This Week in Math Ed: September 23, 2016

I just wrapped up some very long, busy days for the CCTM annual conference. I feel like I missed what was going on in the wider world of math ed. Let's look, shall we?

Math Ed Said

September 16: With a new look to his blog, Dan Meyer gives us "The Desmos Guide to Building Great (Digital) Math Activities."

Shared by: Jennifer Blinzler, Kit G, Danielle Reycer, Alex Jaffurs, Patty Stephens, Jessica Faurote, Megan Balong, Cathy Yenca, Megan Heine

September 17: The California Math Council is dedicating the year to issues related to equity and social justice in mathematics, and has gathered resources here.

Shared by: Cathy Carroll, CMC - CA MathCouncil, Rosa Serratore, Christina Moore, Jeremiah Ruesch

September 18: There was a #MTMSchat around Victor Mateas's article, "Debunking Myths about the Standards for Mathematical Practice" in Mathematics Teaching in the Middle School.

Shared by: Matt Larson, NCTM, Jamie Duncan, Jeremiah Ruesch, Siri Anderson, Lorraine Males

September 19: NPR reported on some reasearch that found "When Blind People Do Algebra, The Brain's Visual Areas Light Up."

Shared by: Francis Su, Steve Phelps, David Hallowell, Egan J Chernoff, Joshua Bowman

September 20: introduced its Classroom Conversation Toolset, a set of controls that gives the teacher the ability to control the pace of students moving through Desmos activities and pause to allow for coming together and conversation. A lot of people liked this.

Shared by:, Dan Meyer, Derek Oldfield, Jennifer Lawler, Jennifer Wilson, John Golden, Eli Luberoff, Shelby Aaberg, Matt Owen, Megan Heine, Dan Anderson, Bob Lochel, Jon Orr, Christopher Danielson, Patrick Honner, Michael Fenton, Bridget Dunbar, Audrey McLaren, Robert Cop, Cathy Yenca, Jennifer Blinzler, Karl Fisch, Alex Overwijk, Jon Orr, Chris Hunter, Avery Pickford

September 21: With his fingerprints on another popular post this week, Dan Meyer addresses "Teaching for Tricks or Sensemaking" in the context of justifying why 4^0=1.

Shared by: Dan Meyer, Nancy Terry, Greg George, Heather Sugrue, Cathy Yenca, Ed Campos Jr, Bethany Mager, Jennifer Blinzler, Brett Parker, Shauhna Feitlin

September 22: Andrew Stadel gave us "Zombie Apocalypse," an activity on Desmos.

Shared by: Nathan Kraft,, Kathy Henderson, Andrew Stadel, Siri Anderson, Shauna Hedgepeth, Jim Pardun

Around the Math Ed Web

Next week NCTM kicks off it's first #MTchat, which rounds out the lineup of article-based chats along with #TCMchat and #MTMSchat. These chats may not have the impact and scope of a conference, but this gives members have a way of interacting with each other and their professional organization on a much more regular basis.

If it's Tuesday night, it's Global Math night. Last week was "Getting Students Talking... Open Questions in the Math Classroom" with Mishaal Surti and next week is "3 Reasons Kids Don’t Know Facts and How to Help."

On the conference front, both the Phoenix and Philadelphia NCTM Regional Conferences are approaching, as is the new Innov8 Conference. NCTM is also asking for proposals for next year's regionals, due December 1st.

Research Notes

A new ZDM is out for October 2016, this time with the theme "Mathematical working spaces in schooling."

Math Ed in the News

Math Ed in Colorado

José Franco of WestEd co-led a teacher presession at
the 2016 CCTM Annual Conference
Today was the big day at the CCTM Annual Conference, and I literally drove home, grabbed something to eat, and started writing this week's post. So pardon me if my head is still buzzing from the events of the day! I'll have more from CCTM when I get it organized, but for now here are some reminders of things going on in Colorado.

Math on the "Planes"

As far as I know, there are still spots available, so register now!

Boaler Book Study

Cassie Harrelson of Aurora Public Schools will be facilitating an online book study on COPilot with Jo Boaler's book Mathematical Mindsets. Participants will need to purchase the book and register online ($45 for CEA members, $145 for non-members). The book study begins October 2nd and will last for 5 weeks. Let Cassie know if you have any questions!

MSP Grants

If interested in applying for a Mathematics and Science Partnership grant, please submit a letter of intent via SurveyMonkey by Oct. 5. Applications will be due Monday, Nov. 14. For additional information and to access the application, please visit the MSP webpage.

Professional Learning Opportunities

Do you have English learners in your class? Do you want to know more about how to help them access mathematical content? Rebekah Ottenbreit of CDE is offering "Teaching Math to English Learners" on October 18 in Grand Junction. The all-day workshop will offer tools and strategies for making math more accessible to English learners through teaching the Colorado English Proficiency (CELP) standards. You can register for the workshop on the CDE website.

