Is Talent a Wall or Launching Pad?

In the quest for delineating the difference between fixed and growth mindsets, educators have created a plethora of lists for contrasting habits, beliefs and statements.


With my students, I summarize all of these lists and graphics with two simple pictures that pose a simple question: “Do you see talent as a wall or as a launching pad?”

Talent Wall

Carole Dweck‘s mindset research shows that self-perception of talent as a limit or as a starting point has a tremendous influence on student learning. The mindset is really about how people perceive their natural abilities and view the potential of their efforts, not just their level of effort.

In fact, this double-pronged image of wall vs launching pad helped me make sense of two things that Dr. Dweck has said regrading effort and growth mindset. The first is that “the most common misconception is simply equating the growth mindset with effort.” (Education Weekly, September 2015).  I didn’t fully grasp the issue that troubled her until I heard her say that it isn’t just the struggling math students who have a fixed mindset, but that even some of the more “successful students” have one as well. An example of an advanced student who possesses a fixed mindset is the one who believes that they cannot learn math (remember mindset is about self-perception), so they must compensate by studying and memorizing in order to pass the tests and get good grades.

This thought leads me to another of my favorite image comparing fixed and growth mindset… the scans of the brain of someone with a fixed mindset versus one with a growth mindset.

Brain Mindsets

brain-coldWhen faced with a challenge, the fixed mindset brain “goes cold.” It literally shuts down.

brain-on-fireHowever, when faced with the same challenge, the growth mindset brain “fires up.” It knows that more is being asked of it, so it kicks into high gear to meet the challenge, rather than duck it.

Some frozen brains walk away from learning by checking out or acting out. Other frozen brains circumvent the learning by grinding through the course with a hyper-powered work ethic. If good grades is the ultimate goal, then one of these fixed mindset responses is valued more than the other. If learning is the true prize of an education, though, then neither response is sufficient; instead, Dweck claims that students need to implement a “repertoire of approaches—not just sheer effort—to learn and improve.” After all, it is how one reveals to setbacks that reveals their true mindset.

To see some of my novice attempts at teaching growth mindset in math class, see the following posts: Nicki the Neuron, Neuron Stickers, Brain Surgeons & Wrinkle Sprinkles, and Neuron Problems and Classroom Norms, or click Growth Mindset in the tag cloud.

Ready, Set, Launch!


Nicki the Neuron

NickyAfter I gave a presentation about my use of Neuron Stickers, Brain Surgeon & Wrinkle Sprinkles at Twitter Math Camp 15, Julie Wright (@julierwright) sent me a tweet that directed me to a stuffed Neuron with eyes. So Bitchen!

I took her suggestion and hung it at the front of the classroom as a class mascot, naming it Nicki the Neuron, since Nicki is a name that is gender and ethnic neutral.

Julie Wright Tweet


Nicki was  a bigger hit than I expected. One of my students insisted on holding our new mascot during class.

Nicky n Fan

This inspired me. I thought to give Nicki temporarily to the group to which the most recent Neuron Sticker was awarded. I was concerned the boys wouldn’t receive this too well, but Nicki quickly became of badge of honor for the groups.

Nicky n Girl

Nicki is now part of the responsibilities of the Brain Surgeon and is generating a great deal of focus on the Process Reward System that I am implementing. Thank you Julie!

Neuron Stickers, Brain Surgeons and Wrinkle Sprinkles

Brain-SurgeonI was inspired at a Growth Mindset workshop by Jo Boaler and Carol Dweck. I knew I was going to be teaching a class of at-risk students, qualified by being on the socio-economic disadvantaged list and having struggled in 8th grade math. Rather than repeating in high school the math course that they failed in middle school, these students would taking Algebra 1 with me. If there is a group of students that need help shifting from a fixed mindset to a growth mindset, it is a group of at-risk students who have struggled in math. However, I did not want to just put a bunch of Power Point slides saying how they should believe in themselves.

So, I came up with three vehicles to develop growth mindsets in my students:

Neuron Stickers

Dr. Boaler emphasizes the plasticity of the brain. This means that the brain actual rewires itself when it learns, by forming new or strengthening current connects between brain cells. We also know now that the outer later of the brain thickens as we learn, much like muscles get bigger from exercise. These facts create a contemporary view of the brain that is in direct opposition to the conventional view in education in which the brain is a passive vessel to be filled with knowledge. These two views are best contrasted by the following images of the brain.

