What Really Matters in My Math Classroom (Jerry Brodkey)
Jerry Brodkey has been a public secondary school teacher since 1975, and has taught most of the subjects in Social Studies and Mathematics. He has also taught for years in private schools. He now teaches remedial algebra and Advanced Placement Calculus. His undergraduate degree was from Rice University (BA 1974), and has graduate degrees from Stanford (MA 1976, Ph.D. 1987).
He has written guest posts for this blog on “smart” boards and stress on high school students.
A few days ago I was sitting watching my 8th grade math students graduate from middle school. I like to sit off to the side at each graduation, listening as each student’s name is called, thinking of each as an individual, seeing each for perhaps the last time.
These students, and all students, have been through too much these last three years – three years of disrupted life and education. The pandemic, covid tests, masks, fear, social isolation, anxiety, over a full year of zoom learning, social media, hurtful texts, economic disruption for their families, inflation, college admission worries (yes, even for middle school students), George Floyd, January 6th, the Ukraine, Buffalo, now Uvalde.
It is amazing they are graduating and moving forward.
I’ve been teaching for a long time. I started in 1975 and taught in public high schools until 2015. I retired for one year, missed teaching, and then found a wonderful nearby middle school where I’ve now been for six years. Even after almost fifty years, teaching continues to be challenging, exciting, and intense.
There is so much discussion and debate over math education. What really matters, what makes a difference? After all of my years teaching it continues to get clearer and clearer to me.
Achievement matters. Each student needs a basic understanding of mathematical ideas. Each student needs a strong foundation, not only for artificial reasons like college applications and success in schools, but more importantly for understanding an important part of the world. How can complex problems be broken down and solved? What does information and statistics tell us? What does it mean to prove a theory or hypothesis? What ideas and insights from the past help us solve today’s challenges?
Parents and students worry about math grades and acceleration. I repeatedly tell them learning math is not a race. The key is to build a strong foundation and create a desire to keep learning.
I tell students and parents there is no magic in learning math. I’m pretty traditional. I tell parents and students: To achieve real success – Have excellent attendance. Do all your homework. Ask questions. Get help fast.
What doesn’t matter? The choice of textbooks doesn’t matter much to me. Most are good enough, none perfect. If I don’t like a problem set or how a topic is presented, I’ll choose another approach. I’ll ask colleagues what they do. I’ll create my own problem sets. Debates over textbooks are noise.
Common Core? Back to Basics? Group learning? Individualized instruction? Programmed Learning? More or less technology in the classroom? Standardized tests? Block schedules or daily classes? Take calculus in 11th grade or 12th grade? Accelerate in 4th or 5th grade? Heterogeneous classrooms or group by ability? Inservice programs? District speeches? . All these debates? Most of these don’t matter much. Perhaps they are useful but mostly they are noise, noise, noise. A balanced approach probably works best.
So what matters most? – Each individual is a unique individual, and the classroom is a unique group experience. A baseball team has 162 games, a teaching year about 180 days of instruction. I taught many of my graduating 8th graders for two consecutive years – approximately 350 hours. There will be ups and downs for each individual, and for each class as a group.
As a teacher, I can help create a classroom tone that fosters achievement and learning. As a teacher I can form a relationship with each student, creating a sense of trust. I can help create a safe classroom where learning can happen. I can do my very best every day, helping students understand new and complex ideas. I can be patient and flexible.I can draw upon my past experiences to find different approaches that work for different students. I can listen. I can model learning.
I have no illusions about what I can and can not do. I know students will, as years pass, forget me and forget much of what they learned. Who remembers their middle or high school math teacher? Perhaps I can gently shape their path through school and beyond. Perhaps I can slightly alter the trajectory of their future experiences. Perhaps I can help them through the difficult times they are now experiencing.
I’m thinking about my students as individuals. Some are constrained by negative attitudes and behaviors. I listed these below. Each period each day I try to move my students’ attitudes and behavior to the left column from the destructive right side. It is a long process, never-ending.
