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Developing Reasoning, Explanation and FluencySt Helens Teaching Alliance
Tara [email protected] @MathsMummy
Made to Measure – Ofsted 2012
Develop the expertise of staffin understanding the progression in strands of mathematics over time, so that they know the key knowledge and skills that underpin each stage of learning
Schools should:
increase the emphasis on problem solving across the mathematics curriculum
Ofsted, 2012
Potential heavy users of mathematics should experience a deep, rich, rigorous and challenging mathematics education, rather than being accelerated through the school curriculum.
A.C.M.E 2012
fosters mathematical understanding of new concepts and methods – this includes teachers’ explanations and the way they require pupils to think and reason for themselves
helps pupils to apply the mathematical knowledge and skills they have been taught, by solving a variety of mathematical problems
how well pupils apply their mathematical skills across the curriculum.
Review
Plan Model the mathematics Practise the model Practise
GamesMissing numbersWord problemsReasoning InvestigationsDecision making
Review
Explanations in Calcualtion
Check my answers Explain my diagram Make the calculations from my numbers Make the calculations from my digits Decision making Missing numbers in calculation Which calculation if this is the answer?
Addition of 3 numbers
161
130
0 1 1 1 1 2 3 6 9
+ +
7.05 10.02 11.91 11.82 13.44 What is the biggest total you can make? What is the smallest total you can make?
0 0 3 4 4 4 7 7 71 2 2 3 3 6 6 70 0 1 1 3 3 3 6 7
What Calculation?
Use all my numbers
15 15 30 25 40 45 15 27 33 38 42 71 27 28 34 46 62 73 21 37 43 49 70 80
Replace my missing numbers
2 □ 8
3 ■ 6
6 4 4
4 □ 5
○ ■ 9
7 8 ▲
8 □ 7
● ■ 9
○ ■ ▲ 6
Are all my answers correct?
174 – 19 = 153 138 + 57 = 185 256
75
200
110
11
321
TU + TU TU – TU
What does this diagram show?
66 70 82
□ □ □ □ □ Largest total Smallest sum Answer that is a multiple of 10 Answer that is a multiple of 3 Odd answer Largest subtraction answer Answer that is a multiple of 10 using subtraction
21 16 28 23 16 40
Something like this?
13, 16, 19, 22, __, __
___ , ___, 29, 34, ___
What’s my rule?
Understanding the score
Under features of good teaching it says: When offering answers or accounts, the teacher expects
pupils to give explanations of their reasoning as well as their methods. Pupils are challenged if their explanations do not reflect their ability.
Under features of satisfactory teaching it says: Questioning is clear and accurate but does not require
explanation or reasoning; pupils describe the steps in their method accurately but do not explain why it works.
Made to Measure
The best questioning probed pupils’ knowledge and understanding, with follow-up questions that helped pupils to explain their thinking in depth and refine initial ideas.
Sequences
• Here are some numbers in a sequence:
…. 23, 27, 31, 35 ….
• Will the following numbers be in the sequence: 3, 16, 21, 58?
• Explain how you know.
Number boards
Questioning
Whole class sessions Group sessions Playing games Written questions Marking Children questioning
Questioning starts
What would happen if….. What do you notice or see? Why do we…… What is the same? What is different? If you know …how could you find out… How might you record that for someone else? How can you be sure…..
Questioning
• Range of questions• Always, sometimes, never true?• What can the answer be? not be ? • Why is this the odd one out?• If we know this, what else do we know?• Give me . . .tell me . . .show me . . . draw me…• The answer is . . .what is the question?• Give me a silly answer for . . .?• Why is that a good mistake?
If you double the area of a rectangle, you double the perimeter.
If you add two whole numbers that end in 6 and/or 8, the answer will end in 2.
You can pay for a lolly that costs 15p using just 2p coins The sum of two consecutive triangular numbers is a square
number When you double a number you get an even answer. The product of two numbers is greater than either of the two
starting numbers.
3 4 5
7 10 12
16 17 60
64 96 120
Assessment
Modelling
Application Talk
Decision making