Brain Pair

The image on the left implies that we are building a brain. I love that idea so much that I enlarged the graphic to poster size and put it up on the classroom wall. I tell my students that is exactly what they are here to do … build their brains. We then publicly discuss the actions that help us build our brains in class, like…

  • Sharing mistakes publicly
  • Offering unique solutions
  • Asking clarifying questions
  • Making connections
  • Having an “Aha!” moment
  • Helping others

To encourage these and other behaviors that contribute to learning, I created Neuron stickers. This was easy, I pulled a drawing of a neuron from the internet and created a sheet that I could print onto a sheet of mailing labels.

neuron color

Neuron Sheet

Each time a student demonstrated action that promoted learning, the student receives a neuron sticker which they get to place on the Brain Poster. Once the poster is filled, I put up a new one and we continue honoring growth mindset throughout the year.

Brain Color Brain Pic Final

Brain Surgeon

Each day we designate a “Brain Surgeon,” who serves as a class leader for the day. I purchased this model of the brain to be given to the day’s Brain Surgeon.

Brain Surgeon Model

The role of the Brain Surgeon comes at the beginning and end of each class.

Opening Class Duties

  • Supervise preparation for class (getting materials ready)
  • Lead Drum Roll (Class Opener)
  • Reading of Instructional Objective
  • Placing Nicki The Neuron with the group who had it last during prior lesson

Closing Class Duties

  • Supervise clean up and storing of materials
  • Return Nicki The Neuron and the Brain
  • Lead Wrinkle Sprinkle 

Wrinkle Sprinkle

Each class concludes with a debrief titled “Wrinkle Sprinkle,” implying that learning adds a new wrinkle to the brain. (Note: Anatomically we know this is not accurate, though we know that the neurons make new connections and the outer layer of the brain thickens.) The brain surgeon calls on students who raise a hand to offer something that they learned that day. These Wrinkle Sprinkles are recorded on the 180Blogs on this site. Wrinkle


Neuron Problems & Classroom Norms in Algebra 2

Day 3, Fri Aug 12, 2016

A vs Don-stepmom-shoulderTarget: Recognize that  Voice = Choice when it comes to having a growth mindset as we solve problems about our amazing brains.

Entrance Ticket
I greeted the students at the door, but today I was checking homework. They only had to do one problem of their choosing from the Neuron Facts last night. If they did not have it, they had to quickly do one outside. Message sent: You are doing your homework in this class.

Growth Mindset
On the growth mindset web site they make a point of the “voice = choice,” meaning that we have a choice whether or not to listen to the fixed mindset thoughts that we all have, They give a 4-step breakdown of how to shift from a fixed to a growth mindset. I had fun soliciting the help of a very ancient visual of a devil and an angel on your shoulder.

Voices choices

Neuron Fact Problems
So then came time to practice recognizing the fixed voice and talking to ourselves in the growth voice, while doing challenging math problems. They already sit in groups of four, so I had them spend the rest of the period working through the Neuron Fact Problems, which I created from the Facts on the front side of the paper.  They were to call out any fixed mindset words or actions demonstrated by their partners. They actually did. I worked the room with Neuron stickers and Nicki. I honored about half the groups. I was pleasantly surprised at how well my crew worked.

During the lesson, as I worked the groups, I asked  one student how she got her answer, and she told me that she had copied from her partner. I praised her for her honesty, then paused the class and brought their attention to our classroom norms.


These were originally shared with us by Dr. Juli Dixon (@thestrokeofluck) in a math training at our district. They became very popular among our teachers. Our new principal has implemented them schoolwide, providing posters for every classroom. I drew the students attention, that we “Share, Don’t Copy.” When we share, one person explains, the other listens, then question follow if we don’t understand or if we disagree. If these three norms are occurring then writing down someone else’s solution is not copying.

After a half hour of solid work, we debriefed where we saw evidence of a fixed mindset and where we saw evidence of a growth mindset. This whole activity was very well received by the students. I gave them advance notice that Monday we will be debriefing their actual solutions to the problems.

Wrinkle Sprinkle

  • Share, Don’t Copy.
  • The equals about 3 lbs.

Introductions & Neuron Facts in Algebra 2

neuron vertical
Day 2, Thurs Aug 11, 2016

The Brain Surgeon
Today, we began my regular routine of designating a daily Brain Surgeon. Since this was our first day of the Brain Surgeon, I introduced the routines of the Drum Roll, Reading of the Dual Target, Music Cues, and the Wrinkle Sprinkle. The students seem to embrace the spirit of of it all.

