Post on 14-Jul-2020
Cathy Seeley (cseeley@utexas.edu)Senior Fellow Emeritus, Charles A. Dana Center
August 2, 2014
Reflecting on Mathematical Habits of Mind
Saturday, August 2, 14
DISCUSSION
•Write one word, phrase, or idea that captures some new learning or ‘Aha!’ from this week.
From a presentation by Cathy Seeley, 2014
Saturday, August 2, 14
• Reflect on the past 3 days
• Think a bit more about mathematical thinking
• Consider your next steps to implement Mathematical Habits of Instruction . . .
In this session...
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Reflections...• Peg Smith: Effective teaching practices in context of a rich task
• Diane Briars: 21st-Century Skills, Deeper Learning and the teaching it takes to get students there
• Dylan Wiliam: Students need to work at least as hard as teachers: Teachers‘ job is to engineer effective learning environments in which students learn
• Thought-provoking sessions focused on Mathematical Habits of Mind and the content we teach--Modeling the 8 effective teaching practices
• Discussions of race, poverty, stereotypes, barriers, equity
• Time for you to reflect on your practice with othersSaturday, August 2, 14
What not to worry about . . .
• Finding all 8 Mathematical Practices in every good task
• Making precise distinctions about which Mathematical Practice or which Process you’re doing or using
• Knowing all the answers to your students’ questions
• Being an expert on Mathematical Modeling or Mathematical Structure or . . .
• Completely implementing your emerging vision of the kind of teacher you want to be the first month of school
Saturday, August 2, 14
Threads and themes...1. Paying attention (teachers and students)
Saturday, August 2, 14
mathreasoninginventory.com
Marilyn Burns, PIFunded by Gates Foundation
Saturday, August 2, 14
https://mathreasoninginventory.com/Home/AssessmentsOverview
Saturday, August 2, 14
DISCUSSION• How did the teacher find out what Marisa
was thinking?
• Had Marisa likely had experiencedeveloping mathematical habits of mind?
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Threads and themes...1. Paying attention (teachers and students)
2. Embracing mistakes and helping students grow smarter
3. Mathematical Habits of Mind--Reasoning, Sense-Making, and Thinking Like a Mathematician (You and Your Students)
Saturday, August 2, 14
Being a ‘Doer’ of Mathematics
From a presentation by Cathy Seeley, 2014
“The only way to know mathematics is to do mathematics.”
Paul Halmos, mathematicianI Want to Be a Mathematician
“It is pretty hard to understand mathematics without doing some mathematics.”
Jordan Ellenberg, mathematicianHow Not to be Wrong
Saturday, August 2, 14
Thinking Like a Mathematician• Doing real mathematics--figuring out hard problems
• Exploration that’s sometimes messy; trying things that sometimes work, sometimes don’t
• Reasoning, explaining and arguing
• Zooming in and zooming out
• Reflecting, considering, analyzing
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
What math do all students need?
From a presentation by Cathy Seeley, 2014
The Big Three:
• Understand mathematics (make sense of it)
• Do the arithmetic (skills, facts, procedures)
• Use mathematics (thinking, reasoning, applying, solving a range of problems)
The New Basics: deep transferable skills for Versatilizing (Deeper Learning):
• Problem solving, reasoning, research, communication, creativity, interpersonal skills
Saturday, August 2, 14
Mathematical Thinking
Overarching goal:
Students who can think mathematically . . .
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Mathematical Habits of Mind
Al Cuoco, E. Paul Goldenberg, June Mark. “Organizing a Curriculum around Mathematical Habits of Mind.” Mathematics Teacher May 2010
• Performing thought experiments
• Finding, articulating, and explaining patterns
• Generalizing from examples; articulating generality in precise language
• Creating and using representations
• Expecting mathematics to make sense
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
DISCUSSION
•What’s the most important mathematical habit of mind Marisa missed?
From a presentation by Cathy Seeley, 2014
Saturday, August 2, 14
Mathematical Habits of Mind--Common Themes
• Solving problems
• Thinking, Reasoning, and Reflecting
• Discussing and Communicating
• Justifying and Explaining
• Generalizing from Patterns
• Connecting
• Making sense
• Patience, persistence
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Threads and themes...1. Paying attention (teachers and students)
2. Embracing mistakes and helping students grow smarter
3. Mathematical Habits of Mind--Reasoning, Sense-Making, and Thinking Like a Mathematician (You and Your Students)
4. Tasks for learning mathematics vs. problems to find answers to
Saturday, August 2, 14
Answer-getting vs. learning mathematics
• Teachers in US:How can I teach my kids to get the answer to this problem?
• Teachers in Japan:How can I use this problem to teach the mathematics of this unit?
–Devised methods for slowing down, postponing answer-getting
• A Modeling Perspective: How can I construct and pose problems that help students learn to think mathematically about the world?
From a presentation by Cathy Seeley, 2014, Thanks to Phil Daro and John PeleskoSaturday, August 2, 14
The difference between Japan and the US
• “You quit teaching too soon and go on to the next thing.”
• “We finish.”• Finishing happens when students
have learned.• And learning is incomplete if students aren’t
developing mathematical thinking.
From a presentation by Cathy Seeley, 2014, Thanks to Phil DaroSaturday, August 2, 14
Threads and themes...1. Paying attention (teachers and students)
2. Embracing mistakes and helping students grow smarter
3. Mathematical Habits of Mind--Reasoning, Sense-Making, and Thinking Like a Mathematician (You and Your Students)
4. Tasks for learning mathematics vs. problems to find answers to
5. It’s all about relationships . . .
Saturday, August 2, 14
It’s all about . . .
• Relationships• Respect• Risk-Free Environment
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Saturday, August 2, 14
From a presentation by Cathy Seeley, 2014
Mathematical Habits of Instruction
Saturday, August 2, 14
• From: “I - We - You”• To: “You - We - I”
• Or: “You - Y’all - We - I”
Upside-down teaching
Thanks to Phil Daro, Deborah Ball, Magdalene Lampert, and Cathy Seeley
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Upside-down teaching
From a presentation by Cathy Seeley, 2014
• Start with a rich problem
• Engage students in dealing with the problem, constructively (productively) struggling with the problem and the mathematics
• Students discuss, compare, interact, question
• Teacher helps students make connections and notice the mathematics they’ve learned: teacher-structured, teacher-engineered, teacher-managed, not teacher-centered
• See a video of a 12th-grade upside-down quantitative reasoning course at utdanacenter.org/amdm
Saturday, August 2, 14
Mathematics Teaching Practices1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning/problem solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual understanding.
7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking.
Principles to Actions, NCTM, 201426
Saturday, August 2, 14
To do . . .
• What’s one thing you’d like to do this school year in support of your ‘Aha!’ or in support of your own Mathematical Habits of Instruction to help your students become stronger mathematical thinkers?
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Achievement Gap
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Untapped Potential
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
What if we raise the floor AND the ceiling?
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Two Sides of Untapped Potential
• Bringing up all students to achieve their highest levels of mathematics and science--raising the floor
• Identifying the stars
• Raising the ceiling and letting them soar
• Untapped potential within each student, within groups of students, and at the school, district, state and national level--potential we haven’t reached . . . YET.
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Untapped Potential
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Unlimited Potential
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
Even our best students...
...will benefit from a strong, diverse, engaging, relevant classroom.
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From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
...and ours is in theirs
Their future is in our hands
From a presentation by Cathy Seeley, 2014Saturday, August 2, 14
E-mail for a copy of the slides: cseeley@utexas.edu
Just published April 2014: Smarter Than We ThinkMessages from today...
Smarter Than We Think*, Upside-Down Teaching*,Clueless, Mathematical Habits of Mind*,
Mathematical Habits of Instruction(Download 5 messages, including those with *)
Faster Isn’t Smarter--Messages About Math, Teaching, and Learning in the 21st Century
Seeley 2009http://mathsolutions.com/fasterisntsmarter (Download 5 messages)
Constructive Struggling*, Crystal’s Calculator*, Balance is Basic*
Cathy’s websites: http://cathyseeley.com http://csinburkinafaso.com
Saturday, August 2, 14