STUDENT ATTITUDES AND BEHAVIORS
POSITIVE NEGATIVE
I can I can’t
I don’t understand, so I will ask for help I am afraid to ask for help
I believe I can be a good math student I will never be a good math student
It’s hard, but I can do it It’s hard, I’ll never be able to do it
I’m engaged in learning I’m withdrawn,hiding, I want to be invisible
The math classroom is a safe place The math classroom is a scary place
I did poorly on this test, but I will figure it out I did poorly on this test and I want to forget it
There is joy in learning, a sense of wonder I fear what will come next
I never have understood this but will now I never understood this and never will
get some help
If the teacher calls on me, I’ll try, and it is OK I am terrified the teacher might call on me
if I make a mistake
I have a sense of real accomplishment I’m frustrated and confused
What’s Important? It’s important my students deeply believe :
I want to learn more – I can learn more – more math, more everything
I’ll carefully listen to each graduate’s name. I have my own sense of wonder. Each student has enriched my life and the lives of their classmates. Each is a miracle. Each matters.
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Practical Wisdom Garnered from Living a Full Life
I wish I could put down in clever, clear, and concise words the practical wisdom, lessons learned from life, that have come to me over many decades. I cannot. Fortunately, others have that capacity and skill. Here is a collection of such wisdom. Savor, nod your head in agreement if that be the case, and, if you are inclined to do so, write your own. Most of all, enjoy!*
David Brooks is a New York Times columnist. This appeared June 2, 2022
We’re inspired by the legendary tech journalist Kevin Kelly, who, for his 68th, 69th and 70th birthdays, shared his life learnings on his Technium blog. Here are some of Kelly’s life hack gems (I’ve reworded several for concision):
When you have 90 percent of a large project completed, finishing up the final details will take another 90 percent.
Anything you say before the word “but” does not count.
Denying or deflecting a compliment is rude. Accept it with thanks.
Getting cheated occasionally is a small price to pay for trusting the best in everyone, because when you trust the best in others, they will treat you the best.
When you get invited to something in the future, ask yourself, Would I do this tomorrow?
Purchase a tourist guidebook to your hometown. You’ll learn a lot playing tourist once a year.
The thing that made you weird as a kid could make you great as an adult.
It’s not an apology if it comes with an excuse.
Just because it’s not your fault doesn’t mean it’s not your responsibility.
Ignore what they are thinking of you because they are not thinking of you.
If you think you saw a mouse, you did, and if there is one, there are others.
Something does not need to be perfect to be wonderful, especially weddings.
The biggest lie we tell ourselves is, “I don’t need to write this down because I will remember it.”
Bravo to Kevin Kelly. Everybody learns life lessons. Not everyone clarifies them with such precision and shares them with such generosity. But even Kelly does not have a monopoly on practical wisdom.
For example, over the last few years I have embraced, almost as a religious mantra, the idea that if you’re not sure you can carry it all, take two trips.
A friend shares the advice: “Always make the call. If you’re disturbed or confused by something somebody did, always pick up the phone….”
Job interviews are not really about you. They are about the employer’s needs and how you can fill them.
If you can’t make up your mind between two options, flip a coin. Don’t decide based on which side of the coin came up. Decide based on your emotional reaction to which side came up.
Take photos of things your parents do every day. That’s how you’ll want to remember them.
Build identity capital. In your 20s do three fascinating things that job interviewers and dinner companions will want to ask you about for the rest of your life.
Marriage is a 50-year conversation. Marry someone you want to talk with for the rest of your life.
If you’re giving a speech, be vulnerable. Fall on the audience members and let them catch you. They will.
Never be furtive. If you’re doing something you don’t want others to find out about, it’s probably wrong.
If you’re traveling in a place you’ve never been before, listen to an album you’ve never heard before. Forever after that music will remind you of that place.
If you’re cutting cake at a birthday party with a bunch of kids howling around you, it’s quicker and easier to cut the cake with dental floss, not a knife. Lay the floss across the cake and firmly press down.
When you’re beginning a writing project, give yourself permission to write badly. You can’t fix it until it’s down on paper.
One-off events usually don’t amount to much. Organize gatherings that meet once a month or once a year.
Make the day; don’t let the day make you. Make sure you are setting your schedule, not just responding to invitations from others.
If you meet a jerk once a month, you’ve met a jerk. If you meet jerks every day, you’re a jerk.
Never pass up an opportunity to hang out with musicians.
Don’t try to figure out what your life is about. It’s too big a question. Just figure out what the next three years are about.
If you’ve lost your husband (or wife), sleep on his (or her) side of the bed and it won’t feel so empty.
Don’t ever look up a recent photo of your first great love.
If you’re trying to figure out what supermarket line is fastest, get behind a single shopper with a full cart over two shoppers each with a half-full cart.
Low on kitchen counter space? Pull out a drawer and put your cutting board on top of it.
You can always tell someone to go to hell tomorrow.