Student Introductions
As with every new school year, I had each student briefly state their name and something interesting about themselves. When they were all done,  I recited all their names. That always impresses a class. Then I told them things about myself. I state that yesterday we started with math, because that is what we are all about here. But since I teach math to them, they are also important and I need to know who they are.

Growth Mindset
Most of our Course Teams across the district agreed to do some kind of growth mindset activity. Here was mine.

I started by summarizing the plethora of lists of fixed vs growth mind set statements with two pictures. I told the students that research in student learning is showing that self-perception of talent as a limit or as a starting point has a tremendous influence on their learning.

Talent Wall

Then I shared that scans of the brain of someone with a fixed mindset versus a growth mindset, shows something very interesting. When faced with a challenge, the fixed mindset brain “goes cold.” It literally shuts down. However, when faced with the same challenge, the growth mindset brain “fires up.” It knows that more is being asked of it, so it kicks into high gear to meet the challenge, rather than duck it.
Brain MindsetsNow it was time to test out where we see ourselves demonstrating  a fixed or growth mindset.

Neuron Facts
I gave the students the worksheet with the Neuron Facts on the front side. I found these on the internet and thought they would make for a good lesson since they highlight the amazing function of our brains. I added the subheadings of Fast, Crowded ,etc. I started with a common practice of mine Notice & Wonder popularized by Annie Fetter (@MFAnnie) of Math Forum.  My Gradual Reel-In process looked something like this:

  1. You Do: Independent response.
  2. Ya’ll Do: Each member of the group shares both their notice and wonder.
  3. We Do: Each group decides on one Notice and one Wonder from those shared. These get shared out by each group as I write them on the board.
  4. I Do: I summarize the major point(s) that I want all students walking out with. Here it was the process of Noticing and Wondering and how we facilitate group discussion in class… And of course how amazing our brains are.

The groups were then tasked with doing one problem together. Homework was to do one more.

Wrinkle Sprinkle
Tying into the concept of the plasticity of the brain, I joke that when we learn we get a new wrinkle on the brain. Each class then concludes with what we learned that day. The brain surgeon leads and records the discussion. The students today stated that they learned…

  • Negative thoughts shut down your brain
  • Speed of the brain cell
  • The amount of oxygen the brain uses

First Day – Algebra 2

Day 1, Wed  Aug 10, 2016

{I am new to Chaparral High School, having transferred within my district as a Math Specialist.}

Opening Quiz Alg 2 on the 6Cs: After greeting each student at the door with a high-5, I started the year by answering the transformation question: “How will you (the students) be different in June than you are now, because of my class?” I am still answering that question with the same 6Cs that I launched 2 years ago. My Claims-Based grading system and the students portfolios are structured as such also.

6 Cs PicAs I do with all classes each year, I gave the students the blank copy of the quiz below, and told them this was not to be graded nor was it a test of their previous knowledge. It was like a movie trailer of things to come, but I still wanted them to give me their best shot. I then gave them my standard 3-response speech.

As a mathematician I cannot always give an accurate response; I cannot always give a complete response; but I can always, always, always give an intelligent response. Blank is not intelligent.

I pressed them to give me something… numbers, equations, drawings … anything intelligent.

Opening Quiz Alg 2 Pic

They worked on these independently, then in groups, then as a class, followed by my summary. I wanted to model this process of “gradual reel-in” (as opposed to gradual release) right away, because I use it often.

During the class discussion, one senior claimed out loud, “This is the 5th time that I have taken this class!” (She had failed two semesters as a junior, then 2 semesters in summer school.) I told her that this year she will pass because, “You are that smart, and I am that good.” I had the students repeat this:

Me: “You are that …”
Class: …smart!”
Me: “I am that …”
Class: “…good!”

This was a set-up for the Growth Mindset discussion that was coming over the next few days. In the meantime, I hope I sent the message that I believe in them, and that I believe in my ability to teach them (The 3 Growth Mindsets).

The students brought some terrific energy. I’m so looking forward to my first year as a Puma.

Recap: Twitter Math Camp ’16

TMC LogoThe annual Twitter Math Camp is always amazing. This summer’s conference in Minneapolis, at Augsburg College. was no different. My great disappointment was only being able to stay for one full day this year, but the one day did not disappoint. 

As always, portions the Math Twitter Blogosphere (#MTBoS) rallied from around the country in genuine excitement to see and learn from each other after another year of digital friendship and collaboration. Thanks go out to Lisa Henry (@lmhenry9) for being the lead on this terrifically special event.