Colorado School of Mines will offer weekly Saturday training sessions focused on Computer Science Principles. They are following the curriculum and started with Unit 2 on Saturday, September 10, but I think it's fine if you jump in late. You are welcome to attend any of the units/lessons that you think might be valuable, whether you are using or not. Details can be found at the C-START website under the CS Principles link.

Lesson Story: Track Stars

I haven't had my own classroom in a while, so when I got the chance last summer to model a lesson for some math teachers at a summer workshop, I was eager to try a task Bill Penuel turned me on to in a paper by Schwartz and Martin (2004):

Track Stars

Bill and Joe are both on the U.S. Track Team. They also both broke world records last year. Bill broke the world record for the high jump with a jump of 8 ft. Joe broke the world record for the long jump with a jump of 26 ft, 6 in. Now Bill and Joe are having an argument. Each of them think that his record is the best one. You need to help them decide. Based on the data in the table, decide if 8 ft shattered the high jump record more than 26 ft 6 in. shattered the long jump record.

Top High Jumps in 2000    Top Long Jumps in 2000
Height Number of Jumps Length Number of Jumps
6'6" 1 21'6" 1
6'8" 2 22'0" 2
6'10" 3 22'6" 2
7'0" 5 23'0" 9
7'2" 6 23'5" 9
7'4" 7 24'6" 4
7'6" 4 25'0" 1
7'8" 1 25'6" 1
8'0" 26'6"

When I used this task with teachers a few years ago in our task analysis research it was rated quite highly: 5 out of 6 teachers said it rated as "Doing Mathematics" in Smith and Stein's (1998) cognitive demand framework and the task was unanimously judged as a good example of a task likely to engage students in Standard for Mathematical Practice #3, construct viable arguments and critique the reasoning of others.


For the summer workshop I was working with about 20 math teachers who would be grouped by grade band (elementary, middle high) and I asked them to attempt the task using the abilities expected of students at their grade level. I admit, this makes for a somewhat artificial exercise, but I wanted to see if this task would stretch across a lot of different levels of student ability and elicit a very wide range of student strategies (even if the "students" were teachers).

One of my greatest teaching weaknesses has always been in my questioning strategies. Too often I accept quick choral responses to questions in the initiate-respond-evaluate pattern, and I don't do much to (a) push student thinking and (b) promote equitable participation, so for this lesson I used a combination of these resources:
There is a lot of overlap in the 5 Practices, Launch/Explore/Summarize, and the goal of facilitating meaningful discourse. That's a good thing.

The Lesson

I anticipated (the first of 5 Practices) different strategies across the three groups:
  • I expected the elementary school group to focus on measuring distances and visual comparisons, and to bring up struggles around working with feet and inches and the under-developed sense of ratio.
  • I expected the middle school group to calculate means and use proportional reasoning (like, "The record is 110% of the average), and perhaps use mean absolute deviation (MAD) as a measure of variability. I expected to see struggles in accounting for the multiple jumps at each distance, in calculating MAD, and debates around using mean vs. median as a measure of center.
  • I expected the high school group to be similar to the middle school group, but to use standard deviation instead of MAD.
For the launch phase I avoided giving away any hints or clues about possible strategies. It was difficult to design a launch that connected to prior knowledge because of the artificial nature of teachers playing the role of students, so I took a moment to ask the teachers to think about the knowledge they'd expect students to have given the standards at their grade levels.

During the explore phase of the lesson I monitored (the second of 5 Practices) the groups for the strategies I anticipated. I wanted to use pressing questions here to push people's thinking, such as:
  • "Can you tell me why you think that is correct?"
  • "What do you mean by 'farther'? Is it because you added? What else might you do to measure 'farther'?"
Questions like this designed to press for student thinking were often met with teacher speculation about student thinking. As solution strategies came together, I noted them on my phone with the goal of selecting (the third of 5 Practices) two strategies per group to discuss during the whole-group summary phase of the lesson. The sequencing plan (the fourth of 5 Practices) was to discuss elementary first, then middle, then high school, with the less sophisticated strategy presented first at each level.

Here are the two posters from the elementary group:

The elementary group could quickly work through multiple strategies, so from this group I got more than just the two strategies I planned for. One set of strategies focused on how much more the record was than the next longest/highest jump, and the other set used a graphical representation of the jumps. Here are the posters from the middle school group:

One set of strategies compared the record jumps to the mean jumps, and the other set used a graphical display and interquartile range. Here are the two posters from the high school group:

There was less to differentiate these two strategies, as both groups calculated standard deviations and z-scores as a way of measuring how far above the mean was each record jump.

