How do you make an Open Ended Question ?
Open Ended Questions
A question which finds out what students know, understands and are able to do.
Engage all students  enable students to participate more actively.
Require students to explain their reasoning.
Stimulates Mathematical Thinking.
Serve as a prompt  Lead students to understanding.
Serves as an Assessment Tool.
Assessment For Learning in the Mathematics Classroom
Goals
To look at the 4 areas of: Shared Learning Goals, Effective Feedback, Peer & Self Assessment and Questioning.
To give you effective techniques on each of these to use in the class.
To show you how these can work in the classroom.
To show the importance of Assessment for Learning.
Explain why there is a need for change.
Feedback
"Three types of feedback are essential to formative assessment. The first is from teacher to student; the second is from student to teacher; and the third is between students." (Clarke, 2003)
Feedback Sandwich
Positive statement
Constructive criticism with how improve
Positive statement
Giving Feedback
Descriptive Feedback (Clarke, 2003)
Reminder: Draws attention to the learning goal.
Scaffold: Helps to focus on a specific aspect.
Example: Give a suggestion of how to use the scaffold.
Hattie (2009)
Benefits Of Using Effective Feedback
Increased student motivation
Encourages reflection
Encourages SelfAssessment
Improves Student Performance
Black and William (1998)
Peer and Self Assessment
What is Peer Assessment?
Students working together sharing experiences and critiquing each other's work for the benefit of their learning.
Students take charge of their own learning.
What is Self Assessment?
Students review their own work in order to acknowledge what they did well and where they can improve.
Why incorporate Peer and Self Assessment?
This type of formative assessment ‘helps teachers to filter the rich data that arises in class discussion and activity so that professional judgements can be made about the next steps in learning. Feedback, peer and self assessment have an important role to play in this process and, if utilized properly, can result in large learning gains’ (Hodgen and Wiliam, 2006)
Why incorporate Peer and Self Assessment?
The process promotes both active involvement and practiced in making judgement about quality of work – their own and fellow students
Peer and selfassessment plays a vital role in students becoming familiar with the way that mathematical work is judged.
(Hodgen and Wiliam, 2006)
No grading
Comments Only
Written Feedback
Teacher to Student
Student A
Student B
Last year in the Premiership, Wayne Rooney scored (x) goals and Robin van Persie scores 2(x+1) goals. Together they scored 38 goals. Task:
Activities
Make an equation in x to represent this information.
Find how many goals Rooney scored last year.
Student to Teacher
1 minute summary
Muddy Points
Proforma Document
Swap your answer with your partner:
WWW:
What Went Well...
EBI:
Even Better IF...
Assessment
No Hands Up
Assessment
Take your answer back:
NTIW:
Mini Whiteboard
Anonymous
Know all students answers
Assessment
Swap your answer with your partner:
WWW:
EBI:
Assessment
Take your answer back:
NTIW:
Next Time I Will....
Is it Adding to the Workload of the Teacher?
Pupils learn assessment criteria in an interesting way, so they remember it and use it automatically.
Quicker assessment, immediate feedback.
Relaxing – the children do the work, we manage/ overview.
Free time for the teacher to observe pupil learning.
Pupils use each other to discuss, prepare and assess their work. They become independent learners.
Overall Benefits to Students
Self Assessment enhances belief and perseverance.
Peer Assessment allows students to see how information can be represented in different ways.
Students can develop as life long learners.
Reduces classroom 'preaching'.
Students are rewarded for what they did well and instructed on where they can improve (Medals & Missions)
Effective Questioning
Why Assessment for Learning Works
Why Change from the Traditional System?
The world is changing everyday and we should adapt accordingly.
A Changing World
As society shifts from an industrial age, in which a person could get by with basic reading and arithmetic skills, to an information age, which requires the ability to access, interpret, analyze, and use information for making decisions, the skills and competencies needed to succeed in today’s workplace are changing as well (Bond, 1992)
Maths is Changing
The way me learn must change since the way questions are asked are changing.
Questions are not predictable and won't suit the rote leaner.
Rote learners are being taken out of their comfort zone.
What Was....
Use right angled triangles to determine the height of the tree.
Is Now...
You are given a measuring tape, a calculator, a clinometer and a pen & paper. Describe how you would calculate the height of a tree.
Old System vs. New System
Make the Right Call, Not What is Easiest Now!!!
Strategic Questioning
What is Strategic Questioning ?
Examples of Open Questions
Think of a closed question
Write down the answer
Make up a new question that includes the answer.
Present more than one answer and ask the students which one is correct and Why ?
Conclusion
References
Discussion
What is your opinion?
Conclusion
We have looked at the different areas of assessment for learning
Related it to the mathematics classroom
Showed how to use assessment for learning techniques in the classroom
Looked at the reasons for the need for change
Looked at the benefits of Assessment for Learning.
Example 1.
Round 5.7656 to one decimal place.
A number has been rounded off to 5.8, what might the number be ?
Example 2
.
Which of the following are prime
7, 57, 67, 117
Fred thinks that 57 and 67 are prime because they both end in 7, John says he is wrong. Who is correct and why ?
Your Turn
Create an open ended question for the following

What is the LCM of 18 and 24?
Benefits to the Teacher
Know what the students already know
Influence their planning.
Plan to build on existing knowledge
Promotes Student participation.
Assertive Questioning
Students work in Buzz groups.
Work on thought provoking/real life tasks.
Produce a fully argued and justifiable answer.
OECD  Studies with 8 countries
Raised student attainement.
Improved Students ability to learn.
General gain in academic achievements.
High gains for previously underachieving students.
More Questions
Starter :
How can you sort these?
How many ways can you find to ....?
Stimulate Maths Thinking:
What is the same ?
What is different ?
What comes Next? Why ?
Assessment:
What have you discovered?
How did you find that out ?
Why do you think that ?
Final Discussion:
Have we found all ways?
How do we know?
National Council of Teachers of Mathematics
No formal evaluations of systems.
Short scale studies found the rate of learning was approx double that found in other classrooms.
Promoted Greater Engagement
Increased Professional Satisfaction.
Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139–148.
Bond, (1992); National Center on Education and the Economy, (1989); and U.S. Department of Labor, (1991).
Clarke, S. (2003). Enriching Feedback in the primary classroom. London: Hodder and Stoughton.
Hattie, J. (2009). Visible learning: A synthesis of over 800 metaanalyses related to achievement, London: Routledge.
Hodgen, J. and Wiliam, D. (2006). Mathematics inside the black box. London: NferNelson publ.
OECD (2005) Formative Assessment: improving Learning in Secondary Classrooms.
Petty, G. (2009), Evidence Based Teaching. Cheltenham: Nelson Thornes.
William, D. What does Research say the benefits of Formative Assessment are? NCTM.ORG available: http://www.nctm.org/uploadedFiles/Research_News_and_Advocacy/Research/Clips_and_Briefs/Research_brief_05__Formative_Assessment.pdf [07Nov13]
http://books.heinemann.com/math/construct.cfm
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Assessment For Learning
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