- Designing quality open-

ended tasks in

mathematics

Louise Hodgson

May 2012 - Characteristics of good

questions

Require more than remembering a fact or

reproducing a skill,

Students can learn from answering the

questions; teachers can learn about the

students,

May be several acceptable answers.

Sullivan and Lilburn 2004 - 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. - Characteristics of good

teachers

•They plan less

•The lesson is predominately about

interacting with the students.

•Peter Sul ivan 2008 - Making questions open

ended

Method 1: Working

backwards

Indentify a mathematical topic or

concept.

Think of a closed question and

write down the answer.

Make up a new question that

includes (or addresses) the answer. - 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? - 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? - Method 1: Working

backwards

Find the difference between 6 and 1

can become …. - Method 1: Working

backwards

The difference between two

numbers is 5. What might the two

numbers be? - Making questions open

ended

Method 2: Adapting a

standard question

Indentify a mathematical topic

or concept.

Think of a standard question

Adapt it to make an open

ended question. - 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 - Method 2: Adapting a

standard question

731 – 256 =

Can become…

Arrange the digits so that the

difference is between 100 and 200. - Method 2: Adapting a

standard question

Te

T n birds were in a tree. Six flew away.

y

How many were left?

Can become… - 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? - Now have a go

yourselves!

In the number 35, what does

the 3 mean?

. - Some important

considerations

•The mathematical focus

•The clarity of the task/

question

•That it is open ended - 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). - 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, al solutions are found.

•If patterns can be found, then they are evident in the response.

•Where a student has chal enged themselves and shown

complex examples which satisfy the constraints.

•Make connections to other content areas. - 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? - 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. - 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