Washington Mathematics

Washington State Mathematics Council

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Winter 2020

For the Love of Math....

This month’s math problem is from YouCubed and Nrich Mathematics . Once you’ve spent some time making sense of the picture and seeing what you notice and wonder, you may want to check out the task on YouCubed and at Nrich Math: Picture Story. The Math Fellows had a rich discussion about how the task became more open and interesting with fewer directions and scaffolding.

The Task:

Make mathematical sense of this picture:

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President's Message

Dear WSMC Member,

Your board has been working hard answering some tough questions about who we are and what we do as an organization. This has lead to rewriting our mission statement and coming up with a vision statement. Here are our new statements.

Mission: The Washington State Mathematics Council believes that all people can learn and use mathematics. Members are committed to developing, supporting, and encouraging opportunities that lead to effective instruction and successful mathematics learning that empowers all. WSMC serves as a communication and learning network open to anyone interested in mathematics education.

Vision: Empowering mathematical success for each and every learner.

A big thank you goes out to those in Both the WSMC and PSCTM that volunteered to make the 2019 northwest mathematics conference, We All Count, a success. This event helped us work towards our new mission and vision. Also we have the High School Math Contest and Math Olympiad coming up this spring. For more information check out our website at WSMC.net.

Do you believe empowering mathematical success for each and every learner? We are looking for more volunteers to join our board of directors. We have some open positions and some introductory support positions. Specifically in the following ESDs: 171 North Central ESD, 114 Olympic ESD, and ESD 112. Please contact Dan Herforth at WSMCpresident@gmail.com.


Dan Herforth, WSMC President

Math Between Us by Jana Dean

Welcome to Math Between Us. This column will be a regular feature of the WSMC newsletter. The column will feature stories and profiles of people doing mathematics together. It will explore the role of tasks, language and culture in creating space for people to participate in mathematical communities. Each column will end with questions to think about. The editors of WSMC invite you to participate by responding to those questions below.

Math for the Joy of It

At almost eighty, mathematician Martin Kindt doesn’t have to work anymore. All the same, he still comes to the office, as he says “for the feel of the weekend.” In truth, Martin continues to come to work because, for him, doing math with others is pure joy.

Martin’s current projects bring the history of mathematics to Dutch teachers via articles he writes for a math education journal. In my six months at the Freudenthal Institute, each time I walked past his desk, I saw another fascinating geometric representation. Rather than continuing to interrupt his work with my curiosity, I asked if I could interview him. He agreed.

Martin and I talk, but mostly we do math together. He shares a resource with me called Positive Algebra. He explains the title refers to natural numbers, that is, the counting numbers. “These numbers -- one, two, three and so on -- are the most real to students,” he tells me, “and so a wonderful way to support learning algebra.”

As we thumb through the booklet we play a game called “The Price of Algebra” which challenges us to write efficient expressions by assigning higher point values to more powerful operations. Next, we look at patterns in prime numbers. And then we begin to examine the Number Spiral. By the end of our hour, I no longer believe Martin keeps a workweek to better enjoy the weekend. I see that he comes to work for the joy of mathematics.

Joy is an important enough emotion that the Dalai Lama and Desmond Tutu devoted an entire book to it. The feeling encompasses amusement, excitement, contentment, wonder, relief, gratitude and pride. Both spiritual leaders, who have faced struggle and hardship including war and exile see joy as something that comes from within, when we genuinely engage with open hearted wonder with the world around us. In the Book of Joy, they write “Being joyful is not just about having more fun. We’re talking about a more empathetic, more empowered, even more spiritual state of mind that is totally engaged with the world.”

Early on in the ‘interview’ Martin tells me that math tasks should be productive. When I ask him what he means by that, he tells me, “Well, not reproductive,” then adds that Hans Freudenthal used the term to say “Math should be the creation of the person doing it, not an imitation of what someone else has done. That way it is of interest to the learner.”

Of course, only if the math is of interest can the learner bring themselves with open-hearted wonder to it. And only then can it possibly be a source of joy. The math Martin and I did together had nothing in common with the worksheets or textbooks many of us associate with learning algebra. Endlessly repeating procedures to practice something that captures little interest or imagination, while an accomplishment, rarely brings real joy.

We only had a few minutes left of our hour when we got to the Number Spiral. I had seen it on a poster in the office and had begun to examine it, but I hadn’t wanted to look too closely because that version already had expressions written on it. I didn’t want to short-circuit any of my own joy of discovery by seeing the patterns through others’ eyes before I had a chance to puzzle with it myself.

