedded more quickly, reinforcing the skills
  • Teach, and then revise problem-solving skills whenever they are needed to successfully complete a unit of learning
    • The old favourite technique of underlining or highlighting the numbers, identifying language and selecting the mathematical operation works for almost all learners, but for those with EF difficulties, the strategy will probably need to be rehearsed and revised repeatedly before it can become second nature. Again, displays can help, and these should be referred to when necessary, both when the task is modelled and while students work independently (or with support).

Sometimes a learner’s natural number skills are so strong that their EF difficulties don’t cause any noticeable trouble in the subject until high school, external examinations or even beyond. Taking things back to basics can help here, too – provided the educator’s skill-set combines the the requisite technical subject expertise with pedagogical knowledge to underpin where necessary.

Further Reading

Kaufman, C. (2010) Executive Function in the Classroom – Practical Strategies for Improving Performance and Enhancing Skills for All StudentsBaltimore: Paul H. Brookes Publishing Co.

Meltzer, L. (ed.) (2007) Executive Function in Education: From theory to practice. New York, NY: The Guilford Press

More blogs on executive function can be found here:

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