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ASDN Webinar Series Spring 2013Session Four March 27, 2013

New Alaska State Standards for Math:Connecting Content with Classroom

Practices

At our last webinar, I had asked people to choose one of the practices we have discussed, (1-6) and spend one planning session for math thinking about how to concentrate on that one specific practice. What insights did you have from this experience?If you feel comfortable, please share your thoughts in the chat box while we wait to get started!

Implementation of the Practices

Today’s Targets

Continue to discuss the larger picture- today’s side topic…Questioning

Dig deeper into practices seven and eight:

1.Look for and make use of structure.2.Look for and express regularity in

repeated reasoning. Identify key implications for classroom instruction.

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Thoughts?

What is the first word that comes to mind when you read this paragraph taken from a NCTM (National Council of

Teachers of Mathematics) publication?

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“A documented successful strategy is the ability to ask critical questions when a student is stuck while solving a problem. We often teach students a procedure, and recognize later that some students did not grasp the concept or the "big idea" of the lesson. Instead of re-teaching or correcting students' procedural errors, we can ask questions that will give them the insights into their misconceptions. This strategy can assist students in thinking through a problem, rectifying an error, or clarifying a misconception.

Through questioning, we can better understand a student's thinking and "coach" them in constructing new understandings of a concept. When tempted to show a student how to "do it right," try asking a question that will guide them toward deepening their understanding.”

NCTM (2012)

A Quick Reading from NCTM

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Teachers spend up to 60% of instructional time engaged in classroom discussions.

Discussion sessions tend to rehearse existing knowledge rather than create new knowledge.

Educators listen for the “correct answer” rather than listening for what they can learn about student thinking.

The same 4 or 5 students tend to raise their hands to get called on to answer questions.

What we Know…

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 Varying levels of questioning are used to guide learning and elicit evidence about student understanding and/or misconceptions about learning targets.

•procedural, recall, factual, DOK 1

•compare, contrast, apply, consider, expand, evaluate, DOK 2-3

This is What I Ask Principals and Colleagues to

Look For:

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Poll- How many discussion questions do plan for in advance for a typical math lesson?

(This would be like a whole group/small group mini lesson, or a direct instruction lesson)1. One

2. Two or three3. Four or five4. I wait to see what the kids are

saying or doing.5. I follow a scripted program, so I

don’t plan for any.

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The Eight Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique

the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

Practice Number Seven

Teachers who are developing students’ capacity to "look for and make use of structure" help learners identify and evaluate efficient strategies for solution. An early childhood teacher might help students identify why using "counting on" is preferable to counting each addend by one, or why multiplication or division can be preferable to repeated addition or subtraction. An elementary teacher might help his students discern patterns in a function table to "guess my rule." A teacher of middle school students might focus on the application of rules and reasoning behind why rules work.  

Thoughts about Implementation

In the chat box, list anything from your current curriculum that requires students to “generalize” a pattern, structure or strategy that will work for them in many situations.

For example- “Multiplication is repeated addition.” “Fractions with the same numerator and denominator are equal to one whole.” (Of course, we also want them to know WHY this is true!!!!)

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Questions, Questions

If you have already watched the video, and you are unable to view it during the webinar, please post a question or comment in the chat box. After we have all seen the video, we will respond to your questions or comments.

Chef Soup

Student Work

Sample

Chat box discussion!

(This was actually a recent discussion I listened to at a staff meeting where the teachers were talking about why everyone had to help with the new ELA standards- no matter what they taught.)

How Much Writing Should Students do in Math Class? (Julia won’t be weighing in!)

Practice Eight

Integrating Standard Eight into classroom practice is not only a matter of planning for lessons that require students to look for general methods and shortcuts. It also requires teachers to attend to and listen closely to their students’ noticings and “a-ha moments,” and to follow those a-ha moments so that they generalize to the classroom as a whole. Teachers can create the conditions for students to look for and express regularity in repeated reasoning, and follow and elaborate students’ thinking when they begin to make these connections.

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Thoughts about Implementation

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. As they work to solve a problem, mathematically proficient students maintain the larger picture of the process, while attending to the details. They continually evaluate the reasonableness of their ongoing results.

What can educators do to encourage this behavior?

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Questions, Questions

If you have already watched the video, and you are unable to view it during the webinar, please post a question or comment in the chat box. After we have all seen the video, we will respond to your questions or comments.

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What Fraction is RED?

What would the conversation sound like?

The Eight Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique

the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

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Alice- Grade ThreeBringing it all together…

Questions, Comments, Closing Thoughts?

Were there any comments or questions from the chat box that we should address before closing?

Be well, Do good work and keep in touch.