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Effective Pedagogy

Recently I’ve done a fair bit of reading for my dissertation and two of pieces of literature have had very similar titles, there was The Effective Teaching of Mathematics (Simmons 1993) mentioned here, and then there was “The effective teaching of mathematics: a review of research” (Reynolds and Mujis 1999).

It is the second one which I want to share some thoughts on today. It is an interesting article which is aimed at school leaders and policy makers and looks to a variety of sources to create an idea of effective maths teaching.

The main areas it looks at are pieces of teacher effectiveness research, both from the UK and from the USA, and professional evidence on teacher effectiveness from the UK – namely the three most recent reports on maths teaching from Ofsted (most recent as of 1999).

Whole class teaching

This mixture of academic and professional evidence is analysed and brought together and the article finds that all three areas suggest that “whole class teaching” is the most effective way of teaching maths. That isn’t to say they suggest that we all lecture to silent classes for entire lessons, rather they are advocating a form of “active” instruction, which would punctuate the instruction with questioning to assess the learning and to see where the class needs expanding on and opportunities for practice and consolidation.

This idea seems to make a lot of sense to me, the teachers are the experts in the room, and they are best placed to pass on the knowledge. Listening to a well planned presentation and then internalising this and practising to make sense of it seems a good model.

Group work

While I was reading this it all seemed very sensible, intuitive and a great way to teach mathematical content, but I started to wonder how the other side of mathematics, the logical thinking and problem solving side, would be catered for in this model. Obviously the writers of the report felt the same as they then moved on to looking at group work and other ways to build problem solving ability into your students.

They looked at the idea of group work, suggesting the opportunity to discuss their mathematical ideas with peers and work out between them how it works would be beneficial. They also feel that scaffolding could enable all students to work within their zone of proximal development, allowing all students a chance to develop. They expressed concerns around social loafing, and the possibility of student misconceptions being reinforced.

Their findings led to many examples of group work being an effective tool in problem solving, but they state that to reap the rewards teachers need to spend a lot of time setting it up. I can see that this may be true, and feel that there could be a place for small group work to tackle these types of problems,  especially amongst A level students and others who need to work out how to apply the knowledge learned to solve unfamiliar problems.

The article suggests that group work can be integrated into the active instruction model, taking the place of some of the practice section, and I certainly agree that it could fit. I also feel that modelling a problem solving approach for part of the instruction element of the lesson can give students an insight into how a more experienced mathematician would approach a problem.

Differentiation

A rather interesting finding was that poorer, less effective lessons often include overly complex arrangements for individual work. This was a suggestion that those lessons where the teacher has spent all night creating separate worksheets for each student actually had little to no impact, even a negative impact at times. This certainly suggests that this level of time consuming differentiation is unnecessary and that tasks can be differentiated far more easily and effectively by producing a resource that is stepped in difficultly and allowing different start points or moving them on more easily.

I found that this report was very interesting, it backed up some of the ideas I already had on effective maths teaching and challenged some of the other ones. I am now planning to trial some small group work with some A level students to build problem solving capability.

Reference

Reynolds D & Mujis D, 1999, The Effective Teaching of Mathematics: A Review of the Research, School Leadership and Management, Vol. 19 (3) pp 273-288 (available online here.)

Simmons M, 1993, The Effective Teaching of Mathematics, Longman: Harlow

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  1. Mark Wilson
    April 12, 2016 at 9:50 pm

    Hi,
    This reinforces what I also believe. I mainly teach A level so I would be interested to know how your group work with A level students is structured and how it goes.
    Thanks
    Mark

    • April 12, 2016 at 10:04 pm

      I will share more when I have looked at it.

  2. April 13, 2016 at 3:27 pm

    Yes, some interesting issues discussed here – and for what it is worth here is my ha’penneth. I strongly believe in whole class teaching; the crux issue being how we construct tasks which cry out for students activity: to explore, to be surprised by, to get stuck and unstuck, to seek generality… working individually, in pairs or small groups. At the risk of sounding like a stuck record such tasks need to be offered and worked on in lesson one when a teacher first meets a new group. Re differentiation have a look at: http://www.mikeollerton.com/pubs/atm_pubs/ATM-MT240%20Differentiation.pdf
    This concurs with: “that tasks can be differentiated far more easily and effectively by producing a resource that is stepped in difficulty”… though I did wonder if the word “stepped” was meant to be “steeped”!
    Regards
    Mike

    • April 13, 2016 at 3:32 pm

      Haha, it auto corrected to steeped actually, and that would also fit. I’m not even sure stepped is the right word, I mean as in it increases in steps!

      Thanks for the comment and I will have a read of that on differentiation.

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