In the summarize phase of the lesson I focused my questioning around linking moves, such as:
  • "How does your strategy compare to the first one from the elementary group?"
  • (Following an explanation by Kathryn) "Tammy, do you have any questions for Kathryn?"
  • "Phillip, how might your argument change if you used Dan's method?"
With questions like these, I hoped to draw connections (the fifth of 5 Practices) between ideas, such as:
  • Connecting the visual centers of graphical displays with the calculated centers of the data
  • Connecting MAD and SD
  • Connecting the "measuring stick" idea between proportional reasoning at lower levels and the counting of MAD/SD units


I had some hits and misses in my anticipation of the strategies I saw. The elementary teachers didn't share my expectation of focusing on measurement and comparing those measurements. Instead, they made some useful comparisons between the record and second-best jumps. I also didn't anticipate the dot plots and fitted curves in the second poster. I know it's uneasy to underestimate the capabilities of elementary students, but these kinds of graphs were not something I anticipated their teachers producing. The middle school group used proportional reasoning, as I expected, but instead of MAD they used IQR as a reference for judging the two jump records. There was one "student" who quickly worked through some MAD calculations towards the end of the work time, but it was a bit late to fit into my selection strategy. For high school, the work was less differentiated and more advanced than I anticipated. Some of this can be attributed to just labeling the group "high school" rather than "9th grade" or "AP Stats."

I was able to practice my talk moves to some degree, but this artificial scenario was less than ideal. In the explore phase of the lesson my questions were generally met with speculation about student strategies, not answers as students might give them. That was great for us all to think through the task together, but it interrupted the flow of responses you'd expect with talk moves in a more typical classroom scenario.

The discussion in the summarize phase was pretty good. Not only did we compare strategies and connect ideas in the way I anticipated, there was a welcome amount of analysis of the task itself and the different layers of ambiguity in how the data was presented. For example, we don't know if the jumps all represent different jumpers, or if the jumps represent jumps in one vs. multiple competitions. We generally agreed that some amount of ambiguity would be good when using this task in a classroom, particularly to hit the "make sense of problems" part of SMP #1.

As part of the reflection I collected data in the form of a "self-check," created in the style of "practical measures" that we've used in our research projects. In hindsight, this data doesn't focus much on my choice of teaching practice (facilitating meaningful discourse), but I like the idea of asking students for feedback that go beyond mastery of content.

Link to Google Form

The responses are a bit difficult to interpret because I'm not sure how many participants responded as teachers versus the students they were sort-of-pretending to be. The results seem mostly positive, and I agree with the very last comment: While the task had reach across many grade levels, first grade was too much of a stretch.


Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129–184.

Smith, M. S., & Stein, M. K. (1998). Reflections on practice: Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.

A Menu for Making a Math Lesson Story

Lee Shulman
CC BY-NC Flickr
In my last post I talked about different types of lesson plans and suggested that one type, a lesson plan as a story, might have some benefit as a shareable unit of teaching.

When I think of teaching and what makes (or can make) it a profession, I think of attributes of professions described by Shulman (1998):
  • the obligation of a service to others, as in a "calling";
  • understanding of a scholarly or theoretical kind;
  • a domain of skilled performance or practice;
  • the exercise of judgment under conditions of unavoidable uncertainty;
  • the need for learning from experience as theory and practice intersect; and
  • a professional community to monitor quality and aggregate knowledge.
To support teaching as a profession, I value public displays of teaching that reflect Shulman's list of attributes. For the sharing of lesson plans, we can do better than over-templated, step-by-step, anyone-can-follow scripts. We can also do better than brief, make-of-it-what-you-will ideas that lack sufficient implementation guidance. In the stories we tell about teaching, we should seek some middle ground between an over-designed lesson template and an unstructured narrative. Since lesson stories are arguably more about the planning than the plan, they should focus on teacher decision-making and teacher practice, so that other teachers may learn from them. The minimal amount of structure to a lesson story probably starts with these four parts:
  1. A description of the context (grade level, class size, demographics, features of your school environment, etc.)
  2. The rationales behind your lesson planning (not just the choices you made, but why you made them)
  3. A description of the implementation (a low-inference description, mindful of the students' perspectives as participants, of the classroom activity, discussion, and work produced by students)
  4. A reflection (now with more inference, with a focus on how the decisions you made in planning played out in implementation and what that might mean for a lesson revision)

A Menu of Math Lesson Planning Resources

So far this is subject-neutral. In some subjects, rationales in lesson planning might have to be developed and explained from first principles. In mathematics education, however, we're fortunate to have an established body of knowledge related to planning and teaching. To plan a math lesson and then tell its story, I see four categories of resources that form a menu of options.

Planning Guide

For planning and describing the reasons for choices made in the lesson, choose one of the following:

Instructional Model

To structure the delivery of the lesson, choose one of the following:
Lecture and "I do, we do, you do" are also instructional models. They have their place but should probably be used somewhat sparingly. Besides, there probably isn't much demand for lesson plans that consist of a lecture.

Teaching Practice

Teaching is complex and teachers are engaged in many practices at once. However, for improving one's practice and communicating that in a story, it's best to focus on only one or two teaching practices described in NCTM's Principles to Actions:
  • Establish mathematics goals to focus learning.
  • Implement tasks that promote reasoning and problem solving.
  • Use and connect mathematical representations.
  • Facilitate meaningful discourse.
  • Pose purposeful questions.
  • Build procedural fluency from conceptual understanding.
  • Support productive struggle in learning mathematics.
  • Elicit and use evidence of student thinking.
For a different list of teaching practices, you could also consider the TeachingWorks high-leverage practices.


