Thinking Through A Lesson: Lesson Planning as a Means for Improving the Quality of Teaching

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Thinking Through A Lesson Lesson Planning as a
Means for Improving the Quality of Teaching

• Peg Smith
• University of Pittsburgh
• Plenary Session B -- February 17, 2006
• Teachers Development Group
• 2006 Leadership Seminar on Mathematics
  Professional Development

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Why Lesson Planning?

• The effectiveness of a lesson depends
  significantly on the care with which the lesson
  plan is prepared.
• Brahier, 2000

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Why Lesson Planning?

• During the planning phase, teachers make
  decisions that affect instruction dramatically.
  They decide what to teach, how they are going to
  teach, how to organize the classroom, what
  routines to use, and how to adapt instruction for
  individuals.
• Fennema Franke, 1992, p. 156

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Typical Lesson Plan Format

• Goals and Objectives
• Materials
• Motivation
• Lesson Procedure
• Closure

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Typical Lesson Plan Format

• Goals and Objectives
• Materials
• Motivation
• Lesson Procedure
• Closure

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Typical Lesson Plan Format

• Goals and Objectives
• Materials
• Motivation
• Lesson Procedure
• Closure

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Learning from the JapaneseWhat it Takes to Plan
a Lesson

• Anticipating solutions, thoughts, and responses
  that students might develop as they struggle with
  the problem
• Generating questions that could be asked to
  promote student thinking during the lesson, and
  considering the kinds of guidance that could be
  given to students who showed one or another types
  of misconception in their thinking
• Determining how to end the lesson so as to
  advance students understanding
• Stigler
  Hiebert, 1997

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The Thinking Through a Lesson Protocol (TTLP)

• In what ways is this protocol different from
  other lesson protocols or formats you have used
  in the past?

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Key Differences

• Emphasis is on what students will do not solely
  on the teacher actions
• 5-Practices are embedded
• Focus is on questions that the teacher can ask to
  assess and advance students mathematical
  understanding
• Its OVERWHELMING!

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The Five Practices

• Anticipating
• Monitoring
• Selecting
• Sequencing
• Connecting

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The Importance of Questions

• Teachers questions are crucial in helping
  students make connections and learn important
  mathematics and science concepts. Teachers need
  to know how students typically think about
  particular concepts, how to determine what a
  particular student or group of students thinks
  about those ideas, and how to help students
  deepen their understanding.
• Weiss Pasley, 2004

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The Importance of Questions

• Teachers provoke students reasoning about
  mathematics through the tasks they provide and
  the questions they ask. NCTM,
  1991
• Asking questions that reveal students knowledge
  about mathematics allows teachers to design
  instruction that responds to and builds on this
  knowledge. NCTM, 2000
• Questions are one of the only tools teachers
  have for finding out what students are thinking.
  Michaels, 2005

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Simulating Different Aspects of the Protocol

• Articulate your goals for student learning in
  terms of what students will know and understand
  rather than what they will do
• Anticipate student responses including
  misconceptions and errors AND consider how you
  will respond
• Analyze selected pieces of students work and
  consider what questions you would ask to assess
  or advance students thinking given your goals for
  the lesson
• Analyze a set of student responses to a task and
  decide which responses you would select, how you
  would sequence them, and what questions you would
  ask to help students make connections between the
  responses.

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Simulating Different Aspects of the Protocol

• Articulate your goals for student learning in
  terms of what students will know and understand
  rather than what they will do
• Anticipate student responses including
  misconceptions and errors AND consider how you
  will respond
• Analyze selected pieces of students work and
  consider what questions you would ask to assess
  or advance students thinking given your goals for
  the lesson
• Analyze a set of student responses to a task and
  decide which responses you would select, how you
  would sequence them, and what questions you would
  ask to help students make connections between the
  responses.

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The Hexagon Pattern Task

• For the pattern shown below, compute the
  perimeter for the first four trains, determine
  the perimeter for the tenth train without
  constructing it, and then write a description
  that could be used to compute the perimeter of
  any train in the pattern. Find as many different
  ways as you can to compute (and justify) the
  perimeter.

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Articulating Goals

• V1 SWBAT write a generalization for describing
  the perimeter of any train in the sequence
• V2 Students will recognize a relationship
  between the number of hexagons in a train and the
  perimeter of the train (i.e., the perimeter
  depends on the number of hexagons), use this
  relationship to write a generalization that can
  be used to find the perimeter of any train in the
  sequence, and connect their generalization to the
  diagram.

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Simulating Different Aspects of the Protocol

• Articulate your goals for student learning in
  terms of what students will know and understand
  rather than what they will do
• Anticipate student responses including
  misconceptions and errors AND consider how you
  will respond
• Analyze selected pieces of students work and
  consider what questions you would ask to assess
  or advance students thinking given your goals for
  the lesson
• Analyze a set of student responses to a task and
  decide which responses you would select, how you
  would sequence them, and what questions you would
  ask to help students make connections between the
  responses.

