Author: pythagitup

The Marzano Tweet

What follows are my thoughts on the response to the Marzano tweet shown below. I offer these thoughts as my way of grappling with an important issue in education – the interplay between educators and non-educators. My intention is not to criticize or disparage any individual but to work toward a way for me to understand discourse about education. I hope that I at least partly achieve this goal.

Robert Marzano is an educational researcher, consultant, and chief academic officer at Marzano Research. I know him primarily from his book The Art and Science of Teaching.

I did not have the same visceral reaction to the Marzano tweet that so many others did. That’s not to say I liked it. It just didn’t upset me. I have too much on my mind to worry about what Robert Marzano thinks. But I understand why so many teachers felt compelled to criticize him. When someone shares a message about education that we know is false, misleading, or harmful, it’s important for us to dispute that message. It’s important for us to share our own knowledge and perspectives. We can’t let a false narrative dominate. So I understand the response to the Marzano tweet.

But I also don’t understand the response to the Marzano tweet. I saw quite a few comments about Marzano’s background. People criticized him for only having spent two years in the classroom and for not having been in the classroom for 30+ years. The message here seems to be “Who are you to say anything about teaching when you don’t even teach?” I find this troubling.

Are teachers the only ones with valuable insights into teaching? Is anyone else qualified to share their opinions about education? Should we reject all educational research unless it was conducted by a classroom teacher? How long can you be out of the classroom and still have a worthwhile perspective? Coaches and administrators aren’t classroom teachers – do their contributions have any value? What about counselors and school psychologists? Who do we consider close enough to the classroom to judge their ideas worth considering?

Politicians, to take one example, rarely have teaching experience. Yet politicians write every education law, and all too often, teachers have little to no input in the legislative process. It can be distressing to think that education policy has largely been crafted by people with little to no experience as educators. They rely, of course, on input from many groups – researchers, lobbyists, etc. – but ultimately, the politicians pass the laws.

Is it fair to criticize politicians for education law? I think so, but the target of the criticism matters. It’s fair to say that a law is bad policy. It’s fair to say a law is based on shoddy research. It’s fair to say a politician didn’t consult with enough people or with the right people. It’s fair to disagree with a politician’s beliefs, and it seems fair to question a politician’s knowledge and understanding of issues in education. But is it fair to criticize a politician for never having been a teacher?

Ideas should be judged based on their merit. Anyone can have a great idea. An idea isn’t great because it came from a teacher; it’s great because it’s useful somehow. Similarly, a bad idea isn’t bad because it came from a non-teacher. An idea is bad because it offers nothing useful or it’s harmful or it ignores the research or it’s based on misconceptions or for any of a number of other reasons. The idea itself must be flawed. An idea isn’t bad simply because of who offered it.

Perhaps it’s more likely for bad educational ideas to come from non-teachers and for good ones to come from teachers. But we all know that not every idea a teacher has is a good one, and I hope we’ve all heard good ideas from non-teachers.

I don’t agree with the message Marzano shared in his tweet. I don’t agree with it because it’s wrong for so many reasons that people have already shared. It’s wrong if Marzano hasn’t taught in 30 years, and it’s wrong if he went back in the classroom today. What matters is the quality of the idea itself. I worry about what happens to discourse when we reject an idea because the person who suggested it lacks a certain title, background, or experience. But I also wonder how to reconcile this worry with the reality that everyone considers themselves qualified to offer opinions on educational issues. Is there a clear line somewhere? It’s certainly not “teacher vs. non-teacher.” After all, some of the best ideas in math education right now come from Desmos and Illustrative Mathematics, and as far as I can tell, most of their employees are not currently in the classroom. I don’t have an answer. I’m not sure there is an answer. I just needed to write this all down.

What Do My Students Really Know? Part 2

During the second semester, I only assigned homework using Delta Math. This worked well for several reasons, with the most important one being that it gave me better insight into what my students actually understood than pencil-and-paper homework ever did.

The Delta Math homework I assigned surprised me right off the bat. The image below displays one student’s results on the first assignment of the second semester. Many students had similar results.

