Tag Archives: Graham Fletcher

#NCTMLive #T3Learns Webinar: Implement tasks that promote reasoning and problem solving, and Use and connect mathematical representations

On Wednesday, May 2, 2018, Jennifer Wilson (@jwilson828) and I co-facilitated the second webinar in a four-part series on the Eight Mathematics Teaching Practices from NCTM’s Principles to Actions: Ensuring Mathematical Success for All.

Implement tasks that promote reasoning and problem solving,
and Use and connect mathematical representations.

Effective teaching of mathematics facilitates discourse among learners to build shared understanding of mathematical ideas by analyzing and comparing approaches and arguments.

  • How might we implement and facilitate tasks that promote productive discussions to strengthen the teaching and learning of mathematics in all our teaching settings – teaching students and teaching teachers?
  • What types of tasks encourage mathematical flexibility to show what we know in more than one way?

Our slide deck:

Our agenda:

7:00 Jill/Jennifer’s Opening remarks

  • Share your name and grade level(s) or course(s).
  • Norm setting and Purpose
7:05 Number Talk: 81 x 25

  • Your natural way and Illustrate
  • Decompose into two or more addends (show it)
  • Show your work so a reader understands without asking questions
  • Share work via Twitter using #NCTMLive or bit.ly/nctmlive52
7:10 #LL2LU Use and connect mathematical representations

  • Self-assess where you are
  • Self-assessment effect size

Think back to a lesson you taught or observed in the past month. At what level did you or the teacher show evidence of using mathematical representations?

7:15 Task:  (x+1)^2 does/doesn’t equal x^2+1
7:25 Taking Action (DEI quote)
7:30 #LL2LU Implement Tasks That Promote Reasoning and Problem Solving
7:35 Graham Fletcher’s Open Middle Finding Equivalent Ratios
7:45 Illustrative Mathematics: Jim and Jesse’s Money
7:55 Close and preview next in the series

Some reflections from the chat window:

I learned to pay attention to multiple representations that my students will create when they are allowed the chance to think on their own.  I learned to ask myself how am I fostering this environment with my questioning.

I learned to pay attention to the diversity of representations that different students bring to the classroom and to wait to everyone have time to think

I learned to pay attention (more) to illustrating work instead of focusing so much on algebraic reasoning in my approach to teaching Algebra I. I learned to ask myself how could I model multiple representations to my students.

I learned to pay attention to multiple representations because students all think and see things differently.

I learned to make sure to give a pause for students to make the connections between different ways of representing a problem, rather than just accepting the first right answer and moving on.  

I learned to pay attention to the ways that I present information and concepts to children… I need to include more visual representations when I working with algebraic reasoning activities.

Cross posted on Easing the Hurry Syndrome

Embolden Your Inner Mathematician: week 5 agenda

Use and connect mathematical representations.

Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

15 min Homework discussion, Q&A
45 min Apples and Bananas Task
30 min Number Talk – Flexibility: Show what you
know more than one way.
10 min Break
20 min Connecting multiple representations
End of session

Homework:

  • Practice finding and connecting multiple representations in our Number Talks
  • Read: Use and Connect Mathematical Representations
    • What the Research Says: Representations and Student Learning (pp. 138-140)
    • Promoting Equity by Using and Connecting Mathematical Representations (pp. 140-141)
    • Check out Kristin Gray’s (@MathMinds) response to Vicki’s tweet (shown below) and try to answer the question for yourself for a Number Talk you’ve done or will do this week.

Standards for Mathematical Practice

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.


Previous Embolden Your Inner Mathematician agendas:

Embolden Your Inner Mathematician: week 4 agenda

Facilitate meaningful mathematical discourse.

Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

15 min Homework discussion using Connect-Extend-Challenge
Visible Thinking Routine
35 min Which pizza is the better deal?
– Robert Kaplinsky (@robertkaplinsky)
10 min Break
30 min the Whopper Jar 3-Act Task
– Graham Fletcher (@gfletchy)
20 min Number Talks
10 min Closure
End of session

Homework:

  • Facilitate meaningful mathematical discourse using Number Talks.
    • Select a number talk.
    • Anticipate student answers with your team.
    • Notice and note which students used each strategy.
    • What will/did you learn?
  • Read pp. 146-151 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • Examining Mathematical Discourse
  • Deeply Read pp. 175-179 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • What the Research says: Meaningful Mathematical Discourse
    • Promoting Equity through Facilitating Meaningful Mathematical Discourse

Standards for Mathematical Practice 

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.


