Planning learning, not lessons

You may be wondering about the title of the first chapter, Planning learning, not lessons. We think it’s the most important place to start this book, because the most important thing to remember when teaching mathematics is that every decision you make about your teaching should come from thinking deeply about how pupils learn mathematics. Learning comes first and planning for it is the backbone of our practice.

A lesson is an arbitrary unit of time. In some schools it’s an hour, in others two, in others 50 minutes. Learning topics does not conveniently fit into the lesson time that we have, and it is impossible to know in advance how your class will respond to the learning that you plan. You might find that pupils grasp certain ideas more quickly or slowly than you anticipated. If you have carefully planned a task to expose pupils to multiple aspects of a concept but stop before it is completed because ‘time’s up’, the pupils will miss important learning. When we plan lessons, rather than learning, time becomes the dominating factor influencing our activity. When we plan sequences of learning in a continuum and treat the end of the lesson as the rest break before picking up again, we put the learning first.

In this chapter, we give an overview of the things we should think about when planning; many of these ideas will be explored more deeply in later chapters. We begin with the ethos that underpins a successful department: collaboration.

Collaboration

In an ideal world, all the teachers involved in teaching a topic would come together and work collaboratively to plan it. The advantages of a collaborative approach are immense as there is a wealth of experience in every mathematics department. Different teachers have different strengths: deep subject knowledge; experience; enthusiasm for new ideas; keen interest in different ways of working; experience of primary or A level teaching; and so on. They will have worked in different schools in different parts of the country or the world. This treasure trove of knowledge should be drawn on by all.

It is useful to note that collaborative working is not the same as cooperative working. These are often seen as interchangeable but there is a subtle difference between them that has a monumental difference in process and outcomes. Collaboration is a process of negotiation, decision-making and alignment, whereas cooperation is sharing out the tasks in a project. In teaching, cooperative working usually looks like: ‘You do lesson 1 and I’ll do lesson 2’. It shares the workload (always a bonus!) but leads to disjointed progression through the learning sequence and none of the rich, developmental conversations that lead to deeper pedagogical understanding, better classroom practice and improved outcomes for pupils.

Collaborative planning develops our pedagogical understanding, increases teacher confidence and improves morale. It is a process that happens over time. Time should be put aside and dedicated for teachers to bring their ideas, share their previous experiences, make suggestions and listen to each other. There should be opportunities for teachers to research