HW 1 Linear 1

This assignment consisted entirely of review material. We had assessed linear functions at least once in December, and for the most part, students did fine. I knew that students would be a bit rusty after Winter Break. That’s why we completed this assignment. The surprise came from the misconceptions I saw in student responses.

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Although I could only see their answers, I found it relatively easy to determine their misconceptions. Unsurprisingly, I saw all of the classic slope mistakes.

  • Writing slope as an ordered pair instead of a ratio
  • Subtraction errors, especially with negative numbers
  • Putting the change in x in the numerator instead of the denominator
  • Mismatching x and y
  • Forgetting to simplify (not exactly a mistake, but Delta Math marks this wrong)
  • Misinterpreting \frac{4}{0} as either 4 or as 0

These aren’t new mistakes. I’ve seen them many times, and we’ve corrected them together many times. We said “vertical divided by horizontal” at least ten times each class period every day for a month. And the students got this! Like I said, students did fine when we assessed linear functions in December.

So why did so many students continue to display these misconceptions? I’m not naive. I realize that students master the material at different rates. But how could so many of them who had mastered the material make these mistakes? Why did they return to misconceptions that they had overcome a month earlier?

One explanation is that students managed to know the material well enough to pass an assessment, but they did not develop the robust understanding necessary to maintain their skills even a month later. That’s the explanation I originally subscribed to, but I think it lacks something important. Many of my students did understand slope. Throughout the fall, they worked hard to connect proportional relationships, steepness, and lines. They built a solid conceptual foundation. They thought mathematically. They solved problems. I think what they lacked – and this is on me – was a proper emphasis on procedural fluency. Sure, we had plenty of opportunities to practice and to develop that fluency, but rarely did they have the “Uh oh, I’m wrong!” moments that Delta Math gave them. My Delta Math assignments required students to get a certain number of problems correct to get credit. You just can’t fake a right answer. That’s what I like about Delta Math – it holds them accountable.

The other major advantage of Delta Math over pencil-and-paper homework? I can look through as many assignments as I want to in a relatively short time period without having to carry papers around. I have a bit of a problem with keeping papers organized, so moving homework online and avoiding paper altogether saves me some serious time and energy. The obvious drawback is that I cannot see the work that the students did. In the examples above, it’s relatively straightforward to identify misconceptions without seeing the student’s work, but that certainly won’t always be the case. I think, though, that simply being able to see that a student struggled with a problem type may be enough, especially given that some sort of intervention would need to take place anyway.

I’m not sure yet what homework will look like in my classes this year, but it seems like I’ll want to place more emphasis on procedural fluency. Perhaps such an emphasis earlier in the year will lead to better understanding all year long. I hope 2018-19 is the year I finally figure out how to make homework work for me and for my students!

Sandra Cisneros – “One Holy Night”

Sandra Cisneros – “One Holy Night”

Last summer, I read two books with a student. We read The Awakening by Kate Chopin and Mrs. Dalloway by Virginia Woolf. Our conversations about The Awakening proved fascinating, but we didn’t have as much success reading and discussing Mrs. Dalloway. Nevertheless, I found the experience meaningful, and I think the student did too. She sent me the following Remind message before the school year ended:

Hey Carlson, are we reading this summer?

How could I say no? We haven’t yet started, but we plan to read The Piano Lesson by August Wilson. Additionally, I asked one of my students from this past year if she would like to read a book with me, and she agreed. We’ve been reading Woman Hollering Creek and Other Stories by Sandra Cisneros. The story “One Holy Night” led to an interesting discussion. Here are the highlights and my rambling commentary. To maintain her privacy, I will refer to my student simply as C.

In “One Holy Night,” an eighth-grade girl tells of how she loses her virginity to a man who calls himself Chaq Uxmal Paloquín. He claims to be descended from Mayan kings. The people in the neighborhood call him Boy Baby, and no one seems to know much about him. We find out later – after he has left town and our narrator has become pregnant – that he is actually thirty-seven years old and that he is a serial killer. The story is only nine pages long, and it focuses more on mood and feeling than on specific details.

