1. Using assessment to encourage teaching for understanding
Caroline Hamilton & Jess Easton
Mathematics Specialists
White Rose Maths Hub
My name is Paul Rowlandson, Assistant Principal at Trinity Academy…

2. Content Why teach for understanding?
How can summative assessment help encourage teaching for understanding?
How can formative assessment highlight depth of understanding?
In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

3. In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.
Simon Sinek

4. Fractions
2 3
4 5 7
63 8

5. Fractions Tricks and short cuts Dividing fractions….
KFC – keep, change, flip
Fraction of an amount…..
Divide by the bottom, times by the top
Tricks and short cuts
Adding and subtracting….
Multiply the bottom then cross multiply the top
Mixed to improper….
Times by the bottom, add the top

6. Why not?
It worked for us!

7. Why not? Relies on memory Relies on students’ making their own links
Students can struggle to apply knowledge to unfamiliar problems
Doesn’t prepare them for success in mathematics beyond school
Gives some students a false sense of success – they remember the trick so they are good at maths.

8. CPA

9. In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

10. Instead of testing: What is 8 × 5?
In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

11. What is 𝟓 𝟐 𝟕 as an improper fraction
Instead of testing:
What is 𝟓 𝟐 𝟕 as an improper fraction
In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

12. Write an equivalent fraction to 𝟐 𝟑
Instead of testing:
Write an equivalent fraction to 𝟐 𝟑
In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

13. ‘Good assessments are critical
‘Good assessments are critical. They should help students know where they are in their learning, provide students with the opportunity to show their understanding, and show students how to improve.’ Boaler, J (2015)

14. Asking the right question
Look at question A and question B. Which question draws out possible misconceptions?

15. Asking the right question
Question A
Question B
What fraction of the shape is shaded?
Explain your answer.

16. Asking the right question
Question A
Question B
Find the missing number.
953
-328
6 5
Find the missing number.
952
-328
6 4

17. ‘Schools successfully teaching for mastery make sure that teacher assessment, and pupil self-assessment, are an integral part of every lesson.’
Drury.H (2015)

18. Delving into the student’s mind
Look at the examples of questions children have answered. Do the mistakes show a slip or a lack of understanding?

22. If A= B= C= and D= 43 9
it's A because 13 is closest to 5
2 9 is smaller than 2 7 , and 2 3
I think this because is nearly a whole number so if it was it would be 5
Because ninths are the smallest fraction
I ruled out B and C because they are over 5. Then I put A and D over the same denominator and this showed me that or D was closer to 5
5’s are closer to 5 than 4 so just looking at those is bigger than so C is closer.

23. WRMH new and improved schemes of learning
In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

25. In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

26. In 2004, Sybilla Beckmann published an article in the Mathematics Educator journal about textbooks used in Singapore. She reported that from as early as UK’s year 5, students were presented with algebra stories to solve, even before they’d been introduced to algebra. Algebra stories like the one in the starter and similar to the one that my top set year 11 were trying to get their head around. Anyway ‘bar models’ can be used as a problem solving tool to allow students to access complex problems.

28. Schemes Y1 - 6
Schemes KS3
Diagnostic questions
Social media
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Facebook – White Rose Maths Hub

29. Caroline Hamilton & Jess Easton @WRMathsHub
Thank you
Caroline Hamilton & Jess Easton
@WRMathsHub