On the fingers of one hand: Teaching for Mastery On the fingers of one hand: five things to think about in the primary classroom Dr. Ruth Trundley

Overview Many words have been said and written about teaching for mastery but the reality of teachers in classrooms with children without additional funding is sometimes missing. This workshop will use a practical experience of mathematics to consider five things that any teacher can think about in their classroom; five things that will support the learning and reflect teaching for mastery principles.

Thinking is at the heart of mathematics and therefore should be at the heart of mathematics teaching and learning.

73 – 68 Think of a realistic context for this calculation. Does your partner’s context make sense? Is it realistic? Does the context reflect the way you solved it? If not can you create a context that does reflect the way you solved it? Write another subtraction you could solve by using an equivalent subtraction. And another. And another. What do you notice? Write a subtraction you would solve in a different way. And another. And another. What do you notice?

73 – 7 Think of a realistic context for this calculation. Does your partner’s context make sense? Is it realistic? Write another subtraction you could solve by splitting seven into three and four. And another. And another. What do you notice? Write an addition you would solve by splitting seven into three and four. And another. And another. What do you notice? Write a subtraction you would solve by splitting seven in a different way. And another. And another. Write a subtraction you would solve without splitting seven. And another. And another.

Monitoring students’ responses to the tasks during the explore phase; Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell Stein et al 2008 Anticipating likely student responses to cognitively demanding mathematical tasks: Monitoring students’ responses to the tasks during the explore phase; Selecting particular students to present their mathematical responses during the discuss-and-summarize phase; Purposefully sequencing the student responses that will be displayed; Helping the class make mathematical connections between different students’ responses and between students’ responses and the key ideas.

Adapted from Derek Haylock and Anne Cockburn 1989 Language Symbols Mathematically structured image Context Adapted from Derek Haylock and Anne Cockburn 1989

Aim: All children understanding the mathematics Five things Make careful decisions about examples Expect children to notice things and to wonder Anticipate responses – orchestrate productive mathematical discussions Represent the mathematics in different ways Asking the children to find examples and non-examples – let them explore the mathematics for themselves Aim: All children understanding the mathematics

A pupil really understands a mathematical concept, idea or technique if he or she can: Describe it in his or her own words; Represent it in a variety of ways (e.g. using concrete materials, pictures and symbols) Explain it to someone else; Make up his or her own examples (and non-examples) of it; See connections between it and other facts or ideas; Recognise it in new situations and contexts; Make use of it in various ways, including in new situations NCETM 2015 adapted from John Holt ‘How Children Fail’ 1964.