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Anticipating Responses

• Jason
• A hexagon has 6 sides so every time you add one
  more hexagon you add 6 more sides. So the
  perimeter is the train number you have times 6.
  So if you start with the first train you have one
  hexagon which has six sides so the perimeter of
  the train is 6. If you add another hexagon the
  perimeter is 12. It keeps going like this.

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Simulating Different Aspects of the Protocol

• Articulate your goals for student learning in
  terms of what students will know and understand
  rather than what they will do
• Anticipate student responses including
  misconceptions and errors AND consider how you
  will respond
• Analyze selected pieces of students work and
  consider what questions you would ask to assess
  or advance students thinking given your goals for
  the lesson
• Analyze a set of student responses to a task and
  decide which responses you would select, how you
  would sequence them, and what questions you would
  ask to help students make connections between the
  responses.

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Analyzing Selected Responses

• What questions will you ask to assess students
  understanding of key mathematical ideas, problem
  solving strategies, or the representations?
• What questions will you ask to advance students
  understanding of the mathematical ideas?

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Analyzing Selected Responses
Kristens Response
  train 1 train 2
train 3 6
10
14   4
4 What I did was
counted each side for 1-3, but for 4-10 I add
four to each. Then I got 18, 22, 26, 30, 34, 38,
42.  
 
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Analyzing Selected Responses

• Assessing (Probing/Pressing)
• How did you know to add four?
• Tell me where you see the increase by 4 in the
  picture of the train?
• How did you get the perimeter for the 10th train?

• Advancing(Connecting/Extending)
• How would you find the perimeter of the 25th
  train without counting?
• What would the perimeter be for the 100th train?
• Can you write directions that would help someone
  to find the perimeter of any train?

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Simulating Different Aspects of the Protocol

• Articulate your goals for student learning in
  terms of what students will know and understand
  rather than what they will do
• Anticipate student responses including
  misconceptions and errors AND consider how you
  will respond
• Analyze selected pieces of students work and
  consider what questions you would ask to assess
  or advance students thinking given your goals for
  the lesson
• Analyze a set of student responses to a task and
  decide which responses you would select, how you
  would sequence them, and what questions you would
  ask to help students make connections between the
  responses.

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TTAL

• What we are learning about teacher learning

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TTAL in Preservice

• Teachers were assigned to groups of 3 or 4 and
  given a task around which to plan a lesson
• Groups worked collaboratively on the first
  section of the TTAL (i.e., selecting and setting
  up a mathematical task)
• Teachers worked individually in completing the
  remaining sections of TTAL
• Teachers turned in a detailed response to the
  TTAL which was evaluated as one of the course
  requirements

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Key Issues that TTAL Raised for Teachers

• the importance of understanding the mathematical
  ideas in a lesson
• the need to anticipate what students might do and
  how one might respond
• the value of asking questions that assess and
  advance students learning of mathematics

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Impact of TTAL on Teacher Learning

• 12 out of 17 students (approximately 71)
  spontaneously identified the TTAL as having an
  impact on their learning.

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Gwen Triple

• I had to go beyond just writing a lesson plan.
  I had to think about what are the students'
  misconceptions. I had to really think about
  having a plan, but multiple plans, not just one
  plan. And that's what I've been trying to do is
  pretty much one plan and this asks me to go
  beyond - to go out of that tunnel and think of
  well what happens if they don't know this or they
  think this then what avenue? That was really
  hard for me. And just coming up with all the
  different ways that a student would solve - it's
  that thinking into the future where I don't have
  as much practice with. That was like giving
  birth laugh. Cause I was like trying to think
  up the problems or those issues that would come
  up and given my student population, I really had
  to put their heads on, the kids heads on. And
  that's what really we should do but that's not
  the way we're trained. We're trained to pretty
  much stick - and especially now with the
  curriculums that are coming along some even
  scripted that it's so confining but... so this
  was good

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Brenda Daniels

• the questions you ask are really important.
  And to get at those big ideas that you... That's
  kind of what we did with a partner. We sort of
  said what we thought the big ideas were and what
  students might do. I think that just the whole
  assignment of thinking through it all ahead of
  time is really important, and your students will
  probably learn so much more because you know
  those certain questions to ask and, um, so, I
  learned a lot from that.

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Brianna Fitzgerald

• I think Thinking Through a Lesson helped me to
  realize that it's really important to prepare
  before you would go into the classroom to teach
  in this manner--to have an idea of what type of
  solutions the students might come up with. What
  are the ideas, what kind of questioning you might
  want to use, and to really plan for what are some
  of the misconceptions they might have, too. What
  ways they could solve it that may seem right to
  them, but maybe really aren't. So, I think that
  I learned that that's an important part of
  teaching, as well, to think through those things
  as well as the correct solutions.

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So Whats The Point?

• The purpose of the Thinking Through a Lesson
  Protocol is to prompt teachers in thinking deeply
  about a specific lesson that they will be
  teaching. The goal is to move beyond the
  structural components associated with lesson
  planning to a deeper consideration of how to
  advance students mathematical understanding
  during the lesson. This is not to say that
  structural components of a lesson are not
  important, but rather that a focus on structural
  components alone is not sufficient to ensure that
  students learn mathematics.

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