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Patient problem solving

I recently read a piece by D Pearcy called “Reflections on Patient Problem Solving”, from Mathematics Teaching 247. It was an interesting article that looks at how teachers need to allow time for students to try their own ideas out while problem solving, rather than just coax them along in a “this is how I would do it” kind of way.

Pearcy’s definition of problem solving is looking at something you have never encountered before that is difficult and frustrating at times, takes a reasonable amount of time, can be solved more than one way and can be altered or extended upon easily. He then goes on to ask whether this is actually happening in classes or if teachers are just walking students through problems, rather than allowing them to problem solve.

He quotes Lockhart (2009) – “A good problem is one you don’t know how to solve” and states that it follows that if you give hints then it defeats the point of setting problems. He goes on to say that maths advocates talk of the importance of maths as a tool to problem solving – but that this isn’t actually happening if students are not being allowed to get frustrated and struggle through to a solution.

He explains how he finds it difficult not to give hints when students are struggling, both because it is in most teachers nature to help, and because of the external pressure to get through the syllabus quickly. This is something I too have encountered and something I have become increasingly aware of as I try to allow time for struggle. Other factors at play are maintaining interest, and increasing confidence. If we let students struggle too much they may lose interest and confidence in their ability – thus it is important to strike a balance between allowing the struggle but not letting it go too far. This is certainly something I keep in mind during lessons, and I feel it is something that we all should be aware of when planning and teaching.

This is an interesting article that looks at a specific problem and allowing students time to struggle and persist. This importance of this is paramount, in my view, and this is also the view expressed by the author of the article. I find it very hard to not offer hints and guidance when students are struggling. One way I manage to combat this at times is by setting problems I haven’t solved yet, thus leaving me a task to complete at the same time. This can work well, particularly at A Level and Further Maths level as then I can take part in the discussion with the students almost as a peer. This is a technique I have used often with my post 16 classes this year.

I have been reading a lot about problem solving recently, and a recurring theme is that teachers can often stifle the problem solving they are hoping to encourage by not allowing it to take place. This is something we need to be aware of, we need to have the patience to allow students the time to try out their ideas and to come up with solutions or fall into misconceptions that can then be addressed.J
Have you read this article? If so, what are your thoughts on it? Have you read anything else on problem solving recently? I’d love you to send be the links if you have and also send me your thoughts. Also, what does problem solving look like in your classroom? Do you find it a struggle not to help? I’d love to hear in the comments or via social media.

Further Reading on this topic from Cavmaths:

Dialogic teaching and problem solving

Understanding students’ ideas


Pearcy.D. (2015). Reflections on patient problem solving. Mathematics Teaching. 247 pp 39-40

Lockhart, P. (2009). A Mathematician’s Lament. Retrieved from: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf

  1. June 8, 2016 at 10:40 pm

    Agree, and I’d like to think with SOME of my classes I am pretty good at this. But that’s because I know how to keep them motivated without leading them too much. Others, however give up instantly. They just want to know the answer /be able to do it and get really annoyed if I don’t help them. In their eyes I am a dreadful teacher because I refuse to teach them things. Building the resiliance and desire to keep going with students like this is the hardest part of the job.

    • June 9, 2016 at 11:01 pm

      Aye, that certainly rings true for me at times too.

  2. Megan
    June 9, 2016 at 9:55 pm

    Exactly what s/he said^^^^

    In a lesson, when they can’t work it out within ten minutes or so they give up and start talking off task with the attitude, “Well we’re getting nowhere and you won’t help us…”

    Send them home with it and the next day there will be a queue of them with notes in their planners from parents requiring that you help them with it. Parents view homework as something they should be able to achieve unless you’re a rubbish teacher. The ones not in the queue to show you their note from home may well have had it done for them by their tutor, or a family member.

    • June 9, 2016 at 11:02 pm

      Aye, it can certainly be tough to contend with at times.

  3. Megan
    June 9, 2016 at 9:57 pm

    Actually, I must dust off my copy of “8 days a week” for my Y7 for next year and keep on fighting the good fight. I’m just feeling a bit jaded at the moment 🙂

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