Michelle NMichelle Naidu (@park_star),
Saskatchewan Professional Development Unit

A packed room on the topic of intervention was surprising to both me and the presenter, because the MTBoS dialogue mostly revolves around first instruction. The large audience is a testament, though, to the need for reaching ALL kids in the era of 21st Century Standards. Michelle is leading a very successful intervention program in Canada which is focusing on some basic premises:

Differentiating for All Students is like Cowboys Herding Cats, but “it’s a good feeling having the herd [of students] arrive on time without losing a one.”

Early Intervention on the Pre-Requisite Skills (Readiness) that are required to be successful in the current curriculum is the first and most important intervention move. Pre-Assessments on prior content are then necessary to help improve students’ chances for success. Back at home we call this Boot Camp. Michelle affirmed that this work is good, and also inspired me to go back to my site and push to make it a priority.

Unpacking Standards Collaboratively serves two purposes. (1) It allows you to throw out material that is not in the standards, which buys you time for intervention/differentiation (Grade Level)  and (2) It helps you focus on the pre-requisite skills needed for students to learn the new material (Readiness).

Intervening on Readiness = Differentiated Content
Intervening on Grade Level = Differentiated Product

SnowballI also saw an interesting take on the Snowball Activity. Students write down one comment and one question about a topic (notice and wonder), then wad up their papers and throw them around the room. Each student picks up a “snowball” and adds another comment and question. This is done again, until there are three of each. After the fourth toss of the snowballs, the students do not write, but instead debrief publicly as the teacher summarizes the comments and questions on the board. This is a strong way to have ALL students reflect on learning.

Jose Vilson (@TheJLV)JoseV

Jose’s most solid point was that public conversation on math education reform often does not include educators, especially those teaching the marginalized. He accurately stated that if the medical system in America were being discussed on cable news, there would be a doctor on the show, but you never see a teacher on TV talking about education.

In many ways, Jose was calling us out to be activist on our campuses for the changes that we in the Blogosphere write so much about, particularly for students of color. He made a claim that really stuck with me: “We say that we teach math to all kids, but students of color are taught a different type of math than white students.” I know this is true on my campus, While my school is relatively diverse, the lower-level math classes are disproportionately populated by students with Hispanic surnames.

I asked a question of Jose, preluding it with a statement that prejudice on my campus tends to run more along income lines than racial lines (although, racism exists everywhere). Students are accepted and succeed as long as they behave like ‘these kids.’ So I asked, “How do you get teachers and staff to be more accepting of ‘those kids,’ so that they can remain authentically themselves and still learn?” Jose’s response was, “Teach the adults to recognize ‘different types of genius.'” I love that phrase! He went on to explain that kids in poverty are often times going to bring the norms of their own sub-culture to class, which is many times in conflict with the rigid, quite, patient, controlled environment of traditional school. If we can respect that and honor ALL students’ intellects, while also teaching proper social behavior, schools will break down a lot of walls and reach more marginalized students.

Audrey McLaren (@a_mcsquared),

Audrey showed samples of student work from her classes, in which she has students BUILD activities and graphs in GeoGebra and Desmos. The best example was Sticky Points. I love how the challenging of students to create the special points for a function like the x-intercept(s), the y-intercept, and the vertex demands that the students do some algebraically manipulation. The graph offers an immediate feedback loop until students do it correctly. This builds their algebra skills and conceptual understanding simultaneously. I’m using this idea in my class this year for sure.

Desmos Sticky points

Edmund Harris (@Gelada) and Myself (@MathProjects)

Edmund Model.png
I thought Dr. Harris asked for “mathematician modeling!”

I was honored when Dr. Harris, of the University of Arkansas, asked me to present with him on Mathematical Modeling. Edmund and I have been friends since our first Twitter Math Camp (TMC13), and I always look forward to our laughs and deep mathematical conversations. Edmund wanted to share the theoretical meaning of mathematical modeling, and he asked me to add my take on how the teaching of it manifests in the classroom.

Logo Pear DeckWe started by surveying the audience on Pear Deck, prompting for their definitions of mathematical modeling. The vast majority of the responses fell into two categories:

  • Representing a Real-Life Situation
  • Applying the representation to make Predictions.

It turns out that these are quite accurate if we include them BOTH, but the two are not necessarily a comprehensive list, as Edmund explained.

