Wednesday, August 17, 2016

#MTBoSBlaugust Planning for Questioning & Resources

Questions and questioning are at the heart of rich math dialogue.

Questioning “to-do” or “not-to-do” list
  1. Ask meaty questions … not one-word answer questions.
  2. Ask open-ended questions!
  3. Don’t announce questions as easy or difficult.
  4. Give students time to think about your question.
  5. Ask a question, give time to think … then call on a student.
  6. Don’t answer your own questions.
  7. Don’t repeat a student’s answer.  Instead ask another student to explain if clarification is needed.
  8. Ask the follow-up question … “Why?” or “How do you know” or “Can you elaborate?”
  9. Use your poker face during discourse – don’t give your thoughts away with facial expressions.
  10. Invite student questions as much as possible!
  11. Use questioning as a teaching tool in place of the standard lecture.
  12. Don’t use questions as a disciplinary tool.

In Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking, Pearse and Walton stress the importance of preplanned high level thinking questions.  Most of us have heard of research that says in most classes teachers ask mostly low level questions.  It takes specific planning to be sure to use worthwhile questions.  Rarely will they just happen.

I have found a few resources to use to help me in preparing good questions.

1.  I love the NRICH Enriching Mathematics site!  It is many excellent resources from articles to challenging problems!  This article, Developing a Classroom Culture That Supports a Problem-solving Approach to Mathematics, caught my attention.  The author offers ways to think about the questions you ask, how to group them, and possible question stems.  Check it out!

2.  Want to use Socratic Questioning?  This blog post explains six categories of Socratic questions and provides question stems for each category!  Excellent resource!

3.  At the Ontario Ministry of Education, there is an excellent article entitled, "Asking Effective Questions."  In the article there are eight tips for asking effective questions.  Additionally there are many, many questions or question stems providing an amazing framework for asking good questions. Keeping such a list of questions or question stems handy when planning is helpful in designing optimal questions.  In addition to keeping lists handy, using a template for planning discussion around a problem or question is useful.  The book Intentional Talk has such templates.  Those templates are free right now on the Stenhouse Publishers website.  You can also preview the entire book for free there as well. 

4.  Another book to have on your shelf is this book by Schuster and Anderson.  The book is set up by strands in math. The questions are open-ended and challenging.  For example:  "Carla and Fiona are having a mathematical debate about the equation y = 1/2 x + 3.  Carla thinks that every time y changes by one, x changes by 2.  Fiona thinks that every time y changes by one-half, x changes by one.  What do you think?"

5.  I like yet another book for its ideas on differentiating.  It is also organized in strands.  For each topic, the authors, Small and Lin, provide ideas for open questions and 2 parallel questions at different levels.  One example that caught my eye is:  "Another function is a lot like the given function.  What might it be?  Option 1:  y = 3x^2 + 4  Option 2:  y = 3^x.  Follow up questions are provided:  What happens to your function when x gets big?  When x is quite small?  What kinds of things might you change but still have a similar function?  What would you choose not to change?

Do you have resources to help you plan deep, thought-provoking questions?  Share resources in the comments!

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