This Week in Math Ed: October 7, 2016

Math Ed Said

September 30: Six different links (some math-related, some not) were shared four times this day, but one stands out to me: "Pentomino Puzzles" by Jon Orr. The post describes an activity using Pentominoes and a hundred grid chart, with students generalizing the patterns they find.

Shared by: Jon Orr, Fred G. Harwood, Rebecca Price, David Keller

October 1: Nautilus published a nice story about Richard Guy called "An 'Infinitely Rich' Mathematician Turns 100."

Shared by: Steve Humble, POWER Org Math, Patrick Honner, Paul Morris, Steven Strogatz, Egan J Chernoff, Carrie Muir

October 2: Dylan Kane wrote about "Discovery," in which he justifies the reasons he thinks it's not always a good idea to let students figure things out for themselves.

Comment: As I mentioned in the comments of Dylan's post, there's some good research from the field of science education that is useful here. Furtak, Seidel, Iverson, and Briggs (2012) did a meta-analysis of inquiry-based science teaching studies and drew distinctions between types of inquiry, including whether inquiry-based activities were teacher-guided or student-led. When compared to traditional instruction, they found that inquiry approaches had positive effects. However, teacher-guided inquiry approaches had a mean effect size more than double the size than for student-led inquiry. In math education, these kinds of results support the push-back against pure "discovery" approaches, which are often described as having little to no teacher guidance. Historically, this also supports Freudenthal's decision to shift his philosophies about learning mathematics from "reinvention" to "guided reinvention," which stressed the role of the teacher in instruction.

Shared by: Dylan Kane, Michael Pershan, Henri Picciotto, Josh Fisher, Jon Orr, Matthew Oldridge, Bryan Meyer

Cathy Fosnot at the 2015 NCTM Annual Meeting
October 3: The most shared link this day goes to a webinar that's no longer available, sadly. However, with a little digging I can see people were excited about a new book by Cathy Fosnot called Conferring With Young Mathematicians at Work, which builds on her Young Mathematicians at Work series.

Shared by: Pam Harris, Brian Bushart, TCM - NCTM, Katherine Bryant, Christina Moore, Early Math, Jennifer Lawler

October 4: Desmos.com is doing something they call the "Desmos Fellows Potluck," in which they ask for Desmos users to create and share graphs from things that interest them.

Shared by: Desmos.com, Bob Lochel, Dan Anderson, Jennifer Lawler, Mary Bourassa, Michael Fenton, Joshua Bowman

October 5: Jason Merrill shared a model of flipping a water bottle in Desmos.

Shared by: Shauna Hedgepeth, Kate Owens, Brett Parker, Eli Luberoff, Shelley Carranza, Shelby Aaberg, Anna Vance, Denis Sheeran, Michael Fenton, Scott Leverentz, Luke Walsh, Brandi Moore, Andrew Stadel, Chris Lusto, George Carganilla, Chris Adams

October 6: In recognition of World Teachers' Day, Springer has made a number of research articles and book chapters free for the month of October, including the special issue of the Journal of Mathematics Teacher Education that I had an article in, focused on "Mathematics Teachers as Partners in Task Design."

Shared by: Raymond Johnson, Shauna Hedgepeth, Tom Snarsky, Egan J Chernoff, Jennifer Lawler

Around the Math Ed Web

There are only a few hours left to get the early-bird registration discount for the NCTM Regional Conferences in Phoenix and Philadelphia. If you're wanting a discount on Innov8, you have until next Friday, October 14th.

Last week at the Global Math Department meeting, Linda Dacey presented "Unleashing the Power of Math Games and Puzzles, K-5." Next week you can look forward to "Teaching Ideas to Prepare Your Students for the AP Stats Exam" with Amy Hogan, Bob Lochel, and Doug Tyson.

The #TCMchat next Wednesday will focus on the article "Assessming Students' Understanding of Fraction Multiplication."

Research Notes

Added to the Journal of Mathematical Behavior, we have:
And that's it. If you're looking for more, you might check out the journal Research in Mathematics Education, which is published by Routledge and the British Society for Research into Learning Mathematics. I'm not sure why this journal hasn't been on my radar, but you can see the current issue here.

Math Ed in the News

Math Ed in Colorado

Math Day at Colorado State University

Math Day at CSU is Thursday, November 3. Math Day is a day of individual and team competitive mathematics for high school students, with scholarships available for high-performing students. The cost is $20 per student and registration is by recommendation of high school teachers. The registration deadline is Monday, October 24.

Calculus Center @ CSU

For a glimpse at the kind of support CSU students get in calculus, see "New Calculus Center offers study help and camaraderie" in CSU's Source.

Mathematics of Voting

The next meeting of the Rocky Mountain Math Teachers' Circle will be October 8 from 8:30 to noon at 1201 Larimer St., Room 4125. The topic will be the mathematics of voting, and you need to RSVP to attend.

Teaching English Learners Workshop now in Bayfield, Too

If you have emerging bilingual students in your class, and you want to know more about helping them access mathematical content, there are now two upcoming workshops to attend. Rebekah Ottenbreit of CDE is offering "Teaching Math to English Learners" on October 18 in Grand Junction, and on October 20 in Bayfield. 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.

