Designing quality open ended tasks
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- 1. Designing quality open- endedDesigning quality open- ended
tasks in mathematicstasks in mathematics Louise HodgsonLouise
Hodgson May 2012May 2012
- 2. Characteristics of good questionsCharacteristics of good
questions Require more than remembering a fact orRequire more than
remembering a fact or reproducing a skill,reproducing a skill,
Students can learn from answering theStudents can learn from
answering the questions; teachers can learn about thequestions;
teachers can learn about the students,students, May be several
acceptable answers.May be several acceptable answers. Sullivan and
Lilburn 2004Sullivan and Lilburn 2004
- 3. Why open ended questions?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.
- 4. Characteristics of good teachers They plan less The lesson
is predominately about interacting with the students. Peter
Sullivan 2008
- 5. Making questions open endedMaking questions open ended
Method 1: Working backwardsMethod 1: Working backwards Indentify a
mathematical topic orIndentify a mathematical topic or
concept.concept. Think of a closed question and writeThink of a
closed question and write down the answer.down the answer. Make up
a new question thatMake up a new question that includes (or
addresses) the answer.includes (or addresses) the answer.
- 6. Method 1: Working backwardsMethod 1: Working backwards How
many chairs are in the room?How many chairs are in the room? (4)(4)
can become .can become . I counted something in our room. ThereI
counted something in our room. There were exactly four. What might
I havewere exactly four. What might I have counted?counted?
- 7. Method 1: Working backwardsMethod 1: Working backwards Round
this decimal to one decimal place:Round this decimal to one decimal
place: 5.73475.7347 can become .can become . A number has been
rounded off to 5.8.A number has been rounded off to 5.8. What might
the number be?What might the number be?
- 8. Method 1: Working backwardsMethod 1: Working backwards Find
the difference between 6 and 1Find the difference between 6 and 1
can become .can become .
- 9. Method 1: Working backwardsMethod 1: Working backwards The
difference between twoThe difference between two numbers is 5. What
might the twonumbers is 5. What might the two numbers be?numbers
be?
- 10. Making questions open endedMaking questions open ended
Method 2: Adapting aMethod 2: Adapting a standard questionstandard
question Indentify a mathematical topic orIndentify a mathematical
topic or concept.concept. Think of a standard questionThink of a
standard question Adapt it to make an open endedAdapt it to make an
open ended question.question.
- 11. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion What is the time shown on this clock?What is the
time shown on this clock? Can becomeCan become My friend was
sitting in class and sheMy friend was sitting in class and she
looked up at the clock. What timelooked up at the clock. What time
might it have shown? Show this timemight it have shown? Show this
time on a clockon a clock
- 12. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion 731 256 =731 256 = Can becomeCan become Arrange
the digits so that theArrange the digits so that the difference is
between 100 and 200.difference is between 100 and 200.
- 13. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion Ten birds were in a tree. Six flew away.Ten birds
were in a tree. Six flew away. How many were left?How many were
left? Can becomeCan become
- 14. Method 2: Adapting a standardMethod 2: Adapting a standard
questionquestion Ten birds were in a tree. Some flewTen birds were
in a tree. Some flew away. How many flew away andaway. How many
flew away and how many were left in the tree?how many were left in
the tree?
- 15. In the number 35, what does the 3 mean? . Now have a go
yourselves!Now have a go yourselves!
- 16. Some important considerationsSome important considerations
The mathematical focus The clarity of the task/ question That it is
open ended
- 17. Building open ended tasks into aBuilding open ended tasks
into a lessonlesson 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).
- 18. High quality responseHigh 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.
- 19. Discuss the tasks and adaptions.Discuss the tasks and
adaptions. Consider the following: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?
- 20. Lesson structureLesson 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.
- 21. ReferencesReferences 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