I’ve given the book talk (by other names) a few times now, and I’m noticing some patterns of what’s really resonating. One small, but significant piece that’s fostering conversation is a section around Active Caring vs. Passive Caring. I’ve bloggeda bitabout this in the past, so feel free to check out those posts. There appears to be an appetite for this conversation to occur in schools. Feel free to use this chart as a starter set of active caring action moves.
One question that comes up is, “How do I find time to display active caring to each and every student?” A secondary teacher may have well over a hundred students a day, segmented into blocks of time possibly as low as 45 minutes. How is a teacher supposed to show active caring to every student every day?
The short answer is: you probably can’t. Let’s be real honest. If you have a tight schedule and a large student load it’s challenging, bordering on impossible, to take time out for every student every day. It’s a simple math problem: if a teacher has, say, 120 students and five classes of 50 minutes (250 minutes total), you can spend about two minutes per kid before even getting into the day’s lesson.
Rather than throwing up our hands and saying we can’t do it, I’d propose the opposite: we need to be structured, methodical, and intentional with our actions around active caring. Here are three suggestions for tackling this math problem.
1. Make a list.
Print out a class roster and with days of the week and record when you’ve had an interaction you’d classify as one of active caring. If you have a good memory, you could even do this at the end of the day or after a hald-a-day. Try to get around a quarter of your students every class period. That way, by the end of Thursday, you can see which students you have yet to have an active caring interaction with and you can make sure to be intentional on Friday. Keep yourself accountable to showing each student active caring no fewer than once a week.
2. Build in structured personal check-in time.
As students are working, build in, say, five to ten minutes where you are not answering questions about the assignment, but are rather floating and checking in with students. Be disciplined about it. Set a timer if you need to. Depending on the length of your class period and the way your day’s lesson is structured, consider whether you want to block off this time toward the beginning, middle, or end of the class period (or possibly bookending the class period).
3. Work as a staff or grade level team to identify personal connections
I’ve seen a few staff, department or grade level teams do this.
Print out the name of every student and place them on the wall around the room. Teachers place a sticky dot by every student they have a personal connection with. Look for patterns and anything (or anyone) that stands out. This can help a school know which students might not be receiving the level of care that we’d hope. It can prevent students from falling through the “care gap.”
What are some of your strategies for ensuring you are demonstrating active care for all students?
Chris and Melissa gave a great talk on the importance of mathematical play at NCTM-Seattle last week. You can see their Math-on-a-Stick work on their website. There you can see pictures and examples and of children enjoying and playing with math in interesting and delightful ways. One of my many takeaways from their keynote was that play is math and math is play. In their talk, they referenced research that lays out seven attributes of play. Play (a) is purposeless, (b) is voluntary, (c) is inherently attracting, (d) involves freedom from time, (e) involves a diminished consciousness of self, (f) has possibility for improvisation, and (g) produces the desire to continue.
When I saw the mics set up I A) assumed there were going to be questions and B) just knew one of the questions was going to be “but what about older kids?” Sure enough, there was a question about how adolescents might play with math. The premise – which I kind of (but not entirely) disagree with – was that older kids wouldn’t be engaged by things like pattern machines, tiling turtles, and Truchet tiles. Chris and Melissa gave good answers about the age band of the kids of math-on-a-stick and spoke to the non-zero amount of older kids, but I’d like to offer a few examples of older kids playing with math. Unfortunately, I didn’t take as much time playing with math as I should have as a teacher. So I’ll share a few ways I and my kids play with math as regular ol’ humans.
Me: Baseball Prospectus and Sabermetrics
I was trying to think of the first time I played with math post-pubescence. I was such a baseball fan in high school, partially because the Cleveland Baseball Team was quite excellent at the time (despite not having any rings to show for it), but also because of stats. I began reading the great baseball writer and sabermetrician, Rob Neyer. I began organizing various baseball reference spreadsheets. I felt like I was finding out secrets of baseball that most managers (and fewer commentators) knew. Things like “on-base percentage is more important than batting average” and “home runs yielded are a better predictor of future pitching success than other categories.” This secret information yielded by mathematics helped me understand the game while also helping me win my fantasy league to boot. (Note: I’ve written a bit about this before.)
My daughter (age 13): Animation
My daughter is a phenomenal artist. She draws all day, every day. If there is a Gladwell-ian 10,000 hours rule, she eclipsed that at least year ago. She likes to create animations, frame-by-frame. Moreover, she likes to animate to music. She plays with math by timing out the different scenes in a potential song and crafts them into a music video.
