Yesterday, I talked about visible thinking. One of the suggestions
was to use questions that had no one right answer so students had to
explain their thinking. Unfortunately, it is not always easy to find
questions that meet the criteria so its important to know how to change
questions from having only one answer to a more open ended one or create
your own questions.

Lets first look at taking specific questions found in the textbook and turning them into more open ended questions.

Take a process question such as "Calculate 47 x 25" and rewrite it to
read "Calculate 47 x 25 in two different ways.". Or take a question like
"I have a quarter, a dime, and three nickles in my pocket, how much do I
have?" and change it to "I have 5 coins in my pocket, how much might
they be worth?"."

Instead of finding the volume of a
rectangular prism measuring 2.1 by 8.2 by 3.4 and rewrite it so the
student is asked to create a word problem where you need to find the
volume of a rectangular prism in order to solve it. You could also
rewrite it to require students to find all the possible dimensions of a
rectangular prism with a volume of 120 m^3.

Next lets look at techniques for creating open ended questions.

1.
Think of Jeopardy where the answer is given and the contestant provides
the question but in this case there is more than one answer. An
example might be "Area of 30 square feet" which gives four possible
questions such as "What is a rectangle that is 3 by 10, or 2 by 15, or 1
by 30 or 4 by 5". This will be a student's first thought but it also
allows for questions like "What is a triangle with a height of 10 feet
and a base of 6 feet."

2. Use examples that have wrong
answers and have the students decide where the mistake is and how to
correct it. It might be a question like "George thinks 24 + 37 equals
51 but Jill says its 511. Who is correct? Explain your answer." In
this case both answer are wrong so they have to explain that. It could
also be a question involving one person seeing five rectangles in a
design while the other person sees three rectangles and two squares.
The student has to help settle the disagreement.

3. Get
menu's or price lists from real world places and have students
calculate things like "How much would a school lunch cost if it were
bought at this restaurant?" Get a news paper and ask students to
speculate on the relationship between the space articles and ads take up
on a page.

4. Use the Tell Me All technique which
simply asks students to write down what they know on a topic such as
fractions, roots, factoring, etc.

Tomorrow we'll look at creating good "Which one does not belong?" questions. Let me know what you think.