Workshop 4: Posing Purposeful Ques4ons NCTM Interac4ve Ins4tute, - - PowerPoint PPT Presentation

Workshop 4: Posing Purposeful Ques4ons

NCTM Interac4ve Ins4tute, 2016

Name

Title/Posi4on Affilia4on Email Address

Warm Up

Make a 3 x 3 grid on your paper. Select 9 different numbers in the range –20 to 20. Arrange them in any order in your grid.

What type of ques4ons?

When you think about the Bingo game, what types of quesFons were asked? What student understanding would be evident in the game? Talk in your group and describe the focus of the quesFons.

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Ques4oning Techniques

• Factual quesFons

comprise the majority of quesFons asked in a mathemaFcs class

– More than 145 quesFons in 48 minute class period – Less than 2 seconds for response

Dougherty & Foegen, 2010

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Moving from skill to concept

Typical skill task: Simplify: 4(3 + 5y)

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Reversibility question:

– Find an expression that can be simplified to 12 + 20y.

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Change the Task

Generalization question:

– Find an algebraic expression with 4 terms that can be simplified to one with 2

• terms. What do you notice about the

terms? – Find an algebraic expression with 3 terms that cannot be simplified. What do you notice about the terms?

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Change the Task

Flexibility question:

– Write an equivalent expression to 3b – 5. – Write another equivalent expression to 3b – 5.

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Change the Task

Flexibility question

Simplify: 5(4x – 3) 5(4a – 3) 5(4y + 3) 5(3 + 4y)

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Change the Task

Ques4ons to Promote Problem Solving and Generaliza4ons

• Reversibility quesFons:

– Promote the ability to think in different ways – Give the answer, students create the problem

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Ques4ons to Promote Problem Solving and Generaliza4ons

• GeneralizaFon quesFons:

– Ask students to find and describe pa^erns – What pa^erns do you noFce?

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Ques4ons to Promote Problem Solving and Generaliza4ons

• Flexibility quesFons:

– Ask students to solve a problem in mulFple ways OR to use what they know about one problem to solve another one – Solve the problem in another way – How are these soluFons alike? How are they different?

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Your turn

Select a lesson in your text. Write two reversibility, flexibility, and generalizaFon quesFons for the lesson. OR Write two reversibility, flexibility, and generalizaFon quesFons related to a problem set that is focused on problems such as:

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Three types of ques4ons

• Exploring: underlying

mathemaFcal relaFonships and meanings

• Probing: gecng students

to explain their thinking

• GeneraFng: moFvaFng

discussion

What other types of ques4ons can be used?

Use the descripFon of Ms. Quigley’s class.

• Find different types of quesFons that she

uses in her class.

• What are the purposes of the quesFons?
• What do they accomplish?

(5 PracFces for OrchestraFng ProducFve MathemaFcs Discussions, [Smith & Stein, 2011], p. 64–67)

What types of ques4ons are used in your curriculum?

• Look at your own

curriculum.

• What types of quesFons

are suggested for you to use?

• What could you add to

the suggesFons?

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Reflec4on

(Principles to Actions: Ensuring Mathematical Success for All [NCTM 2014], p. 41)

Disclaimer

The National Council of Teachers of Mathematics is a public voice

• f mathematics education, providing vision, leadership, and

professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all

• students. NCTM’s Institutes, an official professional development
• ffering of the National Council of Teachers of Mathematics,

supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of

• viewpoints. The views expressed or implied in the Institutes,

unless otherwise noted, should not be interpreted as official positions of the Council.

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