For whatever reason, our conversation fixated on rape. C rightly pointed out that Boy Baby committed statutory rape. She expressed some discomfort with the story and mentioned that some readers might be deeply disturbed (“triggered”) by the story. We talked about the choice Cisneros made to avoid detail and use poetic language to describe the rape:

Then something inside bit me, and I gave out a cry as if the other, the one I wouldn’t be anymore, leapt out.

C was glad that there wasn’t more detail. Because rape is so disturbing, she asserted, only a bad writer would need to include more detail to bring about the desired response from the reader. This assertion seemed to extend past “One Holy Night” to all literature (and other works of art, for the matter), so I asked if there could ever be a situation in which more detail might be necessary. She said no, again emphasizing that a good writer wouldn’t need to include the details of the rape. I told C that I didn’t disagree but that I wanted to press the point further. Could there be any value in graphic description of such a violent act? And what about other violent acts like murder? C felt that rape belonged to a category of its own, that it was even worse than murder. I wondered whether a rape victim might consider it necessary to express the horror and the violence she went through. C agreed this might be possible, but she expressed her concerns about works of art that use such violence for shock or entertainment value. She talked about the show 13 Reasons Why (which I have not seen) and how she felt like it glamorized suicide. We talked about how the narrator seemed to romanticize her own rape, describing Boy Baby’s face as “the face I am in love with” even after discovering he’s a serial killer. It was a meandering conversation, but it was a meaningful one.

When I chose Woman Hollering Creek and Other Stories, I didn’t know much about its content. I didn’t intend to pick a book with a story about a young girl’s rape, so I’m glad that C and I managed to have such an interesting discussion. I’m forced to wonder where this sort of conversation takes place. Or if it even does. It’s not easy to talk about rape, but it seems important that we do. Sometimes we don’t give our students enough credit for the depth of their insights. I look forward to learning more with C as the summer continues.

Black History Month

I took a risk this February. My school celebrates Black History Month in a number of ways, but I always feel like I need to do more. Here’s what I tried.

I’m not sure what made me think of this, but I decided that we would read a poem by an African-American poet each morning in homeroom. I figured this could be a simple yet powerful way to celebrate African-American culture, and honestly, I just thought it would be interesting. You can find the poems I used here.

I wasn’t really sure what to expect the first day. Would the students really listen? Would anyone want to participate? Would the experience be meaningful to anyone but me?

I explained to my homeroom the plan for the month. I told them that anyone could volunteer to read a poem or even bring in a poem of their choice. As I prepared to read the first poem, I paused and thought “Why not ask for a volunteer now?” I expected dead silence and blank stares. Instead, an energetic, excitable young man – who happens to be African-American – said he wanted to read the poem. Overjoyed. I was absolutely overjoyed.

As the month continued, I kept bringing in poems, and my students kept volunteering to read. It might have only been 7 or 8 students, but when I started, I had no expectations whatsoever. And while my students sometimes struggled to read the poems, they truly committed themselves to their delivery. And the rest of the class? Quiet, respectful, attentive. Did they find the poems interesting or meaningful or enjoyable? I can’t say, but I do know that they respected my idea and made it a reality.

Students read nearly all of the poems. I had to read 1 or 2 because of time constraints, and I asked a guidance counselor to read one. Her reading of Audre Lorde’s “Hanging Fire” truly moved me. I had hoped that having a “guest reader” would be special, but I was totally blown away. I think the kids were too.

For the last day of February, I decided to talk briefly about the idea of Black History Month and close with a short selection from a poem that means something to me. I thanked my students for committing to the poem readings all month and told them that I would really miss not having a poem to read every day. Then, I attempted to tell them how I’d like us all to carry the message of Black History Month forward. That we need to spend all year trying to make our school, our community, and our country more tolerant and more just. I think I stumbled over my words a bit here. I was emotional, especially knowing what would come next. I closed with the last few lines of Amiri Baraka’s “Three Modes of History and Culture.”

I think about a time when I will be relaxed.
When flames and non-specific passion wear themselves
away. And my eyes and hands and mind can turn
and soften, and my songs will be softer
and lightly weight the air.

I’m not a poet. I’m not an English teacher. I’m not a literary scholar. Maybe this poem or any of the others mean something totally different than I think. I don’t think it matters, though. What matters is that we pushed ourselves to do something different, that we worked outside of our comfort zone, that we really tried to learn and understand.

