emergent math

My son attends an “open concept” school, a term that belittles the potential for such learning space. Before he started attending that school, I had heard of “open concept” as a fad that passed through schools in the 1970’s and fell out of fashion due to their unwieldiness. I had an image of two hundred students corralled in a gym-like room with their teachers trying to shout over the hundreds voices reverberating off the walls.

First off, that image is woefully misrepresentative, at least at my son’s school. Each “pod” has two grade levels in it. And even each pod has enough physical distance and visual blocks between the grade levels that there’s never really an issue of noise. In fact, the first thing that struck me when I was touring the school a few years ago was how quiet it felt. The students in the “open concept” school were much better at regulating their voices and being aware of their peers needs than in a smaller classroom with fewer students.

But that’s not the biggest boon offered by this open concept – as realized by my son’s school. The biggest boon is that teaching is a team approach at this elementary school. Each grade has 50 students with two professional instructors. While each student technically assigned to a home teacher, the day is fluid.

When you have two teachers teaching 50 kids, rather than one teacher teaching 25, it opens up endless possibilities for small group workshops, differentiation, and enrichment. One teacher can work with a handful of students while the other teacher can facilitate the rest of the grade. If one teacher is passionate about, say, Science and the other Social Studies, they can utilize their particular teaching strengths or passions. The two teacher divide and conquer certain subjects and certain concepts. By having the same room, their planning time is more natural and organic.

Even more than the logistical, technical, and pedagogical advantages of a team teaching approach for elementary school is the assurance that there is nearly always an adult in the room who knows every student on a deep level (and vice versa). Substitute teachers were always difficult for my son to handle: they don’t know the rules, they’re not following the schedule, and so on. Now, even when one teacher has a substitute, with rare exception he can make eye contact with the other teacher that knows him well and how he struggles in certain environments. If one teacher needs to go to an IEP meeting, the class doesn’t get put in “time out” or “baby-sitting mode.” If a kid is having a melt-down one teacher can take him or her aside without pausing the entire class.

I realize it’s not possible for schools to employ team-teaching. The numbers have to work out kind of nicely, with the number of teachers-per-grade being even. The physical space needs to be amenable to such a work space. The teachers require a level of professionalism and trust that isn’t as necessary when everyone is siloed. But it works at my son’s school and it works for my son. Every day he knows there will be someone in the class who knows him, and he never goes a day without seeing friends from previous years.

At some point this year (2018), I’ll have a book for you to read from Stenhouse that proposes a framework for effective math classrooms. These are the three broad ingredients that create a successful math classroom as well as how a student experiences math. They are:

• Academic Safety – the social/emotional state of a student and her self-regard as a mathematician
• Quality Tasks – the thing that students are doing, working on, and/or creating
• Effective Facilitation – the short- and long-term moves that promote mathematical thinking and sensemaking

Every successful math classroom I’ve been in has each of these three hallmarks in spades. In fact no successful classroom I’ve been in hasn’t had each of these hallmarks working for it. They’re our necessary conditions for great classrooms.

They work independently and in concert and can be the lens through which we can better understand classroom issues. Let’s take a common issue of unproductive or inequitable groupwork. Effective strategies will tackle one, two or all three of these elements. Let’s use this framework to better understand the issue, before we jump into the solution.

Is the issue one of Academic Safety?

Students may not be engaged in groupwork if they self-identify as a “non-math person.” It’s possible they’re only living up to the social academic status they’ve been given. How do students see themselves as mathematicians? Do they see themselves as mathematicians? Do their peers see one another as mathematicians? If so, how so? Are they publicly acknowledging the mathematical smartness of their peers?

Is the issue one of Quality Tasks?

I’ve been in classrooms where the issue around groupwork began with the fact that students weren’t being assigned groupworthy tasks. If you’re going to require an assignment occur in a group setting, the task ought to require (or at least be enhanced by) groupwork. Tasks are often developed for individuals but assigned to groups.

