Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden
Today’s focus and essential learning:
We want all mathematicians to be able to say:
I can make sense of tasks
and persevere in solving them.
(but… what if I can’t?)
Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level. Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)
… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems. (Flynn, 19 pag.)
Agenda and Tasks:
- Flynn, Michael. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, Maine.: Stenhouse, 2017. Print.
- Flynn, Michael. “If My Math Is Correct….” Math Leadership Programs. Mount Holyoke College, n.d. Web. 26 May 2017.
- 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.
- Imm, Kara Louise., Catherine Twomey. Fosnot, and Willem Uittenbogaard. Minilessons for Operations with Fractions, Decimals, and Percents: A Yearlong Resource. Portsmouth, NH: Firsthand/Heinemann, 2007. Print.
- Kaplinsky, Robert. “Do You Have Enough Money?” Robert Kaplinsky. N.p., n.d. Web. 26 May 2017.
- Lichtman, Grant, and Sunzi. The Falconer: What We Wish We Had Learned in School. New York: IUniverse, 2008. Print.
- Reynolds, Peter H. The Dot. Denton, TX: BrailleInk, 2005. Print.
I’m attending the National Council of Supervisors of Mathematics 2017 conference in San Antonio. Here are my notes from Wednesday along with the session descriptions from the presenters.
Conferring with Young Mathematicians at Work:
The Process of Teacher Change
If children are to engage in problem solving with tenacity and confidence, good questioning on the part of teachers during conferrals is critical. Questioning must engender learner excitement and ownership of ideas, while simultaneously be challenging enough to support further development. Video of conferrals in action will be used for analysis, and a Landscape of Learning on the process of teacher change is shared as a lens for coaching.
Leading to Support Procedural Fluency for All Students
Principles to Actions describes effective teaching practices that best support student learning. In this session we will focus on one of those teaching practices: “build procedural fluency from conceptual understanding.” Ensuring that every child develops procedural fluency requires understanding what fluency means, knowing research related to developing procedural fluency and conceptual understanding, and being able to translate these ideas into effective classroom practices. That is the focus of this session! We will take a look at research, connections to K–12 classroom practice, and implications for us as coaches and teacher leaders.
How to Think Brilliantly and Creatively in Mathematics: Some Guiding Thoughts for Teachers, Coaches, Students—Everyone!
This lecture is a guide for thinking brilliantly and creatively in mathematics designed for K–12 educators and supervisors, students, and all those seeking joyful mathematics doing. How do we model and practice uncluttered thinking and joyous doing in the classroom, pursue deep understanding over rote practice and memorization, and promote the art of successful ailing? Our complex society demands of its next generation not only mastery of quantitative skills, but also the confidence to ask new questions, explore, wonder, fail, persevere, succeed in solving problems and to innovate. Let’s not only send humans to Mars, let’s also foster in our next generation the might to get those humans back if something goes wrong! In this talk, I will explore five natural principles of mathematical thinking. We will all have fun seeing how school mathematics content is a vehicle for masterful ingenuity and joy.
Building Conceptual Understanding in the Middle Grades
Jill Gough, Jennifer Wilson
How might we attend to comprehension, accuracy, flexibility, and then efficiency? What if we leverage technology to enhance our learners’ visual literacy and make connections between words, pictures, and numbers? We will look at new ways of using technology to help learners visualize, think about, connect and discuss mathematics. Let’s explore how we might help young learners productively struggle instead of thrashing around blindly.
When Steve Leinwand asked if I was going to sketch our talk, I jokingly said that I needed someone to do it for me. We are honored to have this gift from Sharon Benson. You can see additional details on my previous post.
Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
How can leaders effectively lead mathematics education in the era of the digital age?
There are many ways to contribute in our community and the global community, but we have to be willing to offer our voices. How might we take advantage of instructional tools to purposefully ensure that all students and teachers have voice: voice to share what we know and what we don’t know yet; voice to wonder what if and why; voice to lead and to question.
Leading Mathematics Education in the Digital Age
2017 NCSM Annual Conference
Sunday, April 2, 2017 from 1:00-5:00 p.m.
