2. Reflecting on Practice: Making Connections that Support Learning
Unit 1, Session 4
2016
Reflecting on Practice
Park City Mathematics Institute

3. Responding to questions
Presentations
Number Systems
bit.ly/pcmi16number
Expressions & Equations
bit.ly/pcmi16express
Ratios & Proportional Reasoning
bit.ly/pcmi16ratios
Functions
bit.ly/pcmi16functions
Geometry
bit.ly/pcmi16geometry
Statistics & Probability
bit.ly/pcmi16stats
Presentations here:
tinyurl.com/pcmi16prezs
Great questions from yesterday
Respond to your questions on Padlet 
Reflecting on Practice
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4. There are 3 key findings that come out of How People Learn
Reflecting on Practice
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5. Park City Mathematics Institute
How People Learn
1.Teachers must draw out and work with the pre-existing understandings that their students bring with them.
Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp the new concepts and information that are taught, or they may learn them for purposes of a test but revert to their preconceptions outside the classroom.
Reflecting on Practice
Park City Mathematics Institute
NRC, 2001

6. Park City Mathematics Institute
How People Learn
2.Teachers must teach some subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge.
To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application.
Reflecting on Practice
Park City Mathematics Institute
NRC, 2001

7. Park City Mathematics Institute
How People Learn
3.The teaching of metacognitive skills should be integrated into the curriculum in a variety of subject areas. A "metacognitive" approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them.
Reflecting on Practice
Park City Mathematics Institute
NRC, 2001

8. Learning progressions
These documents indicate what students should have learned when they come to us, but what understanding of these concepts do students actually bring with them?
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9. Park City Mathematics Institute
Pretests
One way to find out what understandings students have is to give a pretest. This is a very formal and popular approach, but what are some potential downsides?
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10. Park City Mathematics Institute
Next… a video clip of Nick Branca leading a professional development session with middle school teachers.
The focus of the session is on understanding what an equation is.
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11. Park City Mathematics Institute
As you watch the video, consider:
How does Branca elicit and use evidence of what teachers know about equations in the video?
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Two truths and a lie
1. a) The only correct answer for 4(x-6)-(x-6) is 3x-18
b) The right answer for 4(x-6)-(x-6) is x = 6.
c) 3(x-6) is equivalent to 4(x-6)-(x-6).
2. a) All functions have inverses.
b) sin(A+B) = sinA+sinB
c) A linear function can have an average rate of change between two points on the line.
Reflecting on Practice
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13. Park City Mathematics Institute
2 Truths & a Lie
Any comments about this technique?
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Another technique to figure out what students remember about a topic is “Write everything you know about …”
What words do you think students will “remember” about lines?
Talk at your table for a minute about what students might say.
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15. Brainstorm – words about lines
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16. Possible ways to organize ideas
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In your own classrooms, how do you pre-assess or determine what your students remember?
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18. Park City Mathematics Institute
“Unit starters”
Short activities pushing students to mentally recall some specific content that will provoke a discussion enabling the teacher to draw and work with the students' previous understandings
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“Unit starters”
In pairs, choose one of the topics below, negotiating at your tables so each pair has a different topic.
Law of Sines/Cosines
Probability
Exponential functions
Proportional relationships
Volume
Identify a grade level, brainstorm the prerequisite knowledge for that grade level, and create a unit starter by modifying one of the examples or create one of your own. Provide a sample student response.
Reflecting on Practice
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Unit Starters
As a group come up with one thing that was really cool that you think the rest of the room needs to hear.
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Readings
Read the common assigned section for next class.
Then, choose one of the four options
As you read, identify
two key ideas and
one thing you found surprising.
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22. Park City Mathematics Institute
References
Boaler, J.
Meyer, D.
Frayer Model:
KWL Chart (Know, Want to Know, Learned)
National Research Council. (2000). How people learn. M. Suzanne Donovan, John D. Bransford, & James W. Pellegrino, (Eds.) Commission on Behavioral and Social Sciences and Education. Washington, D.C.: National Academy Press.
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23. Other possible unit starters
Write into your questions a "memory prompt" that reminds students of an important fact, i.e., use the name hypotenuse in comments before the lesson on right triangle trigonometry.
What is the first question that comes to your mind? (Meyer)
3. KWL chart (what do you know, what do you want to know, what did you learn)/ Frayer model
Reflecting on Practice
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