In addition to using student work/activity in your reflection, choose from:

What We Gain

Suppose we choose resources from the menu above and tell our lesson story. What have we gained? We've built upon a body of knowledge that can help readers. To some extent, we already do this. When I hear a teacher say they taught a 3-Act Task, I immediately have some knowledge about the instructional model they used. When I hear a teacher say they planned a lesson using the 5 Practices, I know that means they took time to (among other things) anticipate student strategies. With a piece from each of these four categories there is still a lot of freedom to tell a lesson story, but the shared pieces communicate a lot about your lesson and provide a foundation for a common understanding across teachers.

Now, to refer back to my last post, let's think about the usefulness of lesson plan repositories again. Generally, lesson plan repositories are arranged by grade level, topic, and content standard. Instead, what if a repository allowed you to search based on the items in the menu? Imagine being able to search or filter by teaching practice, such as "Show me lessons in which the teacher focused on building procedural fluency from conceptual understanding." Or perhaps you're working with a new instructional coach, and you search for lessons in which the teacher had an observer use the SERP 5x8 Card. We stand to improve our signal-to-noise ratio considerably when teachers can look for lesson plans based on more than just lesson content, and the lessons they find are more likely to be a better "fit" if they are known to have a preferred planning guide, instructional model, teacher practice, or reflection tool.

Next post: I attempt to write a lesson story.


Shulman, L. S. (1998). Theory, practice, and the education of professionals. The Elementary School Journal, 98(5), 511–526.

On Lesson Plans and Lesson Planning

CC BY Brian Swartz, Flickr
As someone who studies teacher curriculum adaptation, Chris Lusto's post last summer, "Lessons for Other People," did a lot to get me thinking. Despite their imperfections, curriculum materials have a durability, scalability, and portability that many educational tools or innovations can only wish for. So why not try to preserve and share the evolution of curriculum materials as teachers make them less imperfect, using some kind of revision tracking system?

It turns out that this wasn't exactly a new idea (see here, for example) and there are probably sensible reasons we don't have such repositories yet. Dan Meyer gave us one big reason: Teachers don't seem to be keen on using off-the-shelf plans, especially when the signal-to-noise ratio ("just right" lessons to "ugh, move along" lessons) is frustratingly poor. There are also technical hurdles involved. We would need to get past (way, way past) discussions of JSON vs. TOML and other forms of engineering-speak. I see promise in things like Mike Caulfield's Wikity project, but then again, I'm geeky enough to run my own Mediawiki installation.

There are certainly new angles to explore on the repository front, but for them to be useful we need to get a better handle on what exactly we're putting in them. As far as I know, there isn't much in the research literature about teacher lesson planning. When I worked with preservice teachers, I taught them to use a lesson plan template to detail the objectives and activities of a lesson. But as a teacher myself, I'm not sure I ever filled out a multi-page template with a lot of details. There's a good reason for that, and it's not laziness — the context, purpose, and needs were quite different as a full-time teacher than for someone who is just beginning to learn to teach.

Especially useful to me in thinking about the difference in the purpose of lesson plans is the distinction of plans vs. planning, which Dan Meyer highlighted with a quote from Dwight Eisenhower:

This compliments my own thinking about design work in education: You must accept that much of the positive outcome can lie in engaging in the design process rather than in the thing or product that is ultimately designed. In other words, it's like the quote attributed to Bruce Joyce: We reinvent the wheel not because we need the wheels, but because we need the inventors. For some, this feels inefficient and wasteful, but I say you ignore it at your peril.

Types of Lesson Plans

So what are some different types of lesson plans? I've thought of three:

Lesson Plans as Scripts

Scripts and scripted lessons are loaded terms in education and the connotation is generally negative. I don't think it has to be negative, even though it certainly can be. When I say script, I'm thinking about a detailed, step-by-step description of what should be happening in a classroom, by whom, and at what times, similar to how the script of a play, TV show, or movie describes who is involved in a given scene, the actions they should take, and what they're expected to say. Just as scripted TV differs in quality, scripted lessons can vary in quality also, and they have the potential to be very good.

The most scripted lesson plans I wrote as a teacher were those for substitute teachers. If I had to be away from my students but I still wanted quality work to be done while I was gone, the best I could do was write a very detailed lesson script and hope the substitute could make their way through it.

Lesson Plans as Ideas or Reminders

When teachers plan for themselves, in the context of teaching a thousand lessons a year, many rely on a sparse set of reminders that aren't intended for use by any other teacher. Because of this, we shouldn't be quick to judge the quality of a lesson by this kind of lesson plan. Just because a lesson plan says no more than "Section 4.5, swap out baseball task for the closer, assign evens" does not mean the lesson will be good or bad. There's not enough there to judge, because the lesson wasn't designed for judging.