____________________
*I thank Kim Marshall for including this piece in his blog and sending it along to me.
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Schooling Around the World (Part 7)
India has 1.4 billion people. Of that total 250 million attend rural and urban schools about the same enrollment as China (2021). Consider that the U.S. schooled around 50 million students in the same year.
India’s system of public and private schooling is governed at the central, state, and local levels. About four out of five Indian students attend government schools, as they are called. The rest attend private and alternative kinds of schooling. Since two-thirds of India’s population live in rural areas, 70 percent of all Indian children attend school in those areas. Among adults, nearly 80 percent are literate as determined by the 2011 census (three decades earlier, literacy rate was 41 percent). See here.
Here are a few facts about the Indian system of schooling including how public schooling is organized:
What do rural and urban Indian classrooms look like? A sampling of photos in both settings comes from the Internet:
Physical classes resume in a Ghaziabad school after one student tested positive for Covid-19.
Schools in Maharashtra (Mumbai) were closed down in March 2020 after the outbreak of the pandemic; they reopened mid-December 2021
Photo: Luke Strathmann | J-PAL
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Schooling around the World (Part 6)
After determining how each nation has organized its system of schooling (U.S., France, Germany, Russia, Japan) and seeing photos of different nations’ classrooms, similarities are obvious:
*Every nation compels parents to send their sons and daughters to school up to a decade or more.
*Every one pays the costs for schooling either directly or indirectly.
*Every one is age-graded.
*Every one publishes national (or state) curriculum standards for each elementary and secondary school subject.
*Every one tests student performance in elementary and secondary school subjects.
*Every one has at least one teacher for each classroom.
Some are national (or federal) systems and some are state-operated with the federal government and states splitting funding and supervisory responsibilities. All of these nations and their states set curriculum standards for each subject and administer tests to determine if schools and students are meeting those standards.
Some nations have centralized systems (e.g., France, Russia, Italy, Japan) where ministry officials make decisions for schools and some are decentralized (e.g., Canada, U.S. Norway) with states and local districts having a moderate degree of discretion to alter what national authorities require. Whether centralized or decentralized, individual schools in every nation have some autonomy in adapting national or state curriculum when organizing for instruction. Need I add that once they close their classroom doors, teachers also exercise discretion in teaching the lesson they planned for the students in front of them that day.
What needs to be stressed that these commonalities among nations in establishing and operating systems of schooling over the past century exist side-by-side with inevitable within-nation variations between rural and urban and wealthy and poor schools that exist. Both commonalities and variations influence the schooling and teaching that occurs daily.
For this post, I turn to Sweden. Again, I begin with a chart showing how the nation’s schools are organized followed by a series of photos of classrooms in the country drawn from the Internet. For longer descriptions of the Swedish system and its move from a highly centralized one to reforms in the 1990s that now allow parents to make choices among government schools and publicly funded independent ones (about five percent of students attend these schools), see here and here.
The Swedish system:
Here is a sampling of Swedish classroom photos:
Upper Secondary Classroom
Elisabeth Ubbe—The New York Times/Redux
Kindergarten Class
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Sale of Twitter Shows That Ed Tech Companies Should Be Accountable To Schools (T.Philip Nichols and Antero Garcia)
T. Philip Nichols is an assistant professor in the Department of Curriculum and Instruction at Baylor University. Antero Garcia is associate professor of education at Stanford University. The original article appeared in Ed Source, May 8, 2022.
The recent news that billionaire Elon Musk plans to purchase Twitter shows how abruptly even widely used technology companies can be bought, sold, altered or shut down at the whims of their owners. This ought to concern educators, parents and students: Such instabilities don’t just affect social media giants, but any commercial platform — including those that have, over the past decade, become vital infrastructures for the everyday operation of public schools.
Even before the pandemic accelerated schools’ adoption of third-party platforms for virtual learning, teachers already relied on such technologies to share assignments (Google Classroom), manage student behavior (ClassDojo), monitor school devices (GoGuardian), assess learning (Kahoot), communicate with families (SeeSaw), and supplement instruction (Khan Academy). According to one study, in 2019 U.S. districts accessed, on average, over 700 digital platforms each month. As of 2021, this number has doubled.
As education researchers who study the impact of platform technologies in schools, we find this pattern troubling. The growing dependence of education on a constellation of privately controlled technologies cedes tremendous power to companies that are unaccountable to the publics that schools are meant to serve. And the deeper these platforms are embedded in the life of districts, schools and classrooms, the more tightly tethered administration, instruction and learning are to their owners’ whims.
