1. Open-Ended Assessment Developing mathematical thinking
Mrs Leann de Belder (nee Peters)
@LMPeters16

2. Open-Ended Assessment Developing mathematical thinking
Nothing New….
Mike Ollerton (Presenter)
Jo Boaler (author of The Elephant in the Classroom and Mathematical Mindset)
Dan Meyer (3-Acts Maths website)
Fawn Nguyen (Visual Patterns and Number Talks website creator)
NRICH
ATM
GAIM
Open-Ended Assessment Developing mathematical thinking

3. Session Goals Why use open-ended assessment?
How to use open-ended assessment?
Examples
Resources

4. Why? Open-ended Assessment
Reveal reasoning and thinking process
Develop their mathematical thinking and ability to explain what they are doing
Show their understanding and fluency of their chosen method
Show they understand the connections between different topics across the mathematics curriculum
Open-Ended Assessment Developing mathematical thinking

5. Advantages of Open-Ended Assessments
Students can be more expressive with their answers
Students can show their true ability to call on different areas of mathematics that may be required to answer a question
Rich-task assessments encourage students to think differently, reason more and help to better prepare them for challenges they may face in their jobs or more challenging GCSE/A-Level questions
Open-Ended Assessment Developing mathematical thinking

6. Disadvantages of Open-Ended Assessment
Grading
When using open ended assessment the best grades are given in the form of what pupils have accomplished and what they need to do next to further their learning
Giving a levelled grade such as 1-9 or National Curriculum level
Students who struggle to begin the task or find a starting point.

7. Open-Ended Assessment Developing mathematical thinking
Assessment Questions
Re-word assessment questions:
Instead of true or false: Which one fits and why?
Instead of write the meaning/definition: Show a counter example
Ask for examples that are always/sometimes/never true
Open-Ended Assessment Developing mathematical thinking

8. Ways to Open Questions CLOSED: What is half of 20?
OPEN: 10 is the fraction of a number. What could the fraction and the number be? Explain.
CLOSED:  Find the difference between 23 and 7.
OPEN: The difference between two numbers is 16. What might the numbers be? Explain your thinking.
CLOSED: Round this decimal to the decimal place
OPEN: A number has been rounded to 5.8. What might the number be?
CLOSED: There are 12 apples on the table and some in a basket. In all there are 50 apples. How many apples are in the basket?
OPEN: There are some apples on the table and some in a basket. In all there are 50 apples. How many apples might be on the table? Explain your thinking.
Thank you:

9. Opening up the question
NEW QUESTION
Create two triangles that have two sides the same and one angle the same.
Prove these triangles are congruent.
Prove these triangles are not congruent.
Use diagrams and an explanation in your proofs.
congruent

10. Year 7 Assessment Example
LEVEL
CRITERIA
TICK
Level 3
Construct a bar chart
Level 4
Choose and use appropriate units and instruments for measure
Find the perimeter of simple shapes
Present information in a clear and organised way
Develop my own strategies for problem solving
Use the properties of 2-D shapes
Construct and interpret simple line graphs
Level 5
Understand and use the formula for the area of a rectangle
Distinguish area from perimeter
Draw simple conclusions of their own and give an explanation of their reasoning
Show understanding of situations by describing them mathematically using symbols, words and diagrams
Interpret graphs and diagrams and draw conclusions
Level 6
Solve problems through breaking them into smaller, more manageable tasks, using a range of efficient techniques
Use logical argument to establish the truth of a statement
Q: What is the largest rectangular area of a shape whose perimeter is 24cm?
Start Small
Draw a diagram
Create a table of results

11. Assessment in Practice
Used in place of a probability test
Open-Ended question
Children were given dice as a way to help determine the result of the experiment
We were looking for:
Reasoning
Ability to work systematically
Ability to organise their results of the experiments in a way that they could draw conclusions from it
Recognition that they were looking at experimental probability and that could help them predict the number of boxes of cereal they would need to buy
Differentiation: pupils who could not decide on a starting point were given similar examples to help them get started on their work. High ability pupils were able to take the task further and relate it to different averages.

12. Practise: Work to open these questions
Open-Ended Assessment Developing mathematical thinking

13. Open-Ended Assessment Developing mathematical thinking
Resources
GAIM
Open-Ended Assessment Developing mathematical thinking

15. Open-Ended Assessment Developing mathematical thinking
Resources
GAIM
Open-Ended Assessment Developing mathematical thinking

17. Open-Ended Assessment Developing mathematical thinking
Questions??
Leann de Belder
@LMPeters16