In conversations around lesson plans last summer, I saw teachers saying they wanted ideas more than scripts. I think part of this is because lesson plans in the form of ideas and reminders are what most teachers use most of the time, and therefore it feels familiar and flexible. I do wonder, though, how well this would really work in practice. The intent of one teacher's notes may or may not be understood by another teacher, and a repository full of lesson ideas might suffer the same low-signal, high-noise problem we have now.

Lesson Plans as Stories

I think there's a third kind of lesson plan, one that puts the planning at the forefront and the plan in the background. These lessons are written so that the reader can think along with the writer and learn from their decisions, rather than follow their instructions. These lessons take the form of a teaching case study or reflection, rather than a script or set of reminders.

Learning to teach through case studies was described by Shulman (1986), so it's far from a new idea. Shulman proposed case knowledge as a form of teacher knowledge, and he proposed (and later led research on) the development of prototype cases designed for teacher learning. Still, it doesn't seem to be the kind of lesson plan you're likely to find in current repositories. Thankfully, I know of two examples in math ed: The lesson descriptions from Jennifer Wilson and Jaime Duncan.

Take for example this lesson from Jennifer on coordinate geometry. It reads like a story: "I found a task, it relates to a standard, here's what I think students will do, here's some of the work they actually did, and here are some things that did and did not go as planned along the way." Jennifer's post is way more than just an idea, and has the detail of the script without any of the "Step 1, do this, Step 2, do that" feeling. Importantly, the students are not left to the imagination. They are seen, heard, and described. I see a lot of similar qualities from Jamie's posts, such as this lesson on fractions in first grade.

Pros and Cons

Here's a quick recap of what I see in these three kinds of plans:

Lessons as: Pros Cons Effort to Implement
Scripts Detailed; Greater chance of implementation as intended Feels restrictive; context-unaware Lower
Ideas Short; A seed from which other ideas can grow; adaptable Interpretations vary widely; Quality difficult to judge; Still requires a lot of planning and decision-making Higher
Stories Experience a lesson second-hand; think along with lesson designer Stories can be long, complex, and inconsistent in form Between Low and High

I think lesson plans as stories have real promise as a shareable unit of teaching. They focus more on planning and reflection, and they may help teachers who use them plan and reflect on their own lessons. However, it feels to me that the stories could benefit from some structure and common elements. After all, there's been way too much good work in the field of mathematics teaching to think everyone writing a lesson story should start from scratch and make up everything as they go along. A free-for-all approach doesn't help the writer or the reader. In my next post, I'll lay out a plan for telling a lesson story that I think has some structure without feeling too much like a template.

This Week in Math Ed: September 16, 2016

Math Ed Said

September 9: Folks were sharing this Teaching Channel interview with Kristen Gray about her being a new PAEMST awardee.

Shared by: TCM - NCTM, Lisa Bejarano, Joe Schwartz, Heather Johnson

David Wees at the 2014
NCTM Annual Meeting
September 10: David Wees wrote, "Teaching Problems or Teaching Mathematics." In it, David thinks about teaching mathematics in ways that focus on solving different types of problems, and the challenge of not seeing those solution strategies as isolated from one another.

Shared by: Brian Bushart, Christina Sherman, Matthew Oldridge, Jennifer Lawler, Carmel Schettino, Jennifer Wilson, Ryan R Ruff, Bridget Dunbar

September 11: Despite efforts to the contrary, Ilona Vashchyshyn got called out by a student for being too dismissive of his contribution to class. She reflects about it (and how she'll repair the damage) in "How to sabotage your classroom culture in 5 seconds."

Shared by: Ilona Vashchyshyn, Taylor Belcher, Melinda Knapp, David Butler, Annie Perkins

September 12: Zack Hill has been writing about mathematical discourse over on the Teaching Children Mathematics blog, and in his fourth post, "Putting it All Together", he affirms his commitment to a principle of professionalism by posting a video of his teaching and a request for feedback.

Shared by: TCM - NCTM, NCTM, Rusty Anderson, Matt Larson, Greg George, Richelle Marynowski

September 13: Robert Kaplinsky gives us "Two Ways To Integrate Problem-Based Learning In A Unit (And Another To Avoid)." It's a well-illustrated post that seeks balance between teaching procedure, concepts, and applications.

Shared by: Robert Kaplinsky, Chris Kalmbach, Nat Banting, Bridget Dunbar, Christie Madancy, Kim Webb, Laura Wagenman, Brett Parker, Andrew Gael, Ilona Vashchyshyn

September 14: People were buzzing about the press release from Open Up Resources announcing their launch of a CC-BY licensed middle school math curriculum built upon Illustrative Mathematics tasks. They plan to have it ready for the 2017-2018 school year.

Shared by: Kate Nowak, Bridget Dunbar, Erik Johnson, Diana Suddreth, Nik Doran, Jen Silverman, John Berray, Vanessa Cerrahoglu, Illustrative Maths, Kristin Gray, Laura Wagenman, Bowen Kerins, Jennifer Wilson, David Smith

September 15: Dan Meyer posted "The Desmos Guide to Building Great (Digital) Math Activities," and he says it's good for paper-based activities, too.