Figure 1, The number spiral is a creative solution to a teacher’s problem

Credit: Kindt, Positive Algebra

Figure 1, The number spiral is a creative solution to a teacher’s problem

Credit: Kindt, Positive Algebra

I asked Martin where the spiral came from. He told me that he used to be a teacher and back then the books were not any good so he had to make up his own. One day he needed a number line and the paper he had was only long enough for 15 numbers, so he made the line spiral out from the center of the page. That way he could get the numbers from one to one hundred on a single page. Then when he looked at it, he saw that every line drawn on the spiral corresponded to a function. In parting, Martin said to me, “Every teacher should have a chance to be inspired and to play with mathematics every year.” Indeed, that may be the best way to remember how to bring joy to the problem solving we do with our students all year.

Figure 2, Can you find this pattern in the number spiral?

Credit: Math Education Collaborative

Inspired by my hour with Martin, I thought, why not bring teachers together just for the purpose of finding joy in working side-by-side through a problem together and sharing with one another how we saw it and solved it. I hosted the first “Midday Math Happy Hour” at my house this July. PHOTO HERE

Four of us spent an afternoon completely engrossed in productive algebra. We used tiles to model Becca’s pattern and explained to each other how we each had seen the pattern. We modeled the pattern with algebraic expressions and then finished our time together finding sequences related to the pattern in Martin’s Number Spiral. We ended the afternoon inspired and ready for more.

Do you go to work for the feel of the weekend, or for the joy of the work?

What math brings you joy?

Jana Dean (jdean@reachone.com) teaches middle school in the Olympia. A recipient of the prestigious Fulbright Distinguished Award in Teaching as well as the Presidential Award for Excellence in Math Teaching, she brings a deep curiosity about the intersection of math and language to her writing and to her eighth grade classroom. She has collaborated with the Math Education Collaborative on classroom case studies and with Illustrative Mathematics on task development and has written for Rethinking Schools Magazine. You can read more about her Fulbright adventure to the Netherlands at mathbetweenus.org.

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Equity Notes

Welcome to Equity Notes – a new section of our newsletter in which we explore what equity in

mathematics education means and how to work towards it. This issue explores what we mean

by Equity in Mathematics Education and suggests a few resources. You may have never

considered the role of equity in math learning and teaching or may have colleagues who believe

that “math is math” and equity “issues” are separate or the responsibility of school

administrators, counselors, and/or the equity committee. In this issue, we want to think

through what we mean by equity and explore practices that support or leverage equitable

outcomes for students.

First, what does equity mean? We often hear the words access, equality, and equity used

together or interchangeably. This quote from Caroline Belden from The Inclusion Solution helps

make the distinction:

If “access” is the doorway, we have to ensure there’s a means of getting people through the

door (or even to the door)....Equality is leaving the door open for anyone who has the means to

approach it; equity is ensuring there is a pathway to that door for those who need it.

In mathematics learning and teaching, equity means ensuring that each student has what they

need to have access to the open door of learning. As I reflect on this, I think this means first of

all, that the doors to rigorous, well-taught, heterogeneously populated math classrooms need

to be open to all students. Secondly, students are provided with the supports they need to

succeed in those classrooms. These include student centered teaching practices that support

the eight NCTM Mathematics Teaching Practices as well as culturally responsive teaching

practices in which teachers establish authentic connections with their students that build

mutual trust and respect. For some students ensuring equity may also mean providing

additional scaffolds to support their specific learning needs.

A good resource to start learning more about equity in mathematics is Principles to Action from

NCTM, which describes a commitment to access and equity as an essential element of an

excellent mathematics program. NCTM has many resources to support equity in mathematics

teaching. The series Taking Action: Implementing Effective Mathematics Teaching Practices has

a book for each of three grade bands, K – 5, 6 – 8, and 9 – 12, and throughout each book, they

relate the eight effective teaching practices to specific equity -based practices which have been

shown to strengthen mathematical learning and cultivate positive student mathematical

identities. An additional NCTM resource is Enhancing Classroom Practice with Research behind

Principles to Action, including a chapter devoted to providing access to equitable mathematics

learning that shares a brief review of research on equity-based practices and vignettes from

classrooms and schools.

