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

Conferences

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 Code.org 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 Code.org 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 TWiT.tv 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 jennifer.jacobs@colorado.edu.

Rocky Mountain Math Teachers' Circle

Over at rmmtc.ucdenver.edu 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.

PARCC

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!