Shared by: Dan Meyer, Nancy Terry, Heather Johnson, Jon Orr, Tracy Johnston Zager, Julia Finneyfrock, Dan Anderson, Emily Freeman, Imtiaz Damji, Andrew Stadel, Bowman Dickson, Brian Bushart

Around the Math Ed Web

There was a #TCMChat this week around Kim Morrow Leong's article "Evidence-Centered Assessment" in the latest Teaching Children's Mathematics. If you missed it, you can look back through the chat here.

Next week the Global Math Department will feature Mishaal Surti for his presentation, "Getting Students Talking...Open Questions in the Math Classroom."

Elections are now open for NCTM's second vice president and three regional directors.

The Friday Institute at NC State is offering two free online learning opportunities for teachers. Teaching Mathematics with Technology (promo video) and Teaching Statistics Through Data Investigations (promo video). The courses will launch September 26th and are now open for registration.

Research Notes

In the October 2016 issue of the Journal of Mathematics Teacher Education, you'll find:
A second 2016 issue of the International Journal for Mathematics Teaching and Learning (from Plymouth University in the UK and the College of Nyiregyháza, Hungary) is out:

Math Ed in the News

Math Ed in Colorado

CCTM Conference

Are you registered for the 2016 CCTM Conference? It's next week! Join hundreds of other Colorado educators at the Denver Mart on Thursday and Friday (September 22-23) as we celebrate and explore the conference theme, Building a Community of Math Excellence. Register NOW!

Come to the 2016 CCTM Conference!

Math on the "Planes"

Registration is now open and spots are limited!

Boaler Book Study

Cassie Harrelson of Aurora Public Schools will be facilitating an online book study on COPilot with Jo Boaler's book Mathematical Mindsets. Participants will need to purchase the book and register online ($45 for CEA members, $145 for non-members). The book study begins October 2nd and will last for 5 weeks. Let Cassie know if you have any questions!

Revised eligibility list for the Mathematics and Science Partnership program

The Mathematics and Science Partnerships (MSP) request for proposal (RFP) that was posted last week has been revised to include additional eligible schools and districts, which were inadvertently eliminated from the original RFP. The new eligibility list and RFP will be posted as soon as possible on the MSP webpage. If interested in applying for this funding opportunity, please submit a letter of intent via SurveyMonkey by Oct. 5. Applications will be due Monday, Nov. 14. For additional information and to access the application, please visit the MSP webpage.

PAEMST Awardees Recognized by Colorado's State Board of Education

On Wednesday, September 14, Colorado's four recent PAEMST awardees (two math, two science) were honored during a meeting of the Colorado State Board of Education.

2014-2015 PAEMST Awardees (L to R): Lisa Bejarano, Carrie Jordan, Dawn Bauer, & Jessica Noffsinger
The math awardees, Lisa Bejarano and Carrie Jordan (some news coverage of Carrie here) will be honored again during the CCTM Conference Award Ceremony from 6:30 - 8:30 on Thursday, September 22. Congratulations again (and again and again) to Lisa and Carrie!

This Week in Math Ed: September 9, 2016

Math Ed Said

September 2: Keeping its momentum from last week, Tracy Johnston Zager's post "How Not To Start Math Class in the Fall" was again most-shared.

Shared by: Joe Schwartz, Matthew Oldridge, Amie Albrecht, Ilona Vashchyshyn, Geoff Krall, Judy Keeney, Jennifer Lawler

September 3: In a post from war-torn Canada (math wars, that is), Paul Wells's op-ed in the Toronto Star says "No, teaching math the 'old-fashioned way' won't work."

Shared by: Mike Maki, Earl Samuelson, Ilona Vashchyshyn, Laura Wheeler, Matthew Oldridge, Egan J Chernoff, Melinda Lula, Robert Cop, Matthew Oldridge, Tyler Anderson, Richelle Marynowski, Taylor Belcher, Andy Martinson, Nat Banting, DeAnn Huinker, Susan Wilson, Jocelyn Dagenais, Keith Devlin, Gregory Taylor, Tracy Johnston Zager, Kit G, Jennifer Lawler

September 4: Christopher Danielson has been writing at a companion site for his new book, Which One Doesn't Belong?

Shared by: Tracy Johnston Zager, Karen King, Kassia Wedekind, David Coffey, Matthew Oldridge, Kit G, Christopher Danielson, Alison Hansel, Janice Novakowski

September 5: With the U.S. elections about two months away, I'm sure this won't be the last presidential campaign-related post we'll see popularly shared amongst the math teachers in my list. Paul Krugman wrote, "Hillary Clinton Gets Gored."

Shared by: Karen King, Keith Devlin, Wendy Menard, Mark Dittmer, Paul Morris, Paul Morris, Audrey McLaren, Eddi Vulić

September 6: As often happens on Tuesdays, people are sharing about that night's talk in the Global Math Department. This week it was "Cultivating Mathematical Reasoning" with Marian Small.

