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Mrs Saunders, you are teaching us, not telling us. Pedagogies to improve learning. Students need to trust their teacher to know them as people , know how to teach, and know what to teach
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Pedagogies to improve learning Students need to trust their teacher to know them as people, know how to teach, and know what to teach As the teacher, I am the authority in the room, and from Day 1 I behave consistently, and differently
Teacher as authority • I am in charge, so I arrange the seating • In alphabetical order • Seldom changed, and only by me • Cycle rows forward from time to time
Pause • I wait at least 10 seconds after posing a question before accepting an answer • Why do you think I do this? • Discuss briefly with the person next to you
Re-frame the language • I ban “Miss, is it . . .?” • And give students alternative language to use (and reiterate it): I think it could be . . . It might be . . . I wonder if it could be . . . • We’re all allowed to make mistakes
Random numbers • Each student has a number on the roll and they write it down inside exercise book cover • Alphabetical order means . . . • Use this when I want to choose a student to answer – after pausing
Random number expert • I teach one (volunteer) student how to use their calculator to generate a random number from the class • That student always generates random numbers when I want them
My favourite questions • What do you notice? • What is the same and what is different?
Geometry is visual • What can you see?
Work out what you can and see where it takes you • I use this for geometry and trigonometry in particular
Feedback from asking "What can I see?" to get started It helped me because it broke down the question step by step. It allowed me to think of the answer myself and find different strategies. Finding everything I could 'see' in the question made it easier when writing down my working tofind the final answer.
Kathleen Hart • We need to build a bridge from the concrete to the abstract • Bridge must be 2-way, must work both for doing and undoing • Children's Understanding of Mathematics 11-16 (1981)
Wiesje Geldof’s Bridge (Sigma Publications) Find the area of my garden: 5 m 7 m Vegies Shrubs 4 m 20 m2 28 m2 Lawn Flowers 6 m 30 m2 42 m2
Total area of my garden • Total area = 10 x 12 = 120 m2 = 20 + 28 + 30 + 42 m2 = 120 m2 I articulate my mental strategies every time I use them
8x Total area = (x + 3)(x + 5) = x2 + 5x + 3x + 15 = x2 + 8x + 15 X 5 x2 5x X 3 3x 15
Find possible lengths and widths for my garden 15 m2 12 m2 24 m2 30 m2
Wiesje Geldof’s Bridge (Sigma Publications) Find the area of my garden: 5 m 7 m Vegies Shrubs 4 m 20 m2 28 m2 Lawn Flowers 6 m 30 m2 42 m2
Factorising X2 + 4x - 12 4x X ? x2 X ? -12
Talk to the person next to you • Plus of using garden squares?
Do now! • Every lesson starts with 3 – 5 questions hand-written on board • Usually revision – previous lesson, previous year (simple), algebra skills • Can take up to 15 minutes to do and process
Homework • These students need to learn that doing homework matters • I set a little almost every day, students open book at start of lesson to show me HW while they complete the Do Now • I record in my mark book whether reasonable attempt or not
Feedback • Not just ticks and crosses or N, A, M, E • Always a sentence about what understanding student has shown, and what they need to do to progress. • Talk about A and M: What level have we been working on?