But it’s not enough. I need to do more next year. I need to do more for my students. To let them know that their history and their culture matter. To let them know that they matter. To help us all learn to be better, more tolerant, more understanding, more generous in spirit.

This was a risk. I don’t know if I did a good thing. I don’t know if I made a mistake. I badly want feedback, but I’m also terrified that I sent a message I didn’t intend to send. It’s uncomfortable sometimes – teaching – but it’s worth it for those moments. Those powerful moments when twenty-five thirteen- and fourteen-year-old students devote their attention to listening to a classmate read a poem. I hope that I made a difference.

Reflections on The Classroom Chef

Reflections on The Classroom Chef

Take risks. More than anything else, that’s the message of The Classroom Chef by John Stevens and Matt Vaudrey. It’s 2018. We owe it to our students to do better than just teach the same lesson we’ve been using. We owe them better than life in a textbook universe. We owe them more than just lectures and practice. We owe our students a meaningful classroom experience that will help them develop understanding and not just procedural fluency. We owe them more.

Take risks. I told this to my students when we returned from winter break. I told them that I planned to take risks this semester to make class more interesting, to help them find meaning in what we’re doing, and to allow them to learn and refine academic and life skills.

Take risks. Grades don’t matter. Test scores don’t matter. Coverage doesn’t matter. Standard algorithms don’t matter. Compliance doesn’t matter. The book doesn’t matter. The pacing guide doesn’t matter. Standards don’t matter.

Take risks. What does matter? The students in front of you right now. Their thoughts and ideas and energy and interests and passions and enthusiasm and suggestions and questions and feelings and understandings and beliefs and knowledge and motivation and … What matters? Their future. What matters? They do.

Take risks. We owe our students the best education we can possibly give them. John and Matt understand this. They understand that we need to change if we really want our students to grow. They understand that it’s not enough to do the same old thing – even if it has been effective in the past. They understand that we need to keep pushing forward lest we end up going backward. They understand that education in 2018 can’t look like education in 1950 or 1990 or 2005 or even in 2017. They understand that students need us to value their engagement, their thinking, and their future.

Take risks. The Classroom Chef offers a ton of great ideas and useful advice. But beneath all of the stories and suggestions lies one simple message – take risks.

Ad astra, John Young

Ad astra, John Young

Between 1969 and 1972, twelve men walked on the moon. This is humanity’s greatest accomplishment – that we managed to send astronauts more than 200,000 miles through the unknowns and the dangers of space, that these astronauts set foot on another world, and that they returned home safely. We did this to explore. Yes, there was an element of Cold War competition, but in the end, these missions were about science, about discovery, and about challenging the limits of possibility.

John Young has died, leaving only five surviving astronauts who walked on the moon. Their ages: 87, 85, 85, 82, and 82. Young was 87. Eight others who flew to the moon without landing are still alive; the youngest is 81. I hope that these men have many years left, but realistically, the day will soon come when no living person has set foot on the moon or even left low Earth orbit. Despite all of the advances we have made, we have not yet surpassed this accomplishment from nearly fifty years ago. NASA’s priorities have certainly changed, and they still do lots of wonderful, important work. And perhaps sending an astronaut back to the moon would serve little purpose. But I cannot avoid the sadness I feel knowing that some of our greatest heroes will soon be gone and that they will leave us without successors.

Gemini 3. Gemini 10. Apollo 10. Apollo 16. STS-1. STS-9. What an amazing career.

The image on the left shows Young in 1965, a few weeks before the Gemini 3 mission. The image on the right shows Young (seated, second from right) in 1983, about six months before the STS-9 mission. Young ultimately worked for NASA for 42 years. My words cannot do justice to his great career. Instead, let me share with you some quotes I find particularly meaningful in light of his death.

My favorite description of John Young comes from Andrew Chaikin’s A Man on the Moon:

Inside Young was an unwavering determination, an overriding sense of responsibility – to the space program, to the country, to his crew – and an almost childlike sense of wonder at the universe.

