Author: pythagitup

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?

The Discrete Math Project

The Discrete Math Project

I recently bought Discrete Mathematics for Teachers by Ed Wheeler and Jim Brawner. I have a bit of a habit of buying math books. Learning about math – even if it’s unrelated to the curriculum I teach –  makes me a better teacher. While I’ve taken a bunch of education courses over the last few years, it’s been quite some time since I took a math course. I’ve decided to replicate that experience by working through this textbook. I’m excited!

Discrete math is not an unfamiliar subject to me. I learned a fair amount of discrete math in high school, and as part of my math degree, I took a course in discrete math. I’ve specifically taught sequences, combinatorics, and probability, and I’ve also touched on some set theory and logic. I hope to learn some new things and to refresh some knowledge tucked deep away in the furthest recesses of my brain.

My plan is to work through roughly one section each week. I’ll probably do it on Friday or Saturday night. That’s just how my social life works. There are 39 sections, so in theory, this project could take me the better part of the year. As I go along, I’ll certainly explore certain topics in more depth, and I welcome suggestions for avenues that I might pursue. For each section, I hope to put together some sort of blog post – an interesting problem, curriculum connections, etc.

The following quote from the Preface stood out to me:

The goal is to develop teachers who not only know the mathematics they are teaching, but also understand the larger mathematical context in which the mathematics they teach has life.

My content knowledge has enriched my teaching in so many ways. I look forward to continuing to develop it in the coming weeks. I invite you to join me on this journey.

Reflections on Choice Words

Reflections on Choice Words

I recently finished reading Choice Words: How Our Language Affects Children’s Learning by Peter Johnston. Though the book is ostensibly about reading and literacy education, I found it spoke to much larger issues in education. Indeed, I consider it to be one of the best education books I’ve ever read. This post contains various thoughts about and comments on Choice Words.

Our communication reveals our beliefs about ourselves, our students, and teaching. Johnston writes:

The way we interact with children and arrange for them to interact shows them what kinds of people we think they are and gives them opportunities to practice being those kinds of people.

If we place students in the roles of thinkers, problem solvers, and mathematicians, then they can construct and refine each of those identities. If we value our students’ questions, ideas, and suggestions, then they can develop their curiosity, insight, and creativity. A former colleague once asserted that “if we want students to become responsible, then we need to give them responsibilities and see what happens.” Johnston advocates “creating an intellectual space into which [students’] minds can expand.” This classroom would necessarily encourage discussion, cherish student contributions, foster mutual respect, and cultivate independence and responsibility. Why? Because these conditions define the environment needed to nurture young minds.

But we can also see that it is not simply the names and labels we invoke that affect children, or for that matter the love with which we embrace them, but the ways we unwittingly use language to position them and provide them with the means to name and maim themselves.

Johnston argues that everything we do sends a message to our students. Avoiding a classroom discussion, for example, may suggest that we don’t believe our students can make thoughtful contributions, or that we don’t trust students to engage themselves in meaningful conversation, or that only the teacher has valuable knowledge. When we cling to right-wrong, good-bad, and other dichotomies – especially about what students do and say – we indoctrinate our students to this way of thinking. We shut down the intellectual space that developing minds need.

We cannot persistently ask questions of children without becoming one-who-asks-questions and placing children in the position of the one-who-answers-questions.

When we work on Three-Act Tasks or ask students to Notice and Wonder, we allow them to pose their own questions and to take on the role of mathematician. Language, Johnston says, “creates realities and invites identities.” A teacher who acts as the sole arbiter of right and wrong may preclude students from developing their own evaluative capacities. A teacher who refers to a classroom task as “work” or something students “have to do” may unintentionally set students up to dislike that task, especially in relation to activities they find “fun” or otherwise meaningful. The intended message need not, and often will not, match the received message.

Teachers’ conversations with children help the children build the bridges between action and consequence that develop their sense of agency. They show children how, by acting strategically, they accomplish things, and at the same time, that they are the kind of person who accomplishes things.