My son (age 11): Scorigami
Scorigami is a concept created by Jon Bois, a content creator for SB Nation. A scorigami is a final score of an NFL game that has never occurred before. For instance, the score of seven to eight has never occurred before. Were two teams to end up with that final score, that would be a scorigami. Because of the interesting numbers and combinations of numbers that occur in a football game, many scores have not been achieved in an NFL game. Scores in football come in 6 (touchdowns), 3 (field goals), 2 (safety or two-point conversion after a touchdown), or 1 (extra point, but that has to come after a touchdown, 6).
For instance, there has never been an 18 to 9 final score. There has been an 18-10 final score, but never 18-9.
Every Sunday we watch football and keep an eye out for potential scorigamis. Once it gets to the fourth quarter and we’re looking at, say, a team with 11 points, we’re in scorigami red alert mode. My son plays with math by keeping an eye on the scorigami grid, including the density map, to identify how scores could occur throughout the Sunday games.
Here are a few more rapid fire examples of mathematical play I’ve seen or experienced from adolescents:
Google Sketch up
Messing around with pascal’s triangle
Games of chance
What about you? What have you seen or done that might constitute as mathematical play that secondary kids might be interested in?
Update (12/6): Within hours of publishing this post, my son had an idea for mathematical play (he did not call it that).
Mario Party is a video game for the Nintendo Switch. It acts essentially as a board game with little mini-games throughout. Characters roll dice and move around the board collecting things. What’s interesting and made this ripe for mathematical play is that each playable character has a different die. They all have six sides, but have non-standard values.
For example, the six values for the Luigi die are 1️⃣1️⃣1️⃣5️⃣6️⃣7️⃣. The six values for the Peach die are 0️⃣2️⃣4️⃣4️⃣4️⃣6️⃣. You can also have dice that give you coins instead of moves for some rolls. The goomba dice yields +2 coins, +2 coins, 3️⃣4️⃣5️⃣6️⃣.
For seemingly no reason at all, my son decided last night he wanted to tabulate the average (mean) values to determine the best character die. He also assigned commentary (“high risk, high reward”) to the dice. I do not know how he factored in the coin values.
He then sorted the dice into tiers – really good, okay, and bad based on the mean rolled value.
Why did he do this activity? Well, he’s not allowed to have screen-time during the school week, so this might have been his way of coping. But regardless, it was generally pointless, which, when it comes to mathematical play, is essentially the point.
This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.
As we stand on the balcony and gaze out at our own version of the MCU (Math Class Universe) that consists of Routines, Lessons, Problems, and Projects, we must be sure we’re not missing the crucial ingredient that stitches it all together: caring. More specifically, active caring.
Many, if not most teachers demonstrate passive caring. Such teachers show a general, blanket kindness to their students. They’re open to students’ questions. They typically like their students and certainly don’t show unkindness. Often, the student-teacher relationship hinges on the student’s academic aptitude or natural charisma. A teacher might have a decent relationship with all his students, but truly special relationships only with students who excel in their classroom or have otherwise magnetic personalities.
A teacher who is actively caring cares for each student as an individual and views each student as a mathematician. He reaches out to students individually, not broadly. Consider the difference between “if anyone needs help come and see me” versus going to each student to see if they need help. Think of the difference between welcoming the class all at once versus greeting students individually, by name, at the door. These individualized acts of kindness and care are as essential as the task at hand – the routine, the lesson, the problem, or project. Well thought out curricula and tasks are nice, but active caring will ensure that they land for each student in your classroom. Active caring often involves a disruption of social or academic norms: students who typically don’t engage in math receive the same level of care as students who do.
To be sure, active caring is a challenge for a teacher who may see upwards of 100 students a day (or more). It’s difficult to get around to each student in such a compressed amount of time. Don’t beat yourself up if you’re unable to. But make an achievable goal: perhaps every two days you’ll have a personal conversation or check-in with each student. It’ll require a level of intentionality that might seem forced at first. You may have to print out a class roster and check off your interactions with each student as they come. But in the end it’s worth it. An excerpt from a, uh, certain book:
Briana is a 10th grader, talking about her middle school math experience. “I was invisible to the teacher,” she begins. “I always got my work done. I never got in trouble. I would raise my hand to ask a question but my teacher would never call on me. It got to the point where I would ask my friend to ask a question for me so I could get something answered.” Briana is soft-spoken, but clearly motivated. It’s tragic and understandable how she would feel “invisible” to her teachers. In the hustle and bustle of a noisy middle school classroom, soft-spoken students get short shrift.
