Problem solving

I’m trying to solve a problem. When is it that we become good at solving problems and how the devil do we learn to problem solve?

Had you asked me the aforementioned questions a couple of years ago, I would’ve said that you can teach anybody the ability to problem solve, by… well getting learners solving problems.

 

I once taught Functional Skills Maths for a year and honestly thought I had it nailed, giving the learners really applicable and functional problems to solve in each lesson. Results weren’t bad, but my current line of thinking is that I was probably doing them a disservice.

 
The thing is, I have realised that to solve problems, and I mean really be able to solve them, without ‘googling’ it, you need to have a core knowledge of the subject in question. For instance, if you presented me with your diet plan and asked me why you weren’t losing weight, my sports science background would allow me to critically analyse the problem in order to come up with a solution (I hope). If however, you asked me to look at your car because it had broken down, I wouldn’t have a clue where to start. I can just about check the oil level on my car. In other words, I don’t have the core knowledge needed to solve problems in automotive based problems.

 

Going back to my ‘amazing’ Functional Skills Maths lessons, the reason they were doing functional maths was because they’d either failed or not attempted their GCSE maths at school. This indicates a shortfall in their core maths knowledge. Why then did I not bridge the gap by giving them this knowledge, rather than getting them to solve problems, problems that actually required knowledge that they hadn’t got?

 

Perhaps there are ways to approach problems in better ways and perhaps this can be taught, but the fundamental ‘thing’ needed to solve problems is knowledge about a subject. In his book, ‘Why Students Don’t Like School’, Dan Willingham asserts that any form of critical thinking requires background knowledge. He goes on to suggest that a long term memory full of factual information gives the working memory more capacity to solve problems, because it is not consumed by trying to understand the problem. My own experience corroborates this assertion. Learners spend much of their time trying to decipher the problem (in the case of Functional maths), as opposed solving it, therefore, I ask, do we need to stop thinking so much about the skills and more about the knowledge in our day-to-day practice?

 

In answer to my initial problem. I think I’ve just about got the knowledge to answer.

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7 thoughts on “Problem solving

  1. Of course you need maths knowledge to solve maths questions but it helps if you also know how to approach novel maths problems in general. For example however much maths you know you’ll screw up if you don’t read the question carefully. Skills need teaching too. See Evidence based teaching ch 21 for detail. Note the vital review after using a skill: ‘how did you do that?’ Where else could you use that process.

    1. Thanks for the comment, Geoff. Much appreciated. My point really, is that there is too much focus on teaching the skills. The skills are redundant without focussing on core knowledge, as you allude to in your comment. I also think that teaching in traditional ways to ‘pass on’ knowledge is still frowned upon and should be promoted more through CPD and ITT.

      In your example, the reading ‘carefully’, happens when you know what you’re looking for. The more you know, the less the working memory has to ‘compute’ (for want of a better phrase). Perhaps there is a way to approach the reading of the questions’ that can be taught however?

      Haven’t got the book, but will try grab a copy this week and maybe it will change my views. 🙂

      1. I think we agree more than we disagree. Skills teaching should take very little time, but it adds a great deal. It is best done in the context of using the skill on content, then there needs to be a review of the content, and then crucially, a review of the skill.
        “How did we do it?” (use the skill)
        “What was the strategy we used exactly?”
        “Why did we do it that way?”
        “Where/when else could we use that skill?”

        This is called metacognition and bridging, or just meta-cognition which has a very high effect size. I’m really surprised D M Willingham thinks only facts increase skill development when the research on metacognition is so well established.

        This review of the skill can take, say 4 minutes out of a 60 minute lesson which is otherwise focussed on content.

        I agree with you that if the teaching concentrates greatly, say 50% on skill teaching that is not a good idea at all as a long term strategy. I haven’t observed many lessons lately, and I would find it alarming if a lot of time was spent on skills teaching.

        I have blogged on skills teaching more generally
        http://geoffpetty.com/teaching-skills-is-vital/

        And I’ve a webpage on it
        http://geoffpetty.com/for-teachers/skills/

        You’ve raised a crucial issue here, I’d be interested to hear what others think about the time spent on skills teaching, but everyone will soon be on the beach – and so they should be!

  2. Ive been thinking about this a lot myself. Been working on the idea of a planning mat to help them get some initial thoughts down on paper. Break down the questions and to start attacking it from different points of view.

    Integral to that is as you say, subject expertise. This needs to be a start point but what then comes after…

    current version of planning mat with my thoughts can be found here.

    https://mrlyonsmaths.wordpress.com/2015/07/07/the-pain-of-problem-solving/

    1. Love this post. I went through a similar experience with weak A level Physics students many years ago and pages 9 and 10 of ‘Approaches to Generic Skills Teaching’ has the results, You can download it from this page:
      http://geoffpetty.com/for-teachers/skills/
      rather similar to your mat though level 3. We started out with simpler versions of the diag on page 9 then progressed to the full Monty.

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