This week’s guest blog is by Lauren Reynolds, better known to her students as Miss Ren or @ReynoldsITT.  Lauren works in ITT and maths education in the North West and is a frequent contributor to #mathschat.

Recently I have been thinking about the types of activities that pupils and teachers engage with during lesson time. I have wondered whether it would be beneficial to spend time, in class, looking at the efficiency of solutions.

For example, how many of our students would look at the problem:

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and proceed to dive straight in to a method for calculating sums involving mixed numbers? There are clearly many ways to approach this calculation but adding to both values creates the sum:

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with an answer of 2 1/2 and a much easier mental calculation and thus a more efficient approach to solving that particular sum.

 

After engaging with a variety of CPD sessions regarding the approach of our Asian counterparts, there seems to be a common theme that pupils are encouraged to share their solutions and discuss their approach. We often do ask our students to come to the board and show their thinking but do we look at this from a point of efficiency? And would it be beneficial to do so?

 

When working with students on a Subject Enhancement Course, we talked in great depth about the efficiency of solutions and not only did we find that the discussions challenged and strengthened the students’ own subject knowledge but it also proved to test me as their teacher. Any lesson where you as the teacher is tested must be one filled with a higher level of discussion, right?

If we look at the following example from the Mathematics Assessment Project:

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http://map.mathshell.org/lessons.php?unit=7320&collection=8&redir=1

Clearly this type of activity lends itself to a variety of approaches which is great as this will generate purposeful discussion and assessment opportunities but with the additional view point of efficiency we can make a rich task even richer. A follow up to the above question, before seeing any solution would be to ask pupils to see if they can provide a more efficient solution. This gives pupils an opportunity to review their solution as if it were a first draft and it gives them an opportunity to develop patience in problem solving and a “what if I did this instead” approach.

This is something I have started at the beginning of this year. if you would like to find out how successful I’ve been then do please get in touch at @ReynoldsITT. Please do let me know if you try discussing efficiency of solutions in your class.

Best of luck!