In our work with teachers, for instance, we often hear complaints when an instructional app pushes out updates that remove favorite features or change its functionality. Such instabilities can thwart a lesson or force teachers to restructure a unit. But the consequences could be even greater with a larger company. If, tomorrow, Google decided to offload or shutter its educational services, there are few U.S. schools that wouldn’t be impacted. And because Google isn’t accountable to the public education system, those schools would have no recourse but to pivot to a different third-party platform that, likewise, offers no assurance of a long-term commitment to teachers’ and students’ needs – or, it’s worth noting, the security and privacy of their data.
Hypotheticals like this may seem far-fetched, but then, the idea that Musk would attempt to buy Twitter also seemed unlikely – until it wasn’t. Trusting in the stability and benevolence of privately controlled companies in a notoriously volatile industry is a flimsy foundation on which to build sustainable institutions for equitable public education. We shouldn’t settle for this arrangement.
While the size and influence of certain platform providers may make alternatives seem unthinkable, there are steps we can, and must, take to make educational technologies accountable to the public schools that rely on them.
In the short term, we can interrogate the role of such platforms in classrooms. Edtech scholars have shown how teachers can use “technoethical audits” to evaluate how the design and use of common technologies might work with, or against, their pedagogical values or the needs of their students. Our own research, likewise, demonstrates how such inquiries can extend into lessons, where students investigate the place and power of platform technologies in their own lives. Such tactics empower educators and students to make demands of the platforms they use rather than accepting these technologies as they are.
Longer term, we can create policies that make technology companies answerable to the public schools that use them. Amending procurement policies in districts, for instance, can put pressure on platform providers to take educators’ concerns about stability, security and privacy seriously lest they lose out on valuable contracts (or the usage data needed to keep their products viable). There is also room for state and federal protections. The European Union’s recently proposed Digital Markets Act and Digital Services Act offer one such model: creating oversight for technology mergers and acquisitions that affect public well-being and subjecting large “gatekeeper” platforms to additional scrutiny. While imperfect, such policies offer a starting point for thinking about how we can build leverage so the privacy and stability of entire school systems can’t be determined by the business decisions of a few private companies.
If this sounds unrealistic, it is no more radical than the future that privately controlled technology companies have imagined for themselves – where they stand as unregulated infrastructures for all of public education. Challenging this vision requires an equally ambitious alternative: one rooted not in growth or profit, or the mercurial ambitions of tech moguls, but in a commitment to education for the common good, and for the autonomy and flourishing of all students.
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Japanese Classrooms: From Chaos to Complete Control (Mary DeVries)
This account by an American teacher in a Japanese rural elementary school reflects what one teacher experienced. Generalizing to all Japanese schools, rural and urban, large and small, elementary and secondary is a step too far. Other teachers might write different accounts. This is hers. Mary DeVries wrote this piece in Medium on November 17, 2020.
The first thing I noticed when I started working at a Japanese elementary school was how well behaved and focused the students were. The second thing I noticed was how loud, absolutely wild, and seemingly out of control they were at times. I believe these two states are connected.
I was an English teacher in rural Japan for two years. I say English teacher since that was my title but I actually functioned as more of a glorified pronunciation model. I came into each class once a week for their English lesson. The classroom teacher would run the lesson and I would follow their directions. This set up allowed me a lot of opportunities for observation.
In keeping with my preconceived expectations of what a Japanese school would be like, I was immediately struck by how polite and well mannered the students were. As I entered each classroom all eyes were focused on me and the classroom teacher. Students sat quietly and listened to directions.
As I walked down the neat rows of desk stopping at each one for the obligatory, “Hello, my name is Ms. DeVries. What’s your name?” the selected student would answer, if necessary with prompting from the teacher to encourage the exact formulary to use. Meanwhile, despite the mundaneness of this exercise the rest of the class sat quietly waiting for their turn. How different from my experiences in most American classrooms.
Then we moved into the main content of the day’s lesson, colors. After a quick review of English color names, it was time for a game. I would say “Please touch something red.” The students would quickly scramble around the room to find something red to touch. I would repeat with a different color and they would be off again.
I was surprised by the atmosphere in the classroom during this game. The subdued students of moments before were transformed into a wild mob, laughing, yelling, and jostling each other as they reached for interesting objects to touch. Some students called out to friends who were struggling to find something with suggestions and encouragement. One student grabbed a chair, pulled it over to the wall, kicked off his shoes before climbing on the chair to reach up precariously on tiptoe to touch a red item up high.
