Effective Math Questioning

Why are the questions we ask our students so important? Promotes higher level thinking Facilitates productive discussion in the classroom Students are better able to make sense of ideas, demonstrate understanding, and reflect on their thinking.

Types of Questions Closed Ended – Many of the questions we ask students call for a single number, figure, or mathematical objects. What is 6x8? Open Ended – These questions allow a variety of correct responses and elicit a different kind of student thinking? How could you use 5x6 to find the answer to 8x6?

Closed Ended Questions What is 8x6? 48

Open Ended Questions How could you use 5x6 to find the answer to 8x6?

The Open Ended Question allows students to think critically and demonstrate their own ways of solving the problem.

Creating Open Ended Questions from Closed Ended Questions What is the area of the square? What will happen to the area of the square if the length is doubled? What is the perimeter of the rectangle? Can you draw a rectangle whose perimeter is 20 inches?

Creating Open Ended Questions from Closed Ended Questions Try it!

What are good questions? They require more than remembering a fact or reproducing a skill. Students can learn by answering the question and the teacher can learn about each student from the attempt. There are several acceptable answers.

Effective Math Questions to Ask Students

Effective Math Questions Can you describe the problem in your own words?

Effective Math Questions Can you convince us that your solution makes sense?

Effective Math Questions Will that always work?

Effective Math Questions How does this relate to ______?

Effective Math Questions Could you restate what ________ said?

Effective Math Questions Could you explain your thinking?

Effective Math Questions Could you use materials to show how this works?

Effective Math Questions Will someone who solved it in a different way explain your thinking?

Effective Math Questions What do you already know that could help you figure it out?

Effective Math Questions What would happen if _________?

Invitational Group & Intervention Group Questions Could you explain the problem in your own words? Is there information that can be eliminated or is missing? What have you tried?

Strategies to Improve Questioning Plan questions in lesson design Choose a variety of questions Video some lessons to assess level of questioning Focus questions on student understanding; remove focus from right/wrong answers. Assume all student answers are meaningful. Allow multiple opportunities for interaction centered around math ideas: questioning, discussion, and reflection. Increase wait time.

Resources Asking Effective Questions Article - jigsaw Question Card The Art of Questioning in Math Class Top 10 List

Questions from your plans What if we add more than 10 in our problems? Where do I start, what jumps do I make? Where do I end up? Where do I start for the open number line? Which direction should I go? Can you tell me the connection between subtraction and addition? Can you come up with your own division equation and write it 3 different ways?

How does Questioning tie to the Framework for Fellow Effectiveness? IP1. Ask Clarifying Questions and Extend Student Learning IP3. Encourage Student Discourse SMP 1: Make Sense of Problems and Persevere in Solving Them SMP 3: Construct Viable Argument and Critique the Reasoning of Others

Framework for Fellow Effectiveness Take a couple of minutes and go over IP1 and IP3

SMP 1: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

SMP 1 Video Clip http://www.youtube.com/watch?v=k2kyE6JNXok&feature=c4-overview-vl&list=PL02B59CC509E81FC8 Beginning through 4th grade example Skip to 11:49 Skip to 17:20

SMP 3:Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.

SMP 3 Video Clip http://www.youtube.com/watch?v=cW40_NKZfZs Beginning through 4th grade example Skip to 11:44 Skip to 15:14

Expectations Incorporate a minimum of 2 open ended questions in each session, place questions on sticky notes in your guide to help you remember; record exact questions in your plans Make sure kids are persevering with their problems and making sense of them– SMP1 Allow for students to construct viable arguments and critique the reasoning of others - SMP 3 Hang SMP Posters 1, 3, and 6 at kid eye level. Explain what each means AND you how you will be holding them accountable to each.