The professor started by claiming that shepherds in the field used to count sheep by using stones in their pocket by which a small stone represents one sheep and a larger stone represents 20 sheep. This, he asserted, is an example of abstract modeling. (Leave it to the Brit to bring sheep herding into a math discussion.) Then he drew this diagram on the board:

Edmunds Model Diagram

Edmund teachingHe explained that you start with “something to be modeled,” (noticed he did not say a real-life situation) and then you create an abstract representation of it. This is a back-and-forth process of verifying the accuracy of the model’s description of the something as well as the “thing” that we want to do with it. (Use rocks to keep track of the sheep). So the audience was responses were spot on… collectively. Yes, modeling is Representation AND Application, but not necessarily just Representation OR Application. Furthermore, Edmond wanted to make it clear that modeling does not have to apply to only “real-world” examples. He claims that when we discuss the transformations of a family of functions, we are also modeling… using an abstract representation to “do something” to the original parent function.

Modeling Tweet Me

In my investigating of what is expected of school teachers when it comes to modeling, I studied the common core documents and found very persistent, clearly defined attributes of Mathematical Modeling:

  1. Modeling is a process.
  2. Modeling is a verb.

In other words, using a model that is already provided is a good and healthy step in the learning process of modeling, but it is not modeling itself unless the students are generating the model themselves.

Modeling Tweet Heather

Modeling Tweet Jasmine

Thank you, Edmund. It was a pleasure working with you, my friend. You always make math appear so joyful.

I had several conversations throughout the Camp, but two that stood out were with …

Math Modeling
Edmund Harris (@Gelada), Brian Miller (@TheMillerMath) & Alex Wilson (@fractallove314)

TMC Bar ModelingThe first night of TMC16 was a huge social event by Desmos. Edmund, Brian, Alex and I had a beer-laden discussion about modeling that proved quite passionate (read as: table pounding, finger-pointing, and all in good fun B.S. calling). It was such a blast to throw ideas around with people of high intelligence, strong convictions and the deep desire to get this thing that we call teaching right. Cheers to changing the world one math lesson at a time.

Intellectual Need for VocabularyPic Dan M
Dr. Dan Meyer
Dr. Meyer completed his dissertation last year. Knowing how much those with a doctorate enjoy talking about their research, and being truly curious about it, I ask him to share his findings with me. He joyfully did, including some of the back story behind it. In essence, Dan studied the effectiveness of giving students the academic vocabulary after first posing a task that required its use, rather than front loading the terms. He called this method Functionary. His study showed that the both Functionary (using the vocabulary to communicate) and Traditional methods (making flash cards to memorize definitions) were equally effective in teaching students academic language found on traditional assessments. The Functionary method, however, showed superior results when students were asked to communicate their thinking using the vocabulary terms or to complete less traditional (more CCSS-like) tasks. You can listen to the Defense of his Dissertation on Dan’s Blog

As always, I highly recommend this event to any math teacher. I hope to see you all at Twitter Math Camp in  Atlanta, July 27-30 2017.

How Deep for Teachers?


26570883 - flood level depth marker post with rain falling into the surrounding waterRecently, I conducted a training with a school district in West Virginia.  It was for new teachers (1st-3rd Year) in all subjects K-12. There were approximately 75 participants and 20 mentors. One of our activities dealt with Depth of Knowledge. I showed the typical D.O.K., but I wanted them to have a more meaningful experience with D.O.K. levels in mathematics.

DOK Chart

The activity I created was inspired by the work of Robert Kaplinsky. I love his Tools to Distinguishing Between Depth of Knowledge Levels. I particularly like his example of sums of whole numbers:DOK RK sampleThis is a simple and clear example of the D.O.K. progression. However, it does not show D.O.K. Level 4, so I contacted Robert and he directed me to this Problem Post of his, How Many Soda Combos are There on a Coke Freestyle Machine? 

DOK Soda

Perfect! I compiled these four into one document, scrambling the order, and asked the teachers to discuss the problems in their table groups and to assign a D.O.K. level exclusively to each one. I was intrigued at how different their responses were compared to what Robert (and myself) considered the problems to be. I noted that the group was a broad range of grade levels and subject areas, so I thought I would conduct the same activity with a collection of high school math teachers that I was scheduled to train in California  the following week. I was very curious if math teachers would view the problems differently than non-math teachers. Indeed, they did. However, they also disagreed with Robert and me. Below, are the all responses from the groups at each training, as well as Robert’s determination. Notice the variety of responses that was generated within each training.

DOK RK Response

The choices that earned  the most votes looked like this.

DOK RK tops

Notice that there is not a single example in which all three parties agree. I have no profound analysis of these results; I am simply sharing this very curious experience. I am still pondering the outcomes and their meaning many times over. So much so, that whenever I hear the phrase “D.O.K.,” I smirk and scratch my head.

