Podcast
Questions and Answers
What is the primary role of questions in mathematics education?
What is the primary role of questions in mathematics education?
- To help teachers determine student understanding of mathematics. (correct)
- To help students memorize formulas.
- To fill time during lessons.
- To provide students with direct answers.
What does effective teaching of mathematics achieve through purposeful questioning?
What does effective teaching of mathematics achieve through purposeful questioning?
- It assesses students' reasoning and advances their sense-making about mathematical ideas and relationships. (correct)
- It directs students towards specific problem-solving strategies.
- It simplifies complex mathematical concepts, making them more accessible.
- It reduces the amount of time spent on problem-solving.
What should purposeful questions encourage students to do?
What should purposeful questions encourage students to do?
- Rely solely on the teacher's explanations.
- Explain, elaborate, or clarify their thinking. (correct)
- Memorize mathematical formulas.
- Avoid discussing their difficulties with mathematics.
In the context of proportional reasoning, what is the key mathematical idea that Ms. Hanson wants to make visible?
In the context of proportional reasoning, what is the key mathematical idea that Ms. Hanson wants to make visible?
In the classroom discussion, what is one way Ms. Hanson prompts students to reflect on different approaches?
In the classroom discussion, what is one way Ms. Hanson prompts students to reflect on different approaches?
Why is disagreement valuable in classroom discussions?
Why is disagreement valuable in classroom discussions?
What is the main difference between 'funneling' and 'focusing' patterns of questioning?
What is the main difference between 'funneling' and 'focusing' patterns of questioning?
What does the 'focusing' pattern of questioning involve?
What does the 'focusing' pattern of questioning involve?
Which of the following is a benefit of teachers planning questions in advance of a lesson?
Which of the following is a benefit of teachers planning questions in advance of a lesson?
What does it mean for teachers to make mathematics 'visible' through their questions?
What does it mean for teachers to make mathematics 'visible' through their questions?
What is the purpose of 'assessing questions'?
What is the purpose of 'assessing questions'?
What is the aim of 'advancing questions'?
What is the aim of 'advancing questions'?
What is the role of student work artifacts in planning future lessons?
What is the role of student work artifacts in planning future lessons?
What is a key characteristic of tasks that 'allow students to use different representations and to make connections among representations'?
What is a key characteristic of tasks that 'allow students to use different representations and to make connections among representations'?
What does teacher questioning influence in the classroom?
What does teacher questioning influence in the classroom?
In the context of student solutions to constructed response questions, what type of response requires a common basis for comparison?
In the context of student solutions to constructed response questions, what type of response requires a common basis for comparison?
What is the primary goal when assessing and advancing student learning?
What is the primary goal when assessing and advancing student learning?
When students produce solutions that make connections and apply them accordingly, what should the teacher do?
When students produce solutions that make connections and apply them accordingly, what should the teacher do?
What does equitable teaching of mathematics require?
What does equitable teaching of mathematics require?
How should tasks be structured to encourage a deeper conceptual understanding of mathematical ideas?
How should tasks be structured to encourage a deeper conceptual understanding of mathematical ideas?
What is the teacher's role in adapting to student strategies during problem-solving?
What is the teacher's role in adapting to student strategies during problem-solving?
What is the primary reason for Ms. Hanson to select Jordan as the first presenter?
What is the primary reason for Ms. Hanson to select Jordan as the first presenter?
What can teachers do to promote high-level questions that help make visible that surface and make visible important mathematical structures and connections?
What can teachers do to promote high-level questions that help make visible that surface and make visible important mathematical structures and connections?
What did Weiss and Pasley (2004) conclude about encouraging students to think deeply?
What did Weiss and Pasley (2004) conclude about encouraging students to think deeply?
After multiple students provide different responses to a complex mathematical problem, how can the teacher best engage a broader discussion about the topic?
After multiple students provide different responses to a complex mathematical problem, how can the teacher best engage a broader discussion about the topic?
When planning a math leasson, what does the text say to anticipate?
When planning a math leasson, what does the text say to anticipate?
What is the most effective way to know what questions to ask in a lesson??
What is the most effective way to know what questions to ask in a lesson??
How does questioning in the I-R-E pattern typically affect student thinking?
How does questioning in the I-R-E pattern typically affect student thinking?
Based on the information, which of the following actions reflects the use of 'probing thinking questions' by Ms. Hanson?
Based on the information, which of the following actions reflects the use of 'probing thinking questions' by Ms. Hanson?
Flashcards
Purposeful questions
Purposeful questions
Effective instruction uses questions to evaluate and improve students' mathematical thinking.
Questioning in mathematics
Questioning in mathematics
Questions are a primary tool to determine a student's math knowledge.
Purposeful Question Goals
Purposeful Question Goals
Reveal current understandings, encourage explanation, and clarify thinking.
Probing Thinking Questions
Probing Thinking Questions
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Making Mathematics Visible Questions
Making Mathematics Visible Questions
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Encouraging Reflection and Justification Questions
Encouraging Reflection and Justification Questions
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Gathering Information Questions
Gathering Information Questions
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Funneling Questions
Funneling Questions
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Focusing Questions
Focusing Questions
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Assessing Questions
Assessing Questions
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Advancing Questions
Advancing Questions
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Pose Purposeful Questions
Pose Purposeful Questions
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Equitable Questioning
Equitable Questioning
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Thoughtful Questioning
Thoughtful Questioning
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Focusing Strategy
Focusing Strategy
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Study Notes
Question Types in Mathematics (NCTM)
- Principles to Actions identifies four types of questions important in math teaching
- Three of the question types are open-ended
Four Question Types
- Gathering information questions prompt recall of facts, definitions, or procedures
- Probing thinking questions prompt explanations, elaboration, or clarification of thinking
- Making the mathematics visible questions prompt discussion of mathematical structures and connections between ideas
- Encouraging reflection and justification questions prompt demonstration of understanding in reasoning/actions or arguments for validity
Funneling vs. Focusing
- Funneling uses questions to lead students to a procedure or conclusion, limiting attention to differing responses and not building understanding
- Focusing honors student thinking by pressing them to communicate it clearly
Assessing and Advancing Questions
- Asking questions that reveal mathematical knowledge allows teachers to design responsive instruction
- Assessing questions reveal knowledge and allow the teacher to assess a student's understanding of math
- Assessing questions also allow the teacher to assess a student's knowledge surrounding problem-solving strategies or representations
- Probing and information-gathering questions are assessing questions
- Advancing questions build on this knowledge and move students beyond their current understanding toward lesson goals
- Questions that make math visible or prompt reflection are examples of advancing questions
Discussion-Fostering Question Examples
- Questions: "What do others think about what ____ said?", "Do you agree?", "Can you convince us that makes sense?" and, "Does that make sense?" are examples of prompts to makes sense of mathematics
- Questions: "Why do you think that?", "Why is that true?", "Can you design a model to show that?", and, "How did you reach that conclusion?" are examples of prompts to mathematically correct answers
- Questions: "Does that always work?", "Is that true for all cases?", "How could you prove that?", and, "Can you think of a counter example?" are examples of prompts to mathematically reason
- Questions: "What would happen if...?", "Do you see a pattern?", "How did you think about the problem?", "What are some possibilities here?", and, "Can you predict the next one?" are examples of prompts to conjecture, invent and solve problems
- Questions: "How does this relate to...?", "What ideas that we have learned about before were useful in solving this problem?", "Have we ever solved a problem like this before?" and, "Can you give me an example of...?" are examples of prompts to connect mathematics and applications ideas
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