Shared by: Matthew Oldridge, Glenn Waddell, Jr., Global Math, Jill Gough, Megan Hayes-Golding, Alison Hansel, Deborah Boden, Carl Oliver, Andrew Gael, Jonathan Klupp

September 7: Desmos has a scientific calculator. That is all.

Shared by: Christopher Danielson, David Petersen, Gregory Taylor, Nik Doran, Kent Haines, David Sabol, Audrey McLaren, John Golden, David Coffey, Sarah Carter, John Carter, Ann Gaffney, Chris Mueller

September 8: Amy Hogan writes about "Statistics Education & Social Justice" in her latest post, in which she talks about collecting ideas for including social justice into statistics courses. If you have something to contribute, she links to a Google Doc from her post.

Shared by: Amy Hogan, Steve Phelps, Megan Schmidt, Shauna Hedgepeth, Kay Endriss, Brian R Lawler, Anna Blinstein, Glenn Waddell, Jr.

Around the Math Ed Web

On the 13th the Global Math Department will talk about "How Definitions of Math & Equity Relate to Who Excels in Our Classes."

I'm sure I'm missing things — if you think I am, let me know what else I can include!

Research Notes

The September 2016 issue of the Mathematics Education Research Journal is out:

Daniel Reinholz, presenting at the 2015 RME conference
From AERA Open, an article about a math game:

Math Ed in the News

Math Ed in Colorado


Professional Learning Opportunities

Do you have English learners in your class? Do you want to know more about how to help them access mathematical content? Rebekah Ottenbreit of CDE is offering "Teaching Math to English Learners" on October 18 in Grand Junction. The all-day workshop will offer tools and strategies for making math more accessible to English learners through teaching the Colorado English Proficiency (CELP) standards. You can register for the workshop on the CDE website.

Colorado School of Mines will offer weekly Saturday training sessions focused on Computer Science Principles. They are following the curriculum starting with Unit 2 on Saturday, September 10. You are welcome to attend any of the units/lessons that you think might be valuable, whether you are using or not. Details can be found at the C-START website under the CS Principles link.

Mathematics and Science Partnerships

The 2016-2017 MSP request for proposal (RFP) materials are available on the CDE website. This year's priority is the recruitment and retention of math and science teachers in high need schools. An application training webinar will be held Wednesday, September 28, from 10:00-11:00. See the website for registration details and the list of eligible schools.

Two tech pioneers with contrasting approaches to technology in education

Recently I was catching up on episodes of "Triangulation," an interview show on the network. The network focuses on technology, and guests on Triangulation are often key people from the (near) history of computing. Two recent guests made comments about technology and education, and the difference could not have been more striking. I'll let you judge for yourself.

First, Scott McNealy, co-founder of Sun Microsystems, starting at 26:27 and going through 33:33:

Second, Bill Atkinson, early Apple engineer and creator of MacPaint and HyperCard, starting at 17:17 and going through 22:15:

This Week in Math Ed: September 2, 2016

Math Ed Said

August 26: An academic genealogy analysis featured in Nature found that the majority of mathematicians hail from just 24 scientific 'families'. The Mathematics Genealogy Project extends into mathematics education. I've traced back my own academic roots here.

Shared by: Francis Su, Dana C. Ernst, Justin Lanier, Steven Strogatz, OCTM, Evelyn Lamb

August 27: Annie Perkins shared some wonderful experiences from "Math-on-a-Stick!," the Minnesota State Fair (where other good things come on sticks) exhibit that engages kids in mathematics.

Shared by: Annie Perkins, Tracy Johnston Zager, Megan Schmidt, Sara VanDerWerf, Sharon Vestal, Ilona Vashchyshyn

August 28: Lately I've been seeing parts of the world through one of two lenses: one, a "solution to a problem" lens, and two, a "not a solution but we should have it anyway" lens. A NYT piece by Christopher Emdin titled "Why Black Men Quit Teaching," shines brightly through the second of those lenses. Simply having teachers of color, particularly black men, is not by itself a solution. We absolutely should have a diverse teaching workforce, where students of any underrepresented background can see in their teachers someone like themselves who is professional, intellectual, and a leader. But as Emdin points out, there are structural and systemic issues in teaching and education that also need to be addressed, regardless of the color of the teachers.

Shared by: Terry Jones, Karen King, Wendy Menard, Chris Shore, David Coffey

August 29: With more Minnesota goodness, Sara VanDerWerf appeared on her local news to talk about the variety of math graphing tools and to spread the word about the need for donated technology (old calculators, smartphones, and tablets) that can be used in the classroom.

Shared by: Sara VanDerWerf, Megan Schmidt, Andy Martinson, Laura Wagenman, Bryan Anderson, David Keller, Jonathan Osters

August 30: Graham Fletcher is serving on the 2017 Orlando NCTM Regional Program Committee and asks for your input with his post, "Building a Conference."