Re-Cap: NCSM 2016


Oakland, CA , April 2016NCSM Logo

I have summarized each session with some simple (•) bulleted notes, red underline quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.

Game-Based Learning: The Hype is Starting to Give Way to Some Surprising Substance  — Keith Devlin (Stanford)

  • Pic Keith_DevlinBig Take-Away = Start with the thinking (which is the more important), then follow with the notation.
  • The “Symbolic Barrier”: Symbols are a terrific way to use mathematics, but a horrible way to learn them.
  • The vast majority of our population is taught symbolic notation, yet most need mathematical thinking.
  • Students using Dragon Box Algebra learn the Algebraic thinking needed for solving equations in 90 minutes. However, this ability did not transfer to paper/symbolic test, therefore, both are needed.
  • We teach students to play music, before we teach them to read it. The same should be true of mathematics.

Personal note: I’ve had Dr. Devlin’s book, Goodbye Descartes, for almost 20 years; after his talk he signed it for me.

Developing Deeper Student Thinking  and Reflection — Patricia Rogers (Gilroy USD)

  • Big Take-Away = Use “structured” student collaboration to enhance student reflection, and thus student thinking.
  • Good collaboration needs to be: Regular, Brief, Prepared, Open-Minded.
  • 3 Teacher Moves (Phil Daro)
    • Student thinking made visible (to other students, not just the teacher)
    • “Everyone Ready” (ALL students individually prepare themselves to share thinking.)
    • “Make an Expert” (of a students who has viable strategy) then have the rest of the class “Turn and Talk” when productive struggle weakens in order to focus on targeted math topic.
  • Classroom Discussions (Chaplin, O-Connor, Anderson)
    • Wait Time
    • Revoice (The teacher rephrases what the student just said.)
    • Restate (Student(s) rephrase what a student just said.) 
    • Add-on (Student(s) extend or challenge another student’s conjecture.)
    • Apply (Students apply their own reasoning to someone else’s reasoning …” just try it on.”)

I’ve seen the two techniques of revoicing & restating demonstrated a great deal lately and have now been challenged to bring these into my class more often.

SFUSD logoThe San Francisco USD Mathematics Teaching Toolkit: Changing the Practice Along with the Content — Glenn Kenyon & Kathy Bradley (SFUSD)

  • Big Take-Away = Established Vision, Beliefs and Goals before building district curriculum

“All students will make sense of rigorous mathematics in ways that are creative, interactive, and relevant in heterogeneous classrooms.”

1. All students can and should develop a belief that mathematics is sensible, worthwhile, and doable.
2. All students are capable of making sense of mathematics in ways that are creative, interactive, and relevant.
3. All students can and should engage in rigorous mathematics through rich, challenging tasks.
4. Students’ academic success in mathematics must not be predictable on the basis of race, ethnicity, gender, socioeconomic status, language, religion, sexual orientation, cultural affiliation, or special needs.”

3 Goals
1. Help students express, expand and clarify their own thinking. 2. Help students to listen carefully to one another and negotiate meaning.
3. Help students deepen their reasoning.

“The teaching strategies in the SFUSD Math Teaching Toolkit are designed to support an inquiry-based approached to learning mathematics, with an emphasis on classroom discourse. This approach reflects the shifts of pedagogy required to promote the Common Core Standards for Mathematical Practice.”

  • Unit Design Structure to incorporate tasks

SFUSD Unit Design.png

1) Math Talks
(SMP#3. “Math Talks”, instead of Number Talks, so discussion can broaden {e.g. strategies for computing area})

2) Three-Read Protocol
(Model for close reading of complex math text)
First Read (Teacher Read Aloud) = What is the Situation?
Second Read (Choral Read) = What are the Quantities & Units?
Third Read (Individual Read & Think) = What question can be asked?
This only runs 10-12 minutes. Take away the question to create a rich task.

3) Participation (Group) Quiz A technique to give public feedback on group work. Lists ways a student can contribute (“You can help your group if you can…. create a table, draw a diagram, listen to people’s ideas and ask questions, etc) Also publicly list teacher expectations (e.g. How groups … us shared space? ask question? explain thinking? etc)

  • Video Exemplars & PD modules are available on district web site.
  1. SFUSD has a PHENOMENAL math web site chalked full of resources for supporting teachers implement the vision and the curriculum. Check it out!
  2. The description of their Group Quiz speaks to the need to explicitly teach students how to productively collaborate.
  3. This was the first of three sessions that spoke about the importance of vision. It will be the predominant point that I take home with me from this conference.