Job Opportunity

Fort Lewis College in Durango is looking for a non-tenure track lecturer with statistics experience.

Math on the "Planes"

Registration for next February's conference is open. The focus will be Tier 1 and Tier 2 interventions for K-5 math students, with Dr. Karen Karp as the workshop leader.
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This Week in Math Ed: September 30, 2016

Math Ed Said

September 23: Mark McCourt writes about "#MasteryFail," detailing some of the ways he sees and hears poor practice paraded under a banner of "mastery," such as teaching skills in isolation or hearing someone say, "We do mastery on Tuesdays."

Shared by: Richard Cowley, John Gunn, Mark McCourt, Louise Seeley, Jo Morgan, Simon Gregg, Craig Barton

September 24: Alice Keeler wrote in the Fresno Bee, "I turn 40 next month and, for pretty much my whole life, I have felt dumb. I’m not."

Shared by: Jo Boaler, John Scammell, Lorraine Males, Mathematics Teaching, Jamie Duncan, Sharon Vestal, Anthony Purcell, Kathy Henderson, Stephanie Iacadoro, John Staley, Kyle Pearce, Math Coach Rivera, Laura Wagenman, Peter Cincotta, Jennifer Perez, Megan Heine, Richelle Marynowski, Matt Leiss, Jim Pardun, Kit G, Jenise Sexton, Christopher Rohde, Mr. Harris, Susan Davidson, Stacey Roshan, Rosa Serratore

September 25: What's special about the date 9/25/16? You can count on Patrick Honner to tell us.

Shared by: Patrick Honner, Annie Forest, Jennifer Fairbanks, Kit G, Mark Chubb, Greg George, Matt Leiss, Peg Cagle, Evelyn Lamb, Gregory Taylor

September 26: Christopher Danielson wrote in the TCM blog, "The power of having more than one right answer: Ambiguity in math class."

Shared by: Christopher Danielson, Glenn Waddell, Jr., Megan Schmidt, TCM - NCTM, Michael Fenton, Katherine Bryant, Nicole Bridge, Aran W. Glancy, Jennifer Lawler, Mary Bourassa, Daniel Luevanos, WODB? Math, Bryn Humberstone, Bryan Anderson

September 27: Carmel Schettino wrote in the MT blog, "Aspects of Problem-Based Teaching." In this and future posts, she'll be discussing aspects of problem-based teaching and connections to mathematical practices.

Shared by: NCTM, Jennifer Lawler, NCTM - MT, Mary Bourassa, USU TeachMath, Andrew Gael, Carl Oliver

September 28: Ilana Horn is looking for a postdoc, and she got some help with her search from others on Twitter.

Shared by: Ilana Horn, David Coffey, Carrie Muir, Justin Lanier, Elizabeth Self, Christopher Parrish, Nicole M. Joseph, Raymond Johnson

September 29: Wednesday the 28th marked the debut of #MTchat, which NCTM Storified at "Snapshots of Equitable Teaching in a Highly Diverse Classroom (with images, tweets)."

Shared by: NCTM - MT, NCTM, April Pforts, The Math Forum, Matt Larson, Jennifer Lawler

Around the Math Ed Web

Michelle Stephan at the 2015 NCTM Research Conference
ASCD is hosting a webinar on October 27th called "Lesson Imaging in Mathematics and Science: Mindfully Planning for Inquiry Instruction." The Speakers are Michelle Stephan, David Pugalee, Julie Cline, and Chris Cline, and you can register here.

Last week the Global Math Department had Chritina Tondevold presenting "3 Reasons Kids Don't Know Facts and How to Help." This week, it's Linda Dacey and "Unleashing the Power of Math Games and Puzzles, K-5."

Research Notes

The October 2016 issue of Educational Studies in Mathematics is out with these articles:
Kicking off the December 2016 issue of The Journal of Mathematical Behavior, we have:
In the January 2017 (really?) issue of Teaching and Teacher Education, you'll find:

I usually don't monitor IES on a week-to-week basis, but this study got my attention:

Math Ed in the News

Math Ed in Colorado

Boaler Book Study

Cassie Harrelson's book study of Mathematical Mindsets by Jo Boaler starts today on COPilot! Participants will need to purchase the book and register online ($45 for CEA members; $145 for non-members). The study will last for 5 weeks and you should email Cassie 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.

Teaching English Learners

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.

Math on the "Planes"

Math on the "Planes", Colorado's conference specializing on the mathematical learning of students with learning disabilities, is limited to 60 participants this year. To secure your spot, register now!

A Look Back at the CCTM Conference

Big thanks to all of you who attended last week's CCTM Conference! It was a packed two days and I want to thank the conference organizers for making it come together. In the coming months, CCTM will be reaching out to Colorado educators to get ideas for next year's conference and on how to serve you best. I spent most of my time at the conference taking pictures, which I've now posted. Here are a few highlights:

2016 CCTM Conference Photo Highlights

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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: Desmos.com 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: Desmos.com, 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, Desmos.com, 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 Code.org 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 Code.org or not. Details can be found at the C-START website under the CS Principles link.
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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.

Context

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

Reflection

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.








References

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. http://doi.org/10.1207/s1532690xci2202_1

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.
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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.

Reflection

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.

References

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