Shared by: Graham Fletcher, Matt Larson, Nanette Johnson, Zak Champagne, Nicole Bridge

August 31: Dan Meyer wrote to tell us that Christopher Danielson's latest book, Which One Doesn't Belong, has been released.

Shared by: Dan Meyer, Sara VanDerWerf, Ilana Horn, Martin Joyce, Nancy Terry, Tyler Anderson, Christopher Danielson, Megan Schmidt, Tracy Johnston Zager, Bridget Dunbar, Jill Gough, Spencer Olmsted

September 1: One year I began the school year with not one, but two days of syllabus-explaining and rule-laying-down. It was bad. Later I figured out what Tracy Johnston Zager writes about in her post, "How Not To Start Math Class in the Fall."

Shared by: Mark Chubb, Tracy Johnston Zager, Chris Hunter, Annie Forest, Kassia Wedekind, Alex Overwijk, Susan Davidson, Karyn Vogel, Bridget Dunbar, Danielle Reycer, Dan Anderson, Alison Hansel, Cal Armstrong, WMC - WI MathCouncil, Richelle Marynowski, Jami D. Packer, Ilana Horn, Nanette Johnson, Annie Perkins, Janice Novakowski, Tim Hudson

Around the Math Ed Web

Do you want to present at the 2017 NCTM Research Conference? If yes, you'd better hurry up and submit a proposal — they're due by September 4!

Mike Flynn caught my attention recruiting people to join a Virtual Math PLC.

The National Girls Collaborative Project is hosting a webinar titled "The Importance of a Growth Mindset: Action Steps for Educators" on September 21.

Last week the Global Math Department made sense of logarithms, and this Tuesday they'll be Cultivating Mathematical Reasoning with Marian Small.

Research Notes

I haven't looked through the research in a few weeks, so hold on for a long list! Let's start with a new article in Educational Researcher:
Here are math-related articles in the October 2016 issue of the International Journal of Science and Mathematics Education:
I see a number of good-looking articles in the August 2016 American Educational Research Journal, but only one is math-specific:
The September issue of Mathematics Teacher Educator is out:
Here are three new articles in the September 2016 issue of the Elementary School Journal:
Sandra Crespo
I spotted one new math ed article in the November 2016 issue of Teaching and Teacher Education:
Issue 2 of 2016 of the Journal of Statistics Education is out:
Last one! This was recently added to Technology Innovations in Statistics Education:

Math Ed in the News

Math Ed in Colorado

Award Winning Teachers!

I am super happy to share that the White House has announced new PAEMST awardees, and two of Colorado's math teachers have been honored:
These teachers will be honored at the awards ceremony at the CCTM Conference. Speaking of which...

CCTM Conference

The 2016 CCTM Conference is only weeks away! Please join me and math teachers from across the state on September 22-23 at the Denver Merchandise Mart. Thursday will feature two pre-sessions:

Teacher Pre-Session: Making Mathematics Accessible and Equitable for All with Nora Ramirez and José Franco

Classrooms should be where all students engage in rigorous mathematics, reason mathematically, justify and defend their thinking, and critique the reasoning of others. Engage in this session with activities and discussions, and to examine your beliefs about teaching and learning mathematics for all students.

Leader Pre-Session: Curricular Materials Review: A Professional Learning Opportunity with Cathy Martin and Joanie Funderburk

Join math leaders and school and district administrators to explore rubrics for evaluating curricular materials, learn about open resources, and make reviewing materials a professional learning opportunity for teachers.

Rochelle Gutiérrez
Friday will feature concurrent sessions, blast sessions, Ignite sessions, a keynote, and the exhibit hall. This year's keynote will be delivered by Rochelle Gutiérrez from the University of Illinois. Rochelle is a leading thinker about issues of equity and social justice in mathematics education. Register to see her and the rest of the conference today!

Math on the "Planes"

Registration for the February 2017 Conference opens September 15. Because of the highly interactive nature of the conference, each of the two workshops will be limited to 60 participants. You can find more information on the Colorado Council for Learning Disabilities website.

Dr. Karen Karp will lead these workshops. She is a visiting professor in the Ed.D. Program in the School of Education at Johns Hopkins University. For twenty-one years prior to this appointment, she was Professor of Mathematics Education in the Department of Early and Elementary Childhood Education at the University of Louisville.

Job Openings

Math and Neuroscience Research Opportunity

Jennifer Jacobs at CU Boulder is interested in researching early elementary students with and without language processing difficulties and how that relates to math ability. If you are interested in having a child participate, you can contact Jennifer at

Rocky Mountain Math Teachers' Circle

Over at you can find the 2016-2017 dates for the meetings of the Rocky Mountain Math Teachers' Circle, as well as information about RSVPing for each session.


FYI: PARCC has updated their practice tests to match their latest test designs.

PARCC has also kept me busy over the last month — for several days I immersed myself in high school geometry and helped select items for future field tests, and later I met with other math educators from around the country to examine the data collected from test items that had already been field tested. In both cases, the goal is to come away with the best possible set of items to consider for future tests. If you have questions about the process, feel free to ask!