But more than this, I think, Young felt a responsibility – a commitment – to truth and to knowledge. Chaikin writes:

More than most astronauts, Mattingly thought, John Young seemed mindful of the risks of his profession. Around the Astronaut Office, his memos were well known, sounding the alarm about some engineering problem he’d uncovered. He wouldn’t rest until he knew every detail about the particular system or technique that worried him. And when he had learned all he could, then it was time to go fly – with his eyes wide open. That was the only way to handle this business; that was what made him so good. Maybe Young worried so much because he saw so clearly. But when it came down to the real question – Will you fly it? – John’s answer would always be yes.

John Young, intrepid explorer. Perhaps in looking at heroic figures from the past we see in them what we want to see. Maybe we look for the best of ourselves in them. In John Young, I see a man who lived for the thrill of discovery, a man for whom being bold was a way of life, a man who acknowledged challenges but saw past them, a man with a vision of limitless possibility. Consider the scene Chaikin describes as Young exits the Space Shuttle Columbia after its maiden flight:

Later, after the ground crews had arrived, Young emerged and bounded down the stairway to inspect his ship, punching the air with his fist like a relief pitcher who had just won the World Series. That day, Young told a crowd of well-wishers, “We’re really not too far, the human race isn’t, from going to the stars.”

Nearly thirty-seven years after that flight – and nearly forty-six years since Young walked on the moon – the stars still seem not too far off. NASA, SpaceX, Blue Origin, and others continue to push boundaries and extend our reach into the stars. But no amount of technological advancement can replace the boldness and the vision of men like John Young. We lost a great man on January 5, 2018. Ad astra, John Young. Ad astra.

Discrete Math Project 1.1 – An Introduction to Logic

Section 1.1 covers the basics of logic: Statements, open sentences, truth tables, negation, conjunction, and disjunction. The authors use “Aunt Buosone” in several examples. I’m excited to see what other characters I meet. The math isn’t new to me yet, but the name “Buosone” sure is.

I have never taught logic to this extent. When I taught geometry, we spent quite a bit of time discussing logic and especially reasoning, but we never actually worked with truth tables. In early August each year, I would convince myself that spending time with truth tables and doing a deep dive into logic would be a great learning experience for my students and would pay off in the long run. But each year, I backed off and decided to only spend time on “geometry” logic and not on “discrete math” logic. The payoff for truth tables didn’t seem great enough, and we did a ton of great thinking and reasoning without them. I wonder if many geometry teachers include truth tables in their curriculum. If not, do they show up anywhere in the curriculum? I learned about truth tables in PDM – Precalculus and Discrete Mathematics – using the Chicago series (UCSMP). Given the emphasis on coding, I’m curious where discrete math fits into the curriculum.

Anyway, I like making truth tables. Well, I don’t mind it. I guess it gets tedious after a while, especially once you understand them. I did find the word problems interesting. Here’s an example:

Higher Ed problem

That’s just a good problem, the sort I might have given my geometry students back in the day. Although the problem does not specifically call for a truth table, I made one anyway:

Truth Table

While this made the questions extremely easy to answer, I wonder what value the truth table really has here. I thought about the questions and answered them before making the truth table and used it to confirm my answers. The truth table certainly adds clarity, but in doing so, does it actually remove some of the critical thinking necessary to answer the questions? Or does it seem that way only because I have a fairly strong background in logic?

Curriculum Connections

This chapter included a number of logic puzzles. You know the type – Alice and Bob go to the same school, Bob and Carol both major in history, … Which person studies physics and is under six feet tall? I’ve never done much with this sort of puzzle, but I know students tend to like them. Definitely a good resource to have around to allow for easy differentiation after an activity.

Questions to Ponder

Does constructing truth tables help students develop logical thinking and reasoning skills? Does the process become rote? Is it just another procedure to learn?

How does the knowledge gained through learning about elementary logic help students to learn about mathematical proof? What do we gain by studying logic at this level?

What are the consequences of differences between mathematical language and the vernacular? How can we help students learn how and when to use and, or, and not correctly within a mathematical context? Does the idea of an inclusive or pose a significant barrier to student understanding, and if so, how do we overcome it?