As we work towards providing access to equitable math learning, ensuring that all students

have a pathway to an open door, we have to remember that the responsibility lies with us, the

adults. “The question is not whether all students can succeed in mathematics but whether the

adults organizing mathematics learning opportunities can alter traditional beliefs and practices

to promote success for all ‘(NCTM, 2014, p. 61).

Northwest Mathematics Conference 2020

A huge thank you to everyone who worked so tirelessly to make the recent 58th NWMC such a big success! From the fifteen incredible 3-hour mini-courses on Thursday morning and afternoon, to the poignant and passionate "Designing for Belonging" Opening Keynote by Dan Meyer, Thursday was an incredible experience. Thank you to: Julia Aguirre, Kim Sutton, Leslie Nielsen, Kendra Lomax, Chris Luzniak, Tom Reardon, Patty Stephens, Jim King, Dan Finkel, Dan Meyer, Megan Franke, Elham Kazemi, Nathan Dunham, Michele Hackstadt, Gini Stimpson, Molly Huggins, Darrel Trussel, Sasha Hammond, and Ann Sipe for the amazing mini-courses. Many of the mini-courses also allowed paricipants to earn STEM clock hours as did sessions and workshops on Friday and Saturday.

A true highlight of the conference for me were the 170+ amazing speakers who helped to create a diverse and robust program highlighting the theme of "We All Count". The theme was clearly evident in Dan Meyer's opening keynote, in sessions and workshops by our many talented speakers, and in Julia Aguirre's moving Closing Keynote, "Build Bridges not Walls: Elevating our Vision for Math Strong Children and Youth". There were so many wondrous moments at the conference, from the way teachers interacted with their math heroes (swooning over Ruth Parker in the crosswalk back to the Convention Center or posing for photos with her at the Speaker Pop Up Breakfast), to the amazing way our Social Media experts Angela Ensminger and Traci Cotton kept us connected via Twitter, Facebook, Instagram, and Whoova (Conference App). I think we have set a new bar with the 58 Day Twitter/Facebook/Instagram Speaker Countdown and the live streaming of the Friday night IGNITE talks. I don't think I will every forget the magic of the eight amazing IGNITE talks by Annie Fetter, Ksenija Simic-Muller, Jeff Crawford, Mei Pontano, Chris Luzniak, Saraswati Noel, Peg Cagle, and Chris Shore. Their talks were poignant, moving, inspirational, thought-provoking, and short! They packed so much in those 5-minute talks while their 20 slides advanced automatically!

Here are a few comments from conference attendees: "Our math teachers loved the conference. They said it was life changing." "Ugh, my mind is STILL blown! This is my 20th year of teaching and I'm reminded why attending those is so important! I'll be at Portland next year for sure!" "I've spoken at hundreds of conferences over the years. You are truly the most organized and attentive organizer I've ever connected with!"

A conference like this takes many hours of preparation and many different kinds of expertise. I want to publicly thank our chair, Sharon Young, for her vision for this conference and for keeping all of the moving parts working together.

It was a true honor to be a part of this conference.

Joyce Frost, 58th NWMC program co-chair

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Rita Lowe Scholarship

Do you know an exceptional high school senior or college student interested in becoming a math educator? Are you yourself a math educator seeking to further your education? WSMC awards up to four $1000 scholarships in each of three categories annually: high school seniors interested in math education, college students seeking to become math educators, and current math educators pursuing professional development in math education. Information is available on the WSMC website and applications are due March 15, 2020. Please spread the word!

WSMC Member Supports….

WSMC Educator Support Fund

The Washington State Mathematics Council provides funds to support mathematics-related initiatives, identified by members via an application. Individual awards range from $50 to $500.


Washington State Mathematics Council supports outstanding math educators by offering three awards. Two WSMC members, each an outstanding mathematics educator, are honored annually. The Hall of Fame Award is given to honor an outstanding contributor to the field of mathematics education, one who has given time and effort over a long period of time (ten years or more).

Rita Lowe Scholarships

WSMC gives annual scholarships in the amount of $1000, awarded to:

  • high school students planning to become math teachers
  • college students planning to become math teachers, and
  • math teachers pursuing further professional growth.

Future Events…

March 7 Board Meeting—Cle Elum, 10:00 – 3:30

March 11 HS Math Contest—Regional

April 1-4 NCTM Annual Conference

April 18 HS Math Contest—State

April 15 Mail Out Ballots

April 25 Math Olympiad—State

May 16 Board Meeting—Cle Elum, 10:00 – 3:00

Clock Hours

Including Jo Boaler Course!