Effective+Questions+for+Mathematical+Thinking

__ Questioning Strategies brought to you by PBS.org/teacherline: __ Developing Mathematical Thinking with Effective Questions • How would you describe the problem in your own words? • What facts do you have? • What do you know that is not stated in the problem? • How did you tackle similar problems? • Could you try it with simpler numbers? Fewer numbers? Using anumber line? What about putting things in order? • Would it help to create a diagram? Make a table? Draw a picture? • Can you guess and check? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">If you compared your work with anyone else’s, what did they try? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">How does this relate to…? • <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What ideas that we have learned were useful in solving this problem? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What uses of mathematics did you find in the newspaper last night? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you give me an example of…? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">How did you get your answer? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Does you answer seem reasonable? Why or why not? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you describe your method to us? Can you explain why it works? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What if you had started with… rather than…? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What if you could only use…? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What have you learned or found out today? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Did you use or learn any new words today? What did they mean? <span style="font-family: TimesNewRomanPSMT; color: #00b0dc; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What are the key points or big ideas in this lesson? <span style="font-family: Calibri; color: white; font-size: 7pt; mso-bidi-font-family: ZurichBT-Black; msobidifontfamily: ZurichBT-Black;">resources <span style="font-family: Calibri; color: #002d62; font-size: 15pt; mso-bidi-font-family: ZurichBT-Black; msobidifontfamily: ZurichBT-Black;">Developing Mathematical Thinking with Effective Questions <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Why is that true? How did you reach that conclusion? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Does that make sense? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you make a model to show that? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Is that true for all cases? Explain. <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you think of a counterexample? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">How would you prove that? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What assumptions are you making? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you explain what you have done so far? What else is there to do? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Why did you decide to use this method? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you think of another method that might have worked? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Is there a more efficient strategy? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What do you notice when…? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Why did you decide to organize your results like that? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Do you think this would work with other numbers? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Have you thought of all the possibilities? How can you be sure? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What do you think about what said? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Do you agree? Why or why not? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Does anyone have the same answer but a different way to explain it? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Do you understand what _ is saying? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you convince the rest of us that your answer makes sense? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What would happen if…? What if not? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Do you see a pattern? Can you explain the pattern? <span style="font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">Can you predict the next one? What about the last one? <span style="line-height: 115%; font-family: TimesNewRomanPSMT; color: #ed008d; font-size: 18pt; mso-bidi-font-family: TimesNewRomanPSMT;">• <span style="line-height: 115%; font-family: TimesNewRomanPSMT; color: black; font-size: 9.5pt; mso-bidi-font-family: TimesNewRomanPSMT;">What decision do you think he/she should make?
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To promote problem solving, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To make connections among ideas and applications, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To encourage reflection, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To help students build confidence and rely on their ownunderstanding, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To help students learn to reason mathematically, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To check student progress, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To help students collectively make sense of mathematics, ask… **
 * <span style="font-family: Calibri; color: black; font-size: 9.5pt; mso-bidi-font-family: ZurichBT-Bold; msobidifontfamily: ZurichBT-Bold;">To encourage conjecturing, ask… **