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Designing quality open- ended tasks in mathematics Louise Hodgson May 2012

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Characteristics of good questions Require more than remembering a fact or reproducing a skill, Require more than remembering a fact or reproducing a skill, Students can learn from answering the questions; teachers can learn about the students, Students can learn from answering the questions; teachers can learn about the students, May be several acceptable answers. May be several acceptable answers. Sullivan and Lilburn 2004

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Why open ended questions? They engage all children in mathematics learning. Enable a wide range of student responses. Enable students to participate more actively in lessons and express their Ideas more frequently. Enable teachers opportunity to rove and probe student mathematical thinking.

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Characteristics of good teachers They plan less The lesson is predominately about interacting with the students. Peter Sullivan 2008

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Making questions open ended Method 1: Working backwards Method 1: Working backwards Indentify a mathematical topic or concept. Indentify a mathematical topic or concept. Think of a closed question and write down the answer. Think of a closed question and write down the answer. Make up a new question that includes (or addresses) the answer. Make up a new question that includes (or addresses) the answer.

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Method 1: Working backwards How many chairs are in the room? (4) can become …. I counted something in our room. There were exactly four. What might I have counted?

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Method 1: Working backwards Round this decimal to one decimal place: 5.7347 can become …. A number has been rounded off to 5.8. What might the number be?

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Method 1: Working backwards Find the difference between 6 and 1 can become ….

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Method 1: Working backwards The difference between two numbers is 5. What might the two numbers be?

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Making questions open ended Method 2: Adapting a standard question Method 2: Adapting a standard question Indentify a mathematical topic or concept. Indentify a mathematical topic or concept. Think of a standard question Think of a standard question Adapt it to make an open ended question. Adapt it to make an open ended question.

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Method 2: Adapting a standard question What is the time shown on this clock? Can become… My friend was sitting in class and she looked up at the clock. What time might it have shown? Show this time on a clock

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Method 2: Adapting a standard question 731 – 256 = Can become… Arrange the digits so that the difference is between 100 and 200.

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Method 2: Adapting a standard question Ten birds were in a tree. Six flew away. How many were left? Can become…

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Method 2: Adapting a standard question Ten birds were in a tree. Some flew away. How many flew away and how many were left in the tree?

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In the number 35, what does the 3 mean?. Now have a go yourselves!

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Some important considerations The mathematical focus The clarity of the task/ question That it is open ended

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Building open ended tasks into a lesson It is important to plan two further questions/ prompts: For those children who are unable to start working (enabling prompts). For those children who finish quickly (extending prompts).

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High quality response Examples of evidence of a high quality response includes those that: Are systematic (e.g. may record responses in a table or pattern). If the solutions are finite, all solutions are found. If patterns can be found, then they are evident in the response. Where a student has challenged themselves and shown complex examples which satisfy the constraints. Make connections to other content areas.

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Discuss the tasks and adaptions. Consider the following: 1.What is the maths focus of the closed task? 2.Does the new tasks have the same mathematical focus? 3.Is the new task clear in its wording? 4.Is the new task actually open ended?

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Lesson structure Key components: Open ended tasks which allow all students accessibility, Explicit pedagogies, Enabling prompts for those children who are experiencing difficulty, Additional task or question to extend those children who complete the original task.

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References Sullivan, P., & Lilburn, P. (2004). Open – ended maths activities. Melbourne, Victoria: Oxford. Sullivan, P., Zevenbergen, R., & Mousley, J. (2006). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. International Journal for Science and Mathematics Teaching. 4, 117- 143 louise.hodgson@catholic.tas.edu.au

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