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Asking Questions that Count

While meeting these purposes, teachers can promote mathematical reasoning and critical thinking skills by combining higher-order questions with sound questioning strategies.
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Promote Reasoning Skills with Questioning Strategies

Questioning serves many critical functions in the mathematics classroom. Teachers use questions to

  • identify students’ background knowledge
  • guide students to reasonable answers
  • give students practice using mathematical language
  • informally assess student understanding.
While meeting these purposes, teachers can promote mathematical reasoning and critical thinking skills by combining higher-order questions with sound questioning strategies.
 
The quality of the questions asked is of central importance. Will students be asked to simply recall a fact or compute an algorithm, or will they be asked to do something more? The questions teachers ask greatly impact the learning that occurs in the classroom.
 
Varying Question Structures
Open-ended questions encourage discussion and promote higher-order thinking. They promote reasoning and help students develop a more complete mastery of concepts and skills by requiring them to apply, analyze, synthesize, interpret and evaluate information. In short, to think at the higher end of Bloom’s Taxonomy.
 
Simple calculation questions can be modified to create higher level questions. Rather than asking simple "What is…?" questions, push students to explain and make connections.
 
Simple Question
Complex Question
What is the area of triangle ABC?
What will happen to the area of triangle ABC if the length of the base is doubled? Explain your answer.
 
What is the slope of the line in Graphs A, B, and C?
Compare the slopes of the lines shown in Graphs A, B, and C. How are they similar? How are they different?
 
Add. 4/5 + 3/5
Explain how you can use a number line to find the sum of 4/5 and 3/5.
 
A store offers a 10% discount on a $60 bedside table. If the store offers an additional 10% discount for seniors, how much will Sheila’s grandmother pay for the table?
A store offers a 10% discount on a $60 bedside table. The store offers an additional 10% discount for seniors. Sheila calculates that her grandmother will have to pay $58 for the table. Explain why Sheila’s calculation is incorrect. What mistake did Sheila make?
 
Question Starters
Consider using the following question starts to replace your "What is….?" questions.
  • What evidence is there to….?
  • What is the relationship between….?
  • What would happen if….?
  • How could you determine….?
  • How would you explain….?
  • How would you rate the importance of ….?
As you develop higher-order questions for your lessons, make sure to use a variety of question formats. Variation will not only increase student interest, but it will promote the development of the complete range of critical thinking skills.
 
Wait Time
Waiting just a few extra seconds to call on students after posing a question or to respond to students after they answer questions can have a profound affect on students’ ability to formulate and articulate mathematical ideas in class. Studies have shown that with increased wait time, more students will volunteer answers and the responses will be longer and provide more thorough evidence. Students speculate more and ask more questions. The extra few seconds provides the additional time most students need to begin to reasoning.
 
Safe Classroom Environment
The students who raise their hands in response to a question will naturally tend to be those students who know the answer or believe that they know the answer. By calling only on these students or by quickly calling on another student if an incorrect answer is given, teachers lose valuable opportunities to promote mathematical reasoning. This habit can send the message that students should only contribute their ideas if they know them to be correct. Unsure students shut down and stop contributing. Yet incorrect answers are precisely the tools teachers need to guide students through, model and develop critical thinking skills.
 
Questioning Strategies

To create a classroom environment in which all students feel safe to communicate their ideas, try the following strategies:

  • Establish a system to call on all students and involve as many students as possible. For example, you can write the students names on note cards and draw them at random. When asking a closed-end question, you might ask students to raise a thumbs-up to show agreement and a thumbs-down to show disagreement.
  • Practice effective listening skills. Make sure that your students have the background knowledge they need to understand your questions. Restate students’ answers in clear language or elaborate an idea, and ask them if this is what they meant. "So, what you’re saying is that the outcome of the coin toss does not affect the outcome of rolling the dice. So, they are two independent events. Is that right?"
  • Use probing questions to flush out misconceptions or help students elaborate their assertions. If students state that a rhombus has two parallel sides, you can ask students to draw a rhombus to see whether they are confusing a rhombus with a trapezoid.
  • Avoid telling students the "answer." Anticipate student responses and prepare questions in advance that might help guide students toward correct responses. For example, after students draw a rhombus, you can ask them to compare their drawings to the figures shown in the textbook. Ask them to compare the figure that they drew with the one shown in the book.
 
 
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