Beyond Relevance and Real World: Talking with Teachers About Engagement in Mathematics? — Dan MeyerPic Dan M

  • Big Take-Away = ‘Real World’ does not have to be real, just accessible and engaging.
  • 62% of teachers surveyed : Greatest challenge is “unmotivated” students. Interesting that they didn’t say motivating students was the challenge.
  • Question: Why don’t teachers spend more time developing good questions?
    Teacher Response: “Because we don’t have the time.” (True that.)
    Real Issue: “Lack of creativity. Giving the answers does not require creativity.” (True that, also, but ouch!)
  • A stronger option than the typical “engaging images or context” in a textbook: Redefine Real World. A situation is in the process of becoming real to you if you are able to … 

1. Ask a question about it.
2. Guess about it .
3. Argue about it.

High School Coaching Model: Building Bridges Between Coaching and PLC Culture — Kris Cunningham & Jeanette Scott (Phoenix UHSD)

  • Big Take-Away = Roll out PD through PLC teams.
  • New initiatives first unveiled during PLC team meetings.
  • Most powerful change agent was a lesson study. (1st day by 1 teacher, next day by all teachers)
  • Most teachers took 3-4 years to show change; 4 of 5 teachers showed significant change within 5 years.
  • There exists a Common Lesson Plan format for lessons studies and co-planning.
  • Professional Development certificates tied to evaluations. (i.e. Professional Growth affects evaluation outcome.)

The fact that teachers took 3-4 years to show change aligns with Maggie McGatha’s research shared at last year’s NCSM conference

Practicing the Five Practices: Coaching Teachers to Use Student Work in Planning  — Max Ray-Riek (Math Forum)

  • Big Take-Away = Walk teachers through the 5 Practices of Discourse with student work samples.
  • Max shared with us the Teddy Bear’s Banquet pattern problem. He had us determine the Math Goal for the lesson, and then Anticipate the student responses.
  • Max then offered 16 samples of true student responses (Monitor) and then had us Select and Sequence some of the responses for classroom discourse and share why. We were then asked to Connect the responses to the Math Goal.

This is a great training tool that can be brought into any PLC structure.

I also witnessed Max slyly counting on his fingers. This was his way of giving is all wait time on his prompts. 

Smarter Balance – Making Connections: Eliciting to Acting on Evidence —  Judy Hickman (Director of Mathematics, SBAC)

  • Big Take-Away = When the scoring focus is on Reasoning, students can still score full credit with a minor calculation error, if they show understanding.
  • Do NOT put too much emphasis on Interim Assessments. As “snapshots” they will give you good information, but it will be an incomplete assessment.
  • The authors of the exams were shocked that students answered so few questions correctly.

Four Keys to Effective Mathematics Leadership — Mona Toncheff & Bill Barnes  (Activating the Vision )





  • Big Take-Away = Vision needs to be created by ALL stakeholders
  • The Four Keys:

1. Establish a Clear Vision for Mathematics Teaching & Learning
2. Support Visionary Professional Learning for Teachers and Teacher Leaders
3. Develop Systems for Activating the Vision
4. Empower the Vision of Family and Community Engagement

This was the second of three sessions that spoke about the importance of vision. This one stressed the need to have all stakeholders (admin, teachers, classified staff, parents and the business community) in on the creation of the vision. Mona & Bill then asked, “If you were ask 10 people on your campus, ‘What is our vision,’ how many answers would you get?”

The Secret to Leading Sustainable Change: Vision, Focus, Feedback, and Action! — Dr. Tim Kanold (Turning Vision into Action )

  • Big Take-Away = Set the Vision, Help people advance the Vision,  Celebrate Evidence that the people are advancing the Vision, and take Action on the feedback towards the Vision. 
  • Sustainable change requires evidence that the change is bigger than their opinions.
  • Is the work you are doing formative? Meaningful feedback must be followed with results in action by the teacher or teacher team.
  • Meaningful Feedback = F.A.S.T. Action: Fair, Accurate, Specific, Timely. Action from your feedback is required.
  • Mary Beth call. Dr. Kanold told a story of when he was Superintendent of Stevenson HSD. He called a secretary at one of the schools, restated that ‘engagement’ was part their district vision, and asked “What does engagement look like in your job.” That’s keeping the vision in front of the people!
  • The Popeye Moment: Change happens when the moment of moral courage vocalizes what Popeye often said, “That’s all I can stands, cuz I can’t stands n’more!