Is the issue one of Effective Facilitation?

How was the groupwork time introduced? Did you just assign the task and say “go” or did you have a structure in place? Do students have specific and understandable roles or is it the onus of the student to figure out where they fit into the groupwork dynamic? What norms are present in your classroom (and no, not the norms that are on the wall, but the ones that are actually present)?

Once we start to answer some of these questions, we might be able to better identify potential solutions. Maybe the classroom needs defined group roles. Maybe a norm of “same problem, same time” needs to be enacted. Maybe tasks need to be developed to push students deeper into the math content. Or maybe it’ll generate additional questions or additional need for understanding the issue at hand.

And as I mentioned, it’s possible (probable) that issues will bleed between our three pedagogical elements. Certain tasks can reinforce messages about mathematical self-regard. Unstructured groupwork can reinforce issues of academic status. It’s messy work, this teaching. Hopefully this framework will help you better understand the complex dynamic of a classroom ecosystem.

“I don’t know what to say.”

“I don’t know how to talk to him.”

I’m sitting in a coffee shop with my back facing a mentor and her mentee, a college student who is apparently struggling through her semester. I can hear them clearly, even though I’m trying not to eavesdrop. The mentor is pleading with her mentee to email one of her professors to get help with an assignment, or even figure out when office hours are. “I don’t even know what to say!” the student response. The mentor patiently describes what questions to ask and how to start off the email, to no avail. “I don’t know how to talk to him!” she keeps responding. Pretty soon the student starts doing that thing that teenagers do where they start laughing when they’re really uncomfortable . It’s an unintentional defense mechanism employed by nearly all adolescents. She’s embarrassed by her inability to perform a seemingly simple task, so she starts blushing and laughing.

“I don’t want to talk to someone else.”

“That sounds like so many words.”

Later on, the mentor is trying to get the mentee to call the registrar’s office to find some information about something or other. Again, the student giggles that she doesn’t know how to talk over the phone. The mentor clearly cares deeply for her mentee. The mentee is clearly embarrassed at how nervous she is communicating to professionals.

***

Teachers sometimes scoff when we implore them to teach those other things. Things like communication skills, groupwork skills, self-reflection, these are “soft skills” that don’t appear in our scope and sequence. The state test doesn’t address them, and we have too much content already to cover to worry about these phony-baloney skills. I’m a math teacher, I teach math, that’s what I do. That’s my responsibility.

I can’t speak to the mentee’s instruction, but I’ve seen it frequently enough. Listening to her, she was paralyzed when it came to communicating with other adults, or at all. This is something she did not learn, let alone practice, while in High School. And now it’s preventing her from succeeding at the post-secondary level. Her paralysis wasn’t that she didn’t know her content well enough, it was that she didn’t have the ability to find out how to further her content knowledge. Whether that was technically the purview of her secondary math teacher or not, the responsibility to prepare students for post-secondary life falls on each of her teachers and the system in which they teach.

Does that mean that it is your responsibility – as, say, a math teacher – to teach students how to make phone calls? Or email professionals? Or create a study group? Or manage their time? Or teach all of those non-math skills?

Yes. Yes, it is.

The reason I taught math was because I love math. The reason I taught math the way I did was because I wanted students to grow as communicators and problem-solvers. Thankfully, I taught in a school in which we were unified that these were indeed skills we wanted our students to have when they graduated. I now coach in a model that aspires to make that happen for all students.

In our classrooms, we have students call and set up meetings with mentors in the business or academic communities. We have students stand and defend their work. We assess students on eye contact as well as content knowledge. And we teach them how to do it, not just tell them to and let them flounder. We do these, not in isolation, but as an entire school. In my class, this included these activities, as well as complex math problems that required collaboration, presentation of new and novel ideas, and practice and structures to handle it when these proved exceptionally difficult.

