Creating Open Problems. Bruce Williams


Open Ended Questions


Why are they important?

  • Open ended questions allow access to the question by all students.

  • Students self differentiate by using numbers they feel comfortable with.

  • They demonstrate the level of student understanding.

  • They require more than remembering facts.

  • Student learning is developed by undertaking thinking activities.

  • There is more than one correct solution, and always more than one way to solve the problem.


How do I create “good” questions?

  • Work Backwards from the answer to a closed question. I.e Give the answer and ask for the question.

  • Modifying a Closed Question by leaving out at least one number. (see below)


How do I use open questions in my classroom?

  • Pose the question and ensure all students understand the question. Do not prompt of hint at the solution or appropriate strategies. Make the students think for themselves.

  • Allow students time to work on the problem. aAsk them to draw a picture.

  • Share student strategies and solutions. Remember the strategies are more important than the solution.

  • The teacher pulls all the pieces together into a tidy bundle.


How do I assess student work?

  • Use the student responses to inform your teaching. What areas do I need to give students more exposure to? (Not what do I need to tell them.)

  • Use a rubric:

    • 0. No understanding evident.

    • 1. Made an attempt but shows limited understanding.

    • 2. Acceptable but incomplete.

    • 3. Demonstrates clear understanding.

    • 4. Goes beyond expectations.



Open Ended Questions

Examples:

1. Traditional Closed Question:

Multiply 7 x 8

Made into a Closed Real problem.

I went to the zoo yesterday and saw 7 cages with 8 birds in each.

How many birds were there in total?

Made into an Open Problem.

I went to the zoo yesterday and saw cages with birds. There were 8 birds in each cage. How many birds might there have been in total? (Extension: Draw a picture showing your answer).




2. Traditional Closed Question:

Divide 2 into 24

Made into a Closed Real problem.

I want to share $24 equally between two people. How much money do they each get? ?

Made into an Open Problem.

I want to share $24 equally among my friends. How much does each person receive?




3. Traditional Closed Question:

Subtract 35 from 64

Made into a Real Problem.

I had 64 eggs and 35 of them hatched. How many have not hatched yet?

Made into an Open Problem.

I had 64 eggs and some of them hatched. How many may not have hatched yet if just over half have hatched?
 


4. Traditional Closed Question:

What is ½ of 12

Made into a Real Problem.

I have 12 jellybeans and half are red. How many are red??

Made into an Open Problem.

Half of my jellybeans are red. Draw a picture of my jellybeans.

Bruce Williams. CreatingRealMathematicians.com
 
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