Using mathematics schemes?
I have a love/hate relationship with mathematics schemes. By ‘scheme’, I mean a series of books which teachers use as resources to support them in teaching mathematics to children. They are my bread and butter, that is a earn my daily bread through writing them. BUT, I spent my whole teaching live both and out of the classroom arguing that it is most appropriate for teachers to draw on a range of resources to construct their own scheme of work. Teachers know their own students best and so are best placed to design the resources they will use to support the learning of mathematics.
I have also argued in these blogs that seeing mathematics as a process of working the way through a textbook is not conducive to mathematical thinking, especially when those textbooks have been out together very quickly by publishers trying to find a ‘gap in the market’. I have had very frustrating experiences with one pf my publishers who sent all my writing for a ‘mastery review’ by a self-proclaimed ‘expert. I am afraid the advice that was forthcoming was not mastery expert tried to shoehorn every representation currently encouraged by the UK mastery approach into every lesson. This led to9 some very poor resources which whilst they may have met the requirements of mastery did not offer a rich mathematical experience.
One of the open access articles in the current issue of Mathematics Teaching, Making it count: Thriving with maths schemes, by Rebecca Turvill investigates this dilemma. The scheme was seen as an answer to ‘home-schooling’ at first and that this continued once the children returned to school. However, in common with many such resources the expectation of the textbook was a whole class teaching approach which was not something that the teachers or their learners felt was appropriate. So, the school moved towards a mixed approach. Half the class would use the textbook during a lesson with the other half explored the same area of mathematics using an activity designed by the teacher. The following lesson the two halves would swap. In this way the scheme is acting as a tool for planning rather than a pseudo-teacher. This seems like an appropriate halfway house between a completely teacher designed scheme-of-work and slavish adherence to the scheme.
But do textbook resources need to assume a whole class teaching approach. I don’t think so. All the resources I write assume that teachers will group their learners, usually in all-attainment groups. I also try to offer the sorts of questions that I might ask (as a teacher) on the page or include speech bubble to encourage the learners to engage in conversation themselves.
Here is an example. This is the textbook page for a one-hour lesson. Can I invite you to think how you might use this for a lesson. There is, of course, a page on the teacher-guide for teachers who do not have the confidence to design their own lesson. I think asking students to, “Think of a number that you are certain is smaller/bigger than the number you are estimating” is a more effective way of actually discussing estimating than asking to estimate, then count, then write down how close the estimate was.
A second example is from the ATM publication, Talking maths, talking languages.
Focus on the speech bubbles. If we think about how we might design resources this is a simple way to emphasise the importance of talking to each other. It is rare that after a few minutes conversation someone on the room someone doesn’t suggest that the first speech bubble might read, “4.8 is between 4 and 5 but nearer 5.” If this doesn’t happen I can write a set of key words on a flip chart and this sorts out the problem.
Tony Cotton is editor of Mathematics Teaching. The journal of the Association of Teachers of Mathematics (ATM). For more information on the ATM go to www.atm.org.uk. The views in this blog are Tony’s own.
His book Understanding and Teaching Primary Mathematics has published its 4th edition. https://bit.ly/3kFkM5Q
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