***

I’m heartened by these mentor-mentee relationships. Whether they were established via a specific program or they grew organically, there’s genuine care there. As exasperated as the mentor was, she showed active, authentic caring. I’m glad the mentee has that support system in place now that she’s in college. She’ll need the skills her mentor offers, as she clearly didn’t receive them in High School.

Vivienne Malone-Mayes grew up in Waco, TX, a highly segregated community in a highly segregated state. She attended a highly segregated high school where she graduated two years early at the age of 16 so she could pursue Mathematics at Fisk University, where she graduated in four years with a bachelor’s’ degree and another two years with a masters’. She worked as a professor at Paul Quinn College and Bishop College.

In 1961, she applied to take additional courses to begin her PhD work at Baylor University – my alma mater – but was rejected explicitly for her race. Required by federal law, the University of Texas admitted her (Baylor is a private university). Though she was admitted, she was not welcomed. “My mathematical isolation was complete,” she noted as she described her experience being the only female and the only African-American in many of her courses*.

Despite these challenges, Malone-Mayes obtained her PhD in 1966 with her thesis A structure problem in asymptotic analysis. Throughout her education she took part in civil rights demonstrations.

After she graduated with her PhD, she became the first full-time African American professor at Baylor University, the institution which had rejected her from taking courses just a few years prior. There she was voted the most outstanding faculty member by the student congress in 1971.

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This is an excerpt profiling mathematicians from my forthcoming book. It’ll be in the appendix along with other famous mathematicians and should-be-famous mathematicians.

I say “should-be-famous” because I’d never heard of Malone-Mayes. And I graduated from Baylor University, where she was rejected from taking classes because of her race and later a high profile university professor. I lived in Waco, TX for four years.

Part of the reason I’d never known Malone-Mayes was because of my own stupidity and probably-desired ignorance. But it’s kind of also on the University, isn’t it? I would have liked to have known of the achievements of this incredible woman while I was there. My classmates would have as well.

Why isn’t a fucking building named after Vivienne Malone-Mayes? Again, maybe things have changed since 2008. I’m sure there is a plaque somewhere on campus while I was attending, but I feel such shame for not knowing about Vivienne Malone-Mayes then and up until just a few days ago. I encourage you to look for what mathematical heroes may have been buried in your community. Please share them in the comments so we may unearth this invaluable, generally unspoken history and these amazing men and women.

For more on Malone-Mayes, I recommend this article from the Waco History Project, where the photo is taken from. See also, Complexities: Women in Mathematics.

*Case, Bettye Anne; Leggett, Anne M. (31 May 2016). Complexities: Women in mathematics.

I’m just not good with names: It takes me a long time to remember them and even then I sometimes forget. 

Not anymore. For you are the Name Rememberer. The One Who Remembers Names.

It’s difficult with so many students. These first few months of school it’s hard to get names straight. I’m not a names person. 

It matters not. You will remember their names, Name Rememberer.

I’ve never been good with names. I can remember a face, but names are hard.

Maybe names are hard, maybe they are not. It doesn’t make any difference to you, the Name Rememberer.

I’ll get their names by the end of the month. It’s October, there’s still plenty of school year left.

You will get their names by tomorrow morning 8am. If this means you need to print out flash cards that is what you will do. If it means you need to find their address, drive to their house, wake their house up, and have a 30-minute conversation to remember their names, that is what you will do. That’s what the Name Rememberer does.

But I don’t know their addresses and I don’t have a car.

For every student that is in your class tomorrow whose name you do not know, you will give them free 100’s on assignments for a month. You will give each of them $100 a day until you remember their name. You will do 50 pushups for each student whose name you can’t immediately recall. And you will NOT under any circumstances make that face where you’re trying to think of their name.

But I have these kids that sit next to each other and they really look alike. What if I —

QUIET! You will learn every student’s name and you will learn them all now. Tomorrow morning you will stand by your door, greet each student BY NAME, and welcome them in to your classroom BY NAME.

But – 

SILENCE. You are wasting valuable time, Name Rememberer. Time that could be spent on remembering students’ names. The school day starts in 10 hours and you have names to remember. Or, as the Name Rememberer, do you have them all memorized? You have the proper pronunciations down seamlessly? First and last? There will be no beat skipping when you want to call on a student with his or her hand raised? 

Good. For tomorrow, you – in addition to being the Student Name Rememberer – will also become the What Students are Passionate About Knower. 

I had the honor of co-designing and MC’ing the first ever PBL Chopped competition at the New Tech Annual Conference in July. While this is typically a blog about math instruction, this experience welcomed all content areas and all grade levels, teachers, principals and instructional coaches. It was an absolute blast and the teams were incredible. It’s so fun to be an observer to this cross-curricular design sprint. Below is a recap, followed by a link to additional resources and commentary – geoff

ST. LOUIS, MO — The only thing more intense than the current of the Mighy Mississip was the sweltering PBL Kitchen. Eight teams entered the Steelcase room on an overcast Saturday afternoon hoping to design the “tastiest” of projects based on three mystery “ingredients.” These ingredients came in the form of three randomly selected standards from across the curriculum.

Each team had 20 minutes to design the outline of a PBL unit based on the following standards which were drawn at the time of the competition.

• Natural selection leads to adaptation, that is, to a population dominated by organisms that are anatomically, behaviorally, and physiologically well suited to survive and reproduce in a specific environment. (HS-LS4-3),(HS-LS4-4)
• Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. (CCSSM.A-CED.A.4)
• Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. (CCSS.ELA-LITERACY.RH.6-8.7)

As soon as the standards were drawn, the first round of the competition began in a flurry of ideation and activity. Teams scribbled on whiteboards provided by Steelcase. Participants. The end of the 20 minutes was punctuated by a “3…. 2….1… Markers down! Cooking time is over, chefs!” Exasperated from the intensity, participants – teachers and principals alike – let out a cry of triumph. While the design of a PBL Unit – with carefully selected and uniform standards – can take hours, competitors had come together to create an engaging, meaningful project in 20 minutes.

Sadly, only three teams could advance to the final round. This proved to be the most difficult part of the competition – for the judges. After some deliberation, looking through the eight project ideas, they identified the three projects that allowed their creators to advance to the final round. At this point, standards were drawn again:

• ELA: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
• SS-Geo: Use geospatial and related technologies to create maps to display and explain the spatial patterns of cultural and environmental characteristics.
• Sci: The complex patterns of the changes and the movement of water in the atmosphere, determined by winds, landforms, and ocean temperatures and currents, are major determinants of local weather patterns.

As before, 20 minutes flew by in a flash and the three teams developed PBL Units that would be uniquely engaging and meaningful to their students. They presented to the judges who asked them critical questions to get a sense of the scope of the project and the team’s understanding of the project.

After two rounds of high pressure, minimal time PBL design one team was left standing. The judges – after much deliberation and pained conversations – came to the unanimous conclusion that Scottsburg New Tech‘s final project was the one to take them over the finish line. They were announced as the winners at the next morning’s plenary session.

But while Scottsburg got to take home the lovely 2017 NTN PBL Chopped Trophy (which we can only assume is currently being prominently displayed in a proper trophy case), everyone who competed won something. Some teams walked away with a greater understanding and empathy for teachers of other disciplines. Some teams walked away with a greater camaraderie with their peers. Other teams walked away with an actual project that they promised to refine and implement in a cross-curricular experience.

So congrats are in order to the winner, Scottsburg New Tech, but given the creative explosion in the Steelcase room on that Saturday afternoon, congrats are also in order to the thousands of students who will benefit too, from PBL Chopped 2017.

(Note: in addition to the recap here, you can find additional information, commentary, and details on the New Tech Network blog. [link coming soon!])