How can leaders effectively lead mathematics education in the era of the digital age? There are many ways to contribute in our community and the global community, but we have to be willing to offer our voices. How might we take advantage of instructional tools to purposefully ensure that all students and teachers have voice: voice to share what we know and what we don’t know yet; voice to wonder what if and why; voice to lead and to question?
Sneak peek for our session includes:
How might we strengthen our flexibility to make sense and persevere? What if we deepen understanding to show what we know more than one way?
Interested? Here’s a sneak peek at a subset of our slides as they exist today. Disclaimer: Since this is a draft, the slides may change before we see you in San Antonio.
I wonder what Jennifer’s sneak peek looks like? Do you?
All students benefit from using tools and learning how to use them for a variety of purposes. If we don’t make tools readily available and value their use, our students miss out on major learning opportunities. (Flynn, 106 pag.)
I’m taking the #MtHolyokeMath #MTBoS course, Effective Practices for Advancing the Teaching and Learning of Mathematics. Zachary Champagne facilitated the second session and used The Cycling Shop task from Mike Flynn‘s TMC article.
You can see the notes I started on paper.
Jim, Casey and I used a pre-made Google slide deck provided to us to collaborate since we were located in GA, MA, and CA. We challenged ourselves to consider n wheels after working with 8 wheels.
Here’s what our first table looked like.
Now, I was having trouble keeping up with the number of wheels and the number of cycles. So I did this:
This made it both better and worse for me (and for my group).
Here’s an interesting thing. I’ve been studying, practicing, and teaching the Standards for Mathematical Practices. Jennifer Wilson and I have written a learning progression to help learners learn to say I can use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. (Sage, 6 pag.)
Clearly, I was not even at Level 1 during class. Not once – not once – during class did it occur to me how much a spreadsheet would help me, strategically.
The spreadsheet would calculate the number of wheels automatically for each row so that I could confirm correct combinations. (You can view this spreadsheet and make a copy to play with if you are interested.)
When making mathematical models, [mathematically proficient students] know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. (Sage, 6 pag.)
With a quick copy and paste, I could tackle any number of wheels using my spreadsheet. I can look for and make use of structure emerged quickly when using the spreadsheet strategically. (I want to also highlight color as a strategic tool.) Play with it; you’ll see.
[Mathematically proficient students] are able to use technological tools to explore and deepen their understanding of concepts. (Sage, 6 pag.)
There is no possible way I would have the stamina to seek all the combinations for 25 or 35 wheels by hand, right?
Students have access to a wide assortment of tools that they must learn to use for their mathematical work. The sheer volume of possibilities can seem overwhelming, but with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal. (Flynn, 106 pag.)
Important to repeat, “with time and experience, students can learn how to choose the right tool for the task at hand and how to use it strategically to reach their goal.”
For this to happen, we need to have a solid understanding of the kinds of tools available, the purpose of each tool, and how students can learn to use them flexibly and strategically in any given situation. This also means that we have to make these tools readily available to students, encourage their use, and provide them with options so they can decide which tool to use and how to use it. If we make all the decisions for them, we remove that critical component of MP5 where students make decisions based on their knowledge and understanding of the tools and the task at hand. (Flynn, 106 pag.)
To be clear, a spreadsheet was available to me during class, but I didn’t see it. How might we make tools readily available and visible for learners to choose?
When we commit to empower students to deepen their understanding, we make tools available and encourage exploration and use, so that each learner makes decisions for themselves. In other words, how do we help learners to level up in both content and practice?
What if we make I can look for and make use of structure; I can use appropriate tools strategically; and I can make sense of tasks and persevere in solving them essential to learn for every learner?
How might we offer tools and time?
It’s about learning by doing, right?
Flynn, Michael. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, Maine.: Stenhouse, 2017. Print.
Flynn, Mike. “The Cycling Shop.” Nctm.org. Teaching Children Mathematics, Aug. 2016. Web. 03 Feb. 2017.
“Common Core State Standards.” The SAGE Encyclopedia of Contemporary Early Childhood Education (n.d.): n. pag. Web.