Previous Embolden Your Inner Mathematician agendas:

Embolden Your Inner Mathematician: week 3 agenda

Facilitate meaningful mathematical discourse.

Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Principles to Actions: Ensuring Mathematical Success for All

Slide deck

7:15 Homework Splats! discussion, Q&A, Problem of the Week
7:35 Open Middle: Closest to One (recap)

7:55 3-Act Task:  The Cookie Thief

8:25 3-Act Task: How big is the World’s Largest Deliverable Pizza?

8:55 Book discussion from homework

9:10 Closure
9:15 End of session

Homework:

  • Read pp. 146-151 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • Examining Mathematical Discourse
  • Deeply Read pp. 175-179 from TAKING ACTION: Implementing Effective Mathematics Teaching Practices in K-Grade 5
    • What the Research says: Meaningful Mathematical Discourse
    • Promoting Equity through Facilitating Meaningful Mathematical Discourse

Standards for Mathematical Practice 

  • I can make sense of tasks and persevere in solving them.

  • I can construct a viable argument and critique the reasoning of others.

“Connect Extend Challenge A Routine for Connecting New Ideas to Prior Knowledge.” Visible Thinking, Harvard Project Zero.

Leinwand, Steve. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA.: National Council of Teachers of Mathematics, 2014. (p. 46) Print.

Gough, Jill, and Jennifer Wilson. “#LL2LU Learning Progressions: SMP.” Experiments in Learning by Doing or Easing the Hurry Syndrome. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Gough, Jill, and Kato Nims. “#LL2LU Learning Progressions.” Experiments in Learning by Doing or Colorful Learning. WordPress, 04 Aug. 2014. Web. 11 Mar. 2017.

Smith, Margaret Schwan., et al. Taking Action: Implementing Effective Mathematics Teaching Practices in Grades K-5. The National Council of Teachers of Mathematics, 2017.


Previous Embolden Your Inner Mathematician agendas:

Sketch notes from #TMC17 (a.k.a. Twitter Math Camp)

Becky Holden (@bholden86) and I attended Twitter Math Camp (#TMC17) at Holy Innocents Episcopal School in Atlanta, GA from Thursday, July 27 to Sunday, July 30.

This conference is by teachers, for teachers. The structure of TMC contains the following lengths of presentations:

  • Morning sessions (One session that meets Thursday, Friday and Saturday mornings for 2 hours each morning)
  • Afternoon sessions (Individual 1/2 hour sessions on Thursday)
  • Afternoon sessions (Individual 1 hour sessions Thursday, Friday and Saturday)

To honor Carl Oliver‘s (@carloliwitter) #PushSend request/challenge, here are my sketch notes from the sessions I attended.

Differentiating CCSS Algebra 1
— from drab to fab using Exeter Math 1 & Exploratory Talk
Elizabeth Statmore (@cheesemonkeysf)

The Politics(?) of Mathematics Teaching
Grace Chen (@graceachen)

What does it mean to say that mathematics teaching is political, and what does that mean for our moral and ethical responsibility as mathematics teachers?

Bridging elementary skills & concepts to high school & beyond
Glenn Waddell, Jr. (@gwaddellnvhs)

Micro-decisions in Questioning
David Petersen (@calcdave)

All I Really Need To Know I Learned From The MTBoS
…Not Really, But Close
Graham Fletcher (@gfletchy)

Hitting The Darn ‘Send’ Button
Carl Oliver (@carloliwitter)

Practical Ideas on the Kind of Coaching
We Need to Provide and Demand
Steve Leinwand (@steve_leinwand)

What is not captured in my notes is play: game night, trivia, crocheting, and tons of fun.

How might we grow, learn, and play in community when together and when apart?

Summer PD: Day 3 Empower Learners

Summer Literacy and Math Professional Learning
June 5-9, 2017
Day 3 – Empower Learners
Jill Gough and Becky Holden

I can empower learners to reach for the next independent level in their learning.

Learning target and pathway:

It is not easy, but we need to shift from being the givers of knowledge to becoming the facilitators of knowledge development.  (Flynn, 8 pag.)

UED: 8:45 – 11:15  / EED: 12:15 – 2:45

image5

Slide deck

Resources:

Harnessing the Power of the Purposeful Task with @GFletchy #MtHolyokeMath

I’m taking X.MTHED-404: Effective Practices for Advancing the Teaching and Learning of Mathematics (K-12).

Here are my notes from Session 6, Harnessing the Power of the Purposeful Task, with Graham Fletcher.


Notes from previous sessions: