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

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

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

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

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

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.

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

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 5.7347 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: https://ateacherswonderings.wordpress.com/2014/09/13/open-ended-tasks-and-questions-in-mathematics/

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

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

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.

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

Open-Ended Assessment Developing mathematical thinking Resources https://www.stem.org.uk/elibrary/collection/2780 GAIM http://books.heinemann.com/math/ Open-Ended Assessment Developing mathematical thinking

Open-Ended Assessment Developing mathematical thinking Resources https://www.stem.org.uk/elibrary/collection/2780 GAIM http://books.heinemann.com/math/ Open-Ended Assessment Developing mathematical thinking

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