Developing Deep-Thinking

Mathematical Questions

A quick PD show for teachers of elementary mathematics.

Created by: Christine Giusto-WeiblMath Instructional Support Specialist

What makes a good mathematics question?

The whole is more than the sum of its parts.

~Aristotle ca 330 BC

http://www.flickr.com/photos/inkyhack/4529895620/sizes/m/in/photostream/

The first thing we must ask ourselves is what are the goals of our instruction?

Undoubtedly they include:• Fostering an engaging learning environment• Promoting discourse among students & opportunities

to make conjectures • Helping student self-assess learning• Stimulate interest & curiosity in mathematics

Our questioning within a mathematics lesson should always aim in matching our goals of instruction.

Why Ask Them? Which Ones to Ask?

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Most text questions focus on one answer deemed appropriate. Another term for single response questions are called “closed” questions. Typically these types of questions have students working in the knowledge or application levels of understanding, leaving little room to press further in higher order thinking.

Developing Deeper Understanding

When students are given open-ended questions, it requires them to think more deeply. There is a natural emphasis on problem solving and reasoning through open questions. Students who are required to analyze, criticize and justify their thinking are consistently working in the higher order thinking skills. (Revised Blooms Taxonomy, 2001).

The Good & The “Bland”

• The members in the Jones family are ages 5, 12, 36 and 39. What is the average age of the Jones family? (answer: 23)

• If I have $17 in my wallet, about how much money do I have?• What is the measurement of your arm in inches?• Find the product of 36 and 2.

• What could the ages of the Jones family be if the average age is 23 years?

• My brother asked me how much money I had. I told him about $20. How much money could I have in my wallet?

• Could you find something on your body measuring over 26 inches? What could you measure under 26 inches?

• Name the possible factors when the product is 72.

Using a backwards by design plan will help in creating your questions.

I’m Ready to Learn…How Do I Write My Own?

Remembering these three steps will help:Step 1: Identify the topicStep 2: Think of a closed question along with the expected

answerStep 3: Using your closed question, make up another question

that would include or address your expected answer.

Try It Out!

• Remember the steps: topic, answer, good question

• With experience and practice using good questions the more easily they

will come to you• Remember good questions will not

always have only one answer but rather develop deep understanding

of the concepts within your goal.

Credits/Resources• Discovery Education. (2005). Albert Einstein (1879-1955). [Image]. from http://www.discoveryeducation.com/ • Discovery Education. (2010). Wind Power plants [Image]. from http://www.discoveryeducation.com/

• Jupiterimages Corporation. (2006). Alphabet Building Blocks (1) [Image]. from http://www.discoveryeducation.com/ • Jupiterimages Corporation. (2006). School Bus (2) [Image]. Available from http://www.discoveryeducation.com/ • Mathematics Students [Image] . from

http://www.flickr.com/photos/inkyhack/4529895620/sizes/m/in/photostream/ http://creativecommons.org/licenses/by-nc/2.0/deed.en • Sullivan, P. & Lilburn, P. (2002). Good questions for math teaching. Sausalito, CA:

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