The noise level was very high. The seeming chaos was such that in most American classrooms the teacher would have been drawing an immediate halt to the game and sitting all the students down for a lecture along the lines of, “If you can’t control yourself we won’t be able to play the game anymore and we will all just have to sit at our desks quietly.”
In this Japanese classroom, however, the teacher stood in the corner and beamed proudly at her students as they raced riotously to find the different colors I called out. It was the end of the game that impressed me the most. The teacher clapped her hands, told the students to take a seat, and within seconds all the children were in their seats facing forward waiting for the next set of instructions.
I saw this pattern repeated regularly the entire two years I taught English in Japan. During select activities, teachers allowed much more physical movement, shouting, and frenzied excitement than would be tolerated in the American classroom setting, but when the activity ended they would be able to immediately reign in the class and transition to seatwork.
Another distinction I noticed was the flexible use of classroom space and furniture. Every Japanese classroom I taught in was equipped with standard student desks and chairs arranged in orderly rows when I first entered the classroom. However, throughout the course of a one hour English lesson, those desks and chairs were likely to be rearranged several times. The desks might get pushed to the edges of the room to make space for a circle of chairs in the middle. Or desks were turned around to face each other and make pairs or quads for student interaction. Or all furniture was moved away to make a large open space available for floorwork or other options.
The students would do all the arranging and rearranging of furniture with great speed and a minimum of fuss. This speed allowed for numerous changes even within one class period without excessive loss of instructional time.
My experiences in Japan encompassed two elementary schools in a rural setting. It would be dangerous to extrapolate too far from this limited exposure to make blanket statements about Japanese schools in general. However, I wanted to make use of what I had seen to improve my own teaching techniques as I returned to the US.
How much of what I witnessed was due to cultural differences and how much could be adapted to an American classroom? This is of course a hard question to answer. Certainly, some of the successful classroom management I witnessed was built on cultural expectations of conformity, respect for authority, and the valuing of community over individuality. However, I found that there were lessons to be learned that could be put in place in an American setting.
First, building in regular periods when students could be loud and rowdy releases steam that lets students stay focused on quieter more disciplined work at other times. This is not news to anyone however most teachers tightly constrain students at all times for fear of losing control of the class.
After returning from Japan I began experimenting with my classes to discover that fine line between chaos and control. How far could I let my classes loose to be loud and wild and express themselves during an active lesson without losing control or the ability to reign them in quickly when it is time to transition. This is a skill that takes time and patience to develop but my experiences in Japan showed me what was possible and the benefits I stood to gain in terms of effective classroom management and more time on task.
I also looked at the value of frequent room readjustments. Rearranging the classroom furniture has several benefits. The physical activity wakes up sleepy brains, burns off fidgety energy, and helps students be more ready to focus. It is exciting and signals that something new and interesting is coming. It allows for a wide variety of groupings to meet various educational needs. Having a dynamic rather than static classroom arrangement keeps everyone on their toes and viewing things in a different light.
The trick is doing this rearranging without losing too much valuable educational time. My solution is to put a little time into training students at the beginning of the year. Make a game of it timing the students as they race to rearrange the room to various preset specifications. With practice ahead of time and regular usage throughout the year, furniture rearranging can become the norm with the slight amount of time it takes well paid off by the benefits.
Just as every teacher can benefit from observing their colleagues and copying best practices in their own classroom, we all stand to gain from looking at how education happens in other cultures. What assumptions are we making that may be unwarranted? What can we try to improve our own classrooms? There is so much to learn.
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Schooling around the World (Part 5)
After looking at how public schools are organized and how teachers teach in France, Germany, and Russia, I now turn to schools in Japan. At a national level, Japan, has a Ministry of Education responsible for a national curriculum, funding and staffing schools in 47 prefectures (like states in the U.S.) across the country.
The system of schooling is organized in this fashion:
Here is a sampling of elementary and secondary school classrooms across Japan.
For a short video of a Japanese school and classrooms, see: https://www.youtube.com/watch?v=2QazQyNhDdg
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Cartoons on Aging
Getting really old has been on my mind so I began exploring its humorous side. For this month, then, I have collected a few cartoons on aging in American society. Enjoy!
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Can Principals Raise Test Scores?
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Larry Cuban on School Reform and Classroom Practice 