Recently an administrator I know took part in a “shadowing a student” challenge, in which the administrator identified a student and followed her around for an entire day. From the moment she got off at the city bus stop in front of the school until the moment she got back on it at the end of the day, the administrator followed the student around to each class, every passing period, even lunch. Debriefing the experience, the administrator was stunned by how little teacher-interaction the student received. Other than a greeting here or there, the student received few words from her instructors.
Shy students, or students who don’t have as much academic status, or who are still learning the English language can easily become invisible in a school day, for weeks at a time. Make sure this doesn’t happen. Try some of these strategies:
Document your interactions with students to ensure you’re having conversations with everyone.
Demonstrate vulnerability by sharing details from your personal life.
How do you demonstrate active caring for your students? Let us know in the comments.
Your daily classroom has a lot of moving parts. I’ve attempted to categorize those parts into Routines, Lessons, Problems, and Projects, acknowledging that these are imprecise buckets and you might go between them several times throughout a day. Holding these all together is an atmosphere of active care for each student.
As you think about the upcoming school year, which of these are you curious about? Which do you want to get better at? Do you want to try a project this year? Would you care to create an assessment structure of using “Portfolio Problems” for students’ portfolios of understanding? What’s the right ratio of routines, lessons, problems, and projects?
In addition, what will you do in the first couple weeks of school to demonstrate active caring? How will you touch each student and make sure they’re welcome at the table of our oft-uncaring discipline?
I hope you enjoyed this mini-series. As much as anything it was a think-aloud for myself to wrap my head around all the different ways of being for a math class. I may update the posts going forward as new resources come across my radar. As always, feel free to share insights and ideas.
This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.
I graduated high school twenty years ago this year. What’s remarkable is how little I actually remember about my classes. I remember certain feelings I had towards particular teachers or classes, but not the actual classroom action itself. There are three exceptions. There are four distinct activities I remember from my classes and they’re all projects:
In my combined Physics/Calculus course we divined the accelleration due to gravity based on an experiment me and Eric Durbin concocted. And we were pretty close! We’ll call this theLearning Project.
In AP Stats we conducted soil testing and surveyed the neighborhood to determine whether they cared about this issue. We’ll call this Project-Based Learning.
In English we had to recreate various scenes from The Lost Horizon. We’ll call this the Dessert Project, for reasons which will become clear.
In Biology we had to collect a bunch of leaves. I don’t remember why, but we had to do it. We had to get certain kinds press them is a special way. I hated it. We’re not calling this project anything other than The Leaf Project
That’s it. That’s all I remember about my classwork in High School. Don’t get me wrong: I remember other stuff too, like that time the time my friend Ash was talking so the teacher made him get up and teach the class,I recited “Shaft” in English class (“Who’s the black private dic that’s a sex machine to all the chicks?”), and my creepy Algebra 2 teacher making about ten too many jokes about “french curves.”
But by and large I remember the projects. Don’t get me wrong, there’s other stuff in there. I graduated college and everything, partially with some knowledge I acquired in school. But I only remember these actions.
Projects are an opportunity to illustrate how crucial your discipline is to the world or our understanding of it. They’re also an opportunity to waste several days or weeks of class time and force students to jump through imaginary hoops concocted by the teacher. In both cases, students will remember.
Projects apply mathematical knowhow to an in-depth, authentic experience. A project occurs over the course of two to four weeks. Ideally, projects are outward facing, community based, and/or personally relevant to students.
Let’s take a look at three types of projects. As with this entire mini-series, I’m painting with a broad brush and I’d happily concede that what I call one thing, might actually be another in another’s eyes.
The Dessert Project
I’ll withhold why it’s called the “dessert” project for now. These are typically given at the end of a unit intended to sum up the content. These often occur as a retelling of the content, such as my Lost Horizon example above. We read the book, we identify crucial scenes, and then we reenact them. We’re barely doing any analysis, let alone synthesis.
The best Dessert Projects take what a student has learned and unleashes it on an appropriate real-world scenario. Now that we’ve learned the content, we’re going to see how it looks in a different context. Most end-of-chapters offer this kind of project.
