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Last year, I started using Twitter as an extra credit tool in my classes. I give students homework extra credit after every class for one of three options:
- A summary of class
- A question about class
- An answer to someone else’s question
The benefits of this are many:
- Students make community with each other.
- I get to see what students thought class was about and if there are questions that need answered.
- Students practice summarizing.
- When students miss class, they can check the Twitter feed to see what they missed.
Often students summarize concepts very nicely and creatively. It’s great to see students learning from each other and forming community, which usually spills out of the virtual world and into the physical.
As much as I’ve liked it over the last year, my students this semester have already raised the Twitter community to a new level. Below are several examples of tweets from my students — none of which satisfy the criteria for extra credit — which are fun and reveal a relationship with our class that I can only hope to reproduce in future semesters:
As a bonus, here’s an exchange with a student in my statistics class this Labor Day:
The two most common responses when I tell people I meet that I’m a math teacher are:
- People tell me how much they admire and even like math;
- People tell me how bad they are at math, squirm uncomfortably, and kind of sidle away.
In the second, much more common option, I seem to represent all the inadequacies they have felt about math for much of their lives. They try and fail to put on a polite face, instead looking at me as they would a particularly disgusting plate of food. It’s an occupational hazard to have these awkward moments at parties.
Both responses more or less make an assumption that I love numbers and all things numeric. But, as much as I enjoy learning about and teaching math, I don’t love numbers. I love people and ideas. For me teaching is pretty close to a perfect combining of these two: I get to talk to people about ideas. Teaching statistics, in particular, is about helping people sort through all the individual stories they know, looking for a trend or trends; students learn to organize and communicate about data, helping them make decisions in the world.
And as a teacher, the stories my students tell me about struggling with math and with education in general are often heartbreaking. Everyone has a math autobiography, too often filled with a teacher or relative who said something like “math is hard and it’s not for everyone” — a backhanded way of saying telling the student he or she doesn’t cut it. Sometimes it’s more direct (“Math is not your subject” or even “You’re not smart enough to do math.”) and usually these messages are delivered to children at ages 8, 9, or 10.
Another common narrative is of the young person who enjoys math till a certain class or till a certain teacher — frequently around 9th or 10th grade — where the student gets the message that they have “reached their math level” and anything beyond it is impenetrable for their meager talents.
There are, of course, many other stories (and I invite you to share yours in the comments) and this kind of introduction often leads people who are pro-math-and-science to exhort our society to change its attitude toward math, moving to a more math-positive message for children or to calls for increased time and emphasis on math in school. And while that would be nice, I don’t think it’s the job of society to change its attitude toward math and science. I think it’s the job of teachers to change society’s attitude.
Clearly, many people have been trying for generations to do just that, so I’m not suggesting I have all the answers or that I know what everyone should do. But I would like to share some of my experience co-creating a math course using the principles of backward design, just-in-time remediation, attention to the affective domain, and the assumptions that students are capable of high-quality work and that context is important for learning.
Three years ago, a colleague of mine and I set out to create a course that would prepare students to take college-level statistics using these principles. Unlike myself, my colleague was an experienced statistics instructor and as we talked about what to put in the preparatory course and explored the curriculum together, I constantly asked “why do we cover that topic?” and “what’s the purpose of that skill?” To her credit, she never responded that we do it that way because we always have. She never said “trust me.” She always gave me a good reason — or we tossed out that topic. The result is a course in which, unlike every other math course I have ever taken or taught, there are no extra topics; that is, in our course (“Preparation for Statistics”) every topic and every activity and every assignment are directly relevant to preparing students for the next course.
And while statistics is in general easier to contextualize than algebra, if a student does ask why we are studying a particular topic, the answer is always, in addition to any other uses, that it will be used again next semester.
This intentionality about everything we do in the class creates more buy in for students. Combine it with the assumption that students are capable of doing the work and the practice of appropriate support and we have a course that alters students’ perceptions of math (toward being more useful to them) and of themselves (toward being capable of understanding and using math).
For generations math teachers have debated amongst themselves and with others about the best ways to justify and explain the importance of mathematical education, with more and less success. Arguments about the development of problem solving and reasoning skills assume a privileged