Sharing Good Practice – Problem Solving in the Maths Faculty

I joined the Maths Faculty Meeting last week to find out how they were sharing good practice with each other and to see how their ideas can be transferred to other subject areas. I was told before going that they would be doing lots of Maths, what I wasn’t told was that it was going to be, even for the Maths teachers, really hard Maths – Olympiad Standard (the Maths Challenge).

The team were asked to think about how they set challenging Maths tasks in particular to A-level students and the steps taken to coach the students to the correct answers. They were reminded of 3 questions discussed in a previous meeting:

  • “What do you need?”
  • “What could you draw?”
  • “What algebra can you write?”

 

Elliot and Jimi had put themselves forward to trial this out in front of the Faculty. Jimi was set a maths problem which Elliot had done but was then going to act as the coach. How was he going to help Jimi to solve the problem – with encouragement and tips but without telling him explicitly how to do it or to just give him the answer.

The Faculty then divided into pairs to solve different Maths problems and then to coach each other on how to reach the correct answer. There were circles, congruent triangles and simultaneous equations… to name just some of the mathematical terms.

maths

 

At the end, the Faculty discussed some very important points which could easily be transferred to other subject areas:

  • How much modelling do you? At first you probably model more but at what rate do you take the scaffolding away?
  • How do you coach a particular student? This may be different depending on the confidence of the student. Give them tips as they move along giving them confidence in their use of Maths. Some examples of what you could say:
    • “What can you see?”
    • “What does it make you think of?” (“what associations do you have with…?”)
    • “If I could tell you another bit of information, what would you want me to tell you?”
    • “What else could you do?”; “what could you try?”; “do anything!
    • (“Keep it tidy!”)
    • “What information haven’t you used?”
  • You may give a particular student a problem to grapple with for a couple of weeks – the struggle will do them good, gain confidence in their problem-solving techniques as well as helping them when they get to University as this is what they would expect on a degree course.
  • How long should we leave a student to struggle when they’re heading down the wrong path? That depends on the student.
    • We should immediately point out any mathematical misconceptions in their work, so that misconceptions aren’t embedded.
    • We might point out mistakes like adding errors, or might leave the student to find errors themselves.
    • We can train them to spot wrong paths e.g. if they come across a quartic equation.
    • We could suggest that they check for information that they have not yet used.
    • We could draw their attention to how many marks the question is worth.
  • Encourage the students to verbalise their thought process, by explaining out loud their thinking this will help them to work on through the problem.
  • Look at the question again – think what information have you been given; what can you do with that information and how can you use that information to work out your answer?
  • Link to preparing for the exam – ensure your workings out are neat and think about how much time and marks are given to a particular question.
  • Use of the visualiser, often a very useful tool in the Maths Faculty to model and demonstrate how you are doing your Maths.
  • To explain to the students that you yourself found the question a challenge, so that students understand that problem solving isn’t “magic”. Talk through your own thought processes and your own mistakes before solving the problem.

An enjoyable 30 minutes seeing the Maths Faculty working together doing Maths and I also didn’t expect the Russian writer Chekhov to be quoted whilst solving a Maths problem!

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