Agency involves the power to achieve, the means to bring about desirable results. To me, agency lies at the heart of what we do as teachers. We have all taught the persistent student, the tenacious student, the driven student, the student who relentlessly pursues success. These students have a strong sense of agency, that belief in their own competence and in their capacity for accomplishment. We have also all taught students whose sense of agency remains underdeveloped. It’s not enough to tell students to be tough or to display grit or to believe in themselves or to just give it a try. A student whose narrative involves doubt and failure needs our help in developing agency.

But when a child tries something and does not succeed, we need to turn that event toward a narrative and identity that will be useful for the future. If children are not making errors, they are not putting themselves in learning situations.

Success and failure play important roles in the learning process and in helping students develop their sense of agency. These successes and failures must belong to the student, though. Teachers may support, of course, but students must play the central roles in their own narratives. A passive student becomes a student without agency, a student who relies on others to do the thinking and to solve the problems.

Children with strong belief in their own agency work harder, focus their attention better, are more interested in their studies, and are less likely to give up when they encounter difficulties than children with a weaker sense of agency.

Language matters. How we interact with students matters. The ways learning occurs in our classrooms matter. Most of all, children matter.

YouCubed is wrong about giftedness

I recently watched this video produced by YouCubed and Jo Boaler that talks about giftedness. Essentially, the video argues that labeling students as gifted presents equity issues and does a disservice to students by giving them a fixed idea of what they can learn and do as well as how they should behave.

Giftedness is real. One definition of “gifted” is “a high level of intelligence [indicative of] advanced, highly integrated, and accelerated development of functions within the brain” (Clark, 2013). The Elementary and Secondary Education Act defines gifted students as those who “give evidence of high achievement capability … and who need services or activities not ordinarily provided by the school in order to fully develop those capabilities.” Just as some individuals have extraordinary artistic or athletic talents, some students have significant intellectual gifts. Acknowledging this fact does not force us to believe that some students cannot learn math. Nor does it force us to set limits on what we think students can learn and do.

The problem, I think, is that YouCubed has conflated the concept of giftedness with how this concept has been applied in schools. Even if many teachers and schools wrongly label and limit kids, that doesn’t mean giftedness is not a useful concept. It simply means that teachers need to do better with how we use the idea of giftedness.

This argument refers to ineffective and inappropriate uses of giftedness to suggest that gifted education is inherently inequitable. But we can provide services to gifted students without limiting other children’s potential. It’s bad teaching to suggest that gifted students should always know the answer or should not ask questions. Similarly, it’s bad teaching to suggest that non-gifted students cannot learn high levels of math or to place false limitations on what students can do. But these are problems with teacher behavior. These are not problems with the idea of gifted education.

Indeed, our developing knowledge of neuroplasticity and the idea that brains experience significant growth and change actually support labeling students as gifted. Why? Because acknowledging the incredible potential that some students have forces us to consider ways to help them realize that potential.

Is it inequitable to provide services such as enriched classes to gifted students? No. Equity means allowing every student the opportunity to achieve his or her potential. Equity does not mean offering the exact same opportunities to every student. Our obligation as educators is to create an environment that helps every student to learn and grow as much as possible. We can do so while accepting that some students learn faster or slower, that some students require more support or greater challenges.

Is everyone gifted? No. But that doesn’t mean we should place artificial limits on what students can learn and do. It’s okay to acknowledge the great intellectual capacity and potential that gifted students have. We can do this without saying that gifted students are better or deserve more. We cannot afford to avoid labeling gifted students, however, because doing so will make it harder to meet the needs of exceptional learners.

Note: I wrote a draft of this post after initially viewing the YouCubed video last month. I’ve fleshed out some of my commentary, but it remains mostly the same as I left it late in the evening on November 9th.

References

Clark, B. (2013). Growing up gifted: Developing the potential of children at home and at school. Boston: Pearson.

Elementary and Secondary Education Act, 20 U.S.C. § 7801 (1965).