This was the third of three sessions that spoke about the importance of vision. The story of calling the secretary is tattooed on my brain. Dr. Kanold stressed that the vision should be posted visibly during every PLC meeting, and that any unproductive dialogue can be redirected with the simple statement, “How does this conversation advance this vision?”

A Math Coaching Package — Donna Lione, Rebecca Williams & Chris Shore (Me) (Temecula Valley USD )


My colleagues and I presented the framework for developing a comprehensive math program. The details of each of the 8 components will be posted as separate posts.

  • Vision
  • Relationships
  • Humility
  • Influence
  • Passion
  • Faith
  • Focus
  • A Plan

Recap: NCTM 2016

San Francisco, CA , April 2016
I have summarized each session with some simple (•) bulleted notes, red underline to encapsulate my major take-aways, and occasionally a brief italicized commentary.

The Status Quo Is Unacceptable: A Common Vision for Improving Collegiate Mathematics Diane Briars, & Linda Braddy, Christine D. Thomas & Dr. Uri Treisman

  • Big Take-Away #1 = College failure rates are 55% higher than for more active forms of instruction.
  • Big Take-Away #2 = The math ed reform movement is now reaching the post-secondary level.
  • Big Take-Away #3 = The change must be institutional.

  • The challenge facing the Math Ed Community (the dismal stats)
    1) Only 50% of students earn A, B or C in college algebra.
    2) Women are twice as likely as men to not continue past Calc 1.
    3) While 20% of all Bachelors Degrees are awarded to Blacks & Hispanics, only 12% of Math Degrees are.
    4) Math is the most significant barrier to degree completion in ALL fields.
  • Innovation does not affect normative practice. Out of 81 different projects (2-3 yrs) connected to a grant or leader, NONE replaced normative practice, because they were based on faculty development, not institutional change.  Dr Treisman, “Institutional change is a bitch.”
  • Historically, school system does change when necessary.

The Learning Mindset Movement and Its Implications for Addressing Opportunity Gaps — Dr. Uri Treisman (The Dana Center)

  • Big Take-Away  = Besides Growth Mindset, there is Belonging Mindset and Purpose Mindset.
  • “I find Algebra beautiful, but will it knock the socks off of a 13 year old. Algebra well taught should leave them barefoot in the park.”
  • “Why do kids give up? Most of the work I do is confusing, cause no one gives me problems in the back of the book.”
  • Growth Mindset = “Can I do this?”
    Belonging Mindset = “Is this where I belong?”
    Purpose Mindset = “Does this connect to who I want to be?
  • Dr. Catherine Good:  Building Bridges to Belonging: Mindsets that Increase Participation, Achievement and Learning
  • Build Belonging through effort & engagement, not talent.
  • Positive Belonging Mindset = Assume they belong.
    Negative Belonging Mindset = Need to be invited in.

Paper Cup + Gust of Wind = Yearlong Rich Task — Peg Cagle

  • Big Take-Away = Revisiting the same task through-out the year emphasizes math as reasoning not simply answer-getting.
  • Peg had us roll a paper cup on its side. She then left us to our own devices to answer several questions, each of which addressed a different mathematical topic throughout the school year.
  • Day 35 Question: How can you convince a skeptic of the shape that the cup traces out as it rolls?
  • Day 70 Question: How can you locate the center of the shape that the cup traces out as it rolls?
  • Day 105 Question: How can you use a cup’s dimensions to determine the area of the shape it traces out as it rolls?
  • “Efficiency is overrated: That is a concern after you learn something.”

Coding to Enrich ALL Math Classes — Jason Slowbe

  • Big Take-Away = Coding in Math class helps teach the Math, not just the coding.
  • Coding can be done on the TI-Calculator
  • Can help students understand the meaning and power of mathematics. For example, Archimedes’ method for approximating the area of a circle.

Rich Problem Solving to Support Today’s Standards — Chris Shore (Teacher Created Materials)

I conducted a product promotion for Teacher Created Materials. The session was on Problem Solving and Linda Gojak’s What’s Your Math Problem Anyway? My presentation focused on the following questions about the teaching of problem solving, each of which I will answer in its own post:

  • What is problem solving?
  • Why teach problem solving?
  • Who should learn problem solving?
  • When should we teach problem solving?
  • How should we teach problem solving?
  • Where do we find resources for teaching problem solving?

Innovative math lessons you can use in your classroom today