The Learning Project
In a Learning Project, we learn something germane to the topic at hand through the use of an in-depth investigation. The structure of a Learning Project is more-or-less dictated by the teacher, but there is enough agency awarded to the students to experiment on their own. The WHY and HOW are often provided and the WHAT is relatively self-contained.
In my gravity example above, we were given the task (calculate the accelleration due to gravity), the materials (a video camera that allowed you to fast forward one frame at a time – this was the 90’s mind you), and the format of the product (a lab report). We had
It was a deeply memorable and engaging task. Unlike Dessert Projects, we are asked to actually find out something new, rather than repackaging information. Despite the fact that Learning Projects may not have a community partner, a public presentation, or a shiny final product (ingredients of Project-Based Learning which we’ll get to in a moment), we construct or deepen our understanding of some new knowledge or knowhow.
I’d suggest these as other examples of Learning Projects:
PBL has gotten the most headlines lately. Schools across the country want to provide deep, authentic, and motivating experiences for kids in all subjects. And to be sure, the best of PBL absolutely achieves that. Students are given a open ended, authentic challenge and students develop and present a solution. Through this process, students acquire new mathematical knowledge and skills.
In PBL (like Problem Based Learning), the task appears first and necessitates the content. Students learn the content in order to achieve their final product. Often – if not always – PBL occurs in groups.
But don’t be fooled: quality PBL entails a lot more than just giving the students and letting go of the process entirely. The teacher/facilitator crafts the daily lessons and activities to support the process. The following graphic is taken from the New Tech Network, my employer. It explains well the various phases of a project and a menu of options for lessons, activities and assessments throughout a project.
The project launch occurs at the beginning of the unit. It kicks off and drives the unit. In this case the project is the “meal” as opposed to the “dessert” (recall from early Dessert Projects). The project is how students will learn the material.
Project Launch: Have students read the Entry Document (the letter) and collect “knows” and “need-to-knows”.
To the students of Akins New Tech High School,
The US presidential election of November 7, 2000, was one of the closest in history. As returns were counted on election night it became clear that the outcome in the state of Florida would determine the next president. When the roughly 6 million Florida votes had been counted, Bush was shown to be leading by only 1,738, and the narrow margin triggered an automatic recount. The recount, completed in the evening of November 9, showed Bush’s lead to be less than 400.
Meanwhile, angry Democratic voters in Palm Beach County complained that a confusing “butterfly” ballot in their county caused them to accidentally vote for the Reform Party candidate Pat Buchanan instead of Gore. See the ballot above.
We have provided you the county-by-county results for Bush and Buchanan. We would like you to assess the validity of these angry voters’ – and therefore Al Gore’s – claims. Based on these data, is the “butterfly” ballot responsible in some part to the outcome of the 2000 election? What other questions do the data drum up for you? And what can we do to ensure this doesn’t happen again?
We look forward to reading your analysis and insight, no later than May 5.
Your county clerk
Example project pathway – the 2000 Election
In this example, we still retain many of the lessons and workshops that we would typically teach during this unit, but notably they occur as students are working towards various benchmarks and the final product. The lessons inform the student products.
There is enough to write about PBL to merit its own miniseries. Structures and routines are crucially important in a PBL Unit. Assessment must look different. Managing groups becomes an entirely different challenge. How the authenticity of the product and the external audience enhances the quality of student work.
For now, here are some other tasks that adhere to PBL.
The genesis of this entire mini-series stems from questions I receive about Problems and Projects. Mainly, “how often should I use problems? How often should I use projects?” The unstated part of that question is, “when do I actually, y’know, teach?” (Actually, sometimes that’s stated). I’ll save another post for “putting it all together” or “adjusting the levels” but know for now that’s why I put together this framework of Routines, Lessons, Problems and Projects.
As for the “how many projects?” question, I’ll give a squishy answer and a non-squishy answer.
My squishy answer: design a project whenever (A) the standards uniquely align such that you can create multiple lessons around one scenario and (B) when you can identify a project scenario that will maintain momentum over the course of several weeks.
My non-squishy answer: One or two a year. Most standard clusters don’t lend themselves to multiple investigations around one, single context. But some do! Content clusters around things like Data and Statistics, Area and Perimeter, and Exponential Growth and Decay are ripe for real-world scenarios that can be analyzed through the lens of multiple content standards.
As challenging as it is to design and facilitate projects, and as little time we have as educators to carve out the time for it, we don’t want to deprive students of the real-world insight math can have. We want to provide these experiences that will live on in students’ minds as the power of mathematics, whether or not they go into the field. So be on the lookout. Look for news articles and community opportunities that might embolden students to use math for maximum impact.
Until recently, I would have classified myself as a “happy” person. Now I’m not so sure.
Every day when I or my wife picks up my son at school there’s a 50/50 chance he’s in the counselor’s or principal’s office because he hates himself for something he did or didn’t do. When something – anything – negative happens, it’s a flip of the coin. Sometimes he’s able to slough it off. And sometimes, he goes into a complete and unstoppable downward spiral. He says he’s the “worst person in the world” or the “dumbest person in the world.” Neither of those things are true, nor is he receiving that message from anyone at home or at school (who have gone above and beyond trying to make emotionally safe accommodations).
So all day I’m on edge about 3:08pm, when his class lets out. Will I see my son bounding out with joy, ready for a rollicking afternoon of fun and games? Or will I see that grimace on his teacher’s face when we make eye contact which tells me everything I need to know about how the next few hours will be?
I check my inbox constantly, anxiously just waiting for that email to show up with the subject matter that simply states his name or something foreboding like “Today…” with my wife, his teachers, his counselor, and his principal all cc’ed. Once that email hits, or once I see his school on the caller ID, the rest of the day is over. It’s time to go pick him up early because he won’t be rejoining the class and he’s unsafe at that point. (I just checked it again.)
It’s not easy to enjoy things when your brain is occupied with such concerns. It’s very difficult to work in a profession that requires social interactions. It’s hard to do much of anything – go out to lunch, exercise – when a significant part of your brain is wondering “Is my son wanting to hurt himself right now?”
When people ask how he’s doing, my answer is “good,” because there’s a good chance that yes, at this very moment, he’s “good.” So it’s technically, possibly not a lie! But he’s not good. He struggles with mental illness in a way that we are all unprepared for. That I am unprepared for.
Thankfully, by dint of never seeking medical attention for myself, I have a fair amount of money stored away in an HSA, which I will be using to attend to my own mental health as I start therapy this month. Even after just two sessions, I feel better equipped to manage my own emotions and responses to challenging situations. Even just talking openly and getting acknowledgement of how goddamn hard life can be has been helpful. And hopefully with hard work it’ll get better.
So I guess I should end this blog post with a Point of some sort. So it’s this: consider whether talking through your anxiety / stress / struggles might help. Really consider it. If you have HSA dollars, use ’em. If you have free counseling sessions associated with your work (as my wife did at her previous job) use ’em. Or seek out a therapist that works on a sliding scale if the price point is challenging (which it truly is! Side note: my insurance will pay through the nose for medication and zilch for therapy, which is both dumb and Another Story).
Don’t try to go through things alone. Don’t bottle things up. Talk to your school counselor. Talk to a therapist. Talk to a pastor. These people are great at what they do. They’ll help you feel better about what you do too.
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.
When I was a kid, we had this super high-tech board game called Stop Thief!. The gist was this: someone committed a crime somewhere on the game board, which was rife with jewelry displays, unattended cash registers and safes. Your job as the detective was to identify where the thief was. The location of the thief was tracked by a phone looking device that calls to mind those old Radio Shack commercials with car phones. After each turn, the invisible thief would move some number of spaces away from the crime scene. The phone made these noises indicating where he could be – opening a door, climbing through a window, breaking glass. Based on these clues and the number of turns that elapse, you’d try to identify where he was.
Fast-forward a few years. We all remember this scene from The Fugitive:
These are the artifacts that were going through my head as I designed this lesson, linking the pythagorean theorem and equations of circles. In it, students must overlay a circle to establish a “perimeter” (side note: shouldn’t Tommy Lee Jones have used the term “circumference?”).
While this task only starts from the origin, you could quickly modify it to have other starting points, which would allow students to explore what the equation of a circle looks like when you center it wound non-origin points. I’d expect that to occur the next day or later in the lesson as part of the debrief.
Feel free to tweak it to make it better. The desmos graph is linked below, along with a couple word handouts.
(Note: a version of this task will appear in my forthcoming book from Stenhouse Publishers, Necessary Conditions.)
The set-up: a crime has been committed and it’s up to the students to establish a perimeter based on how much time has elapsed. After using the pythagorean theorem a few times to identify buildings the thief could be hiding in.
Given the time that’s passed and typical footspeed, the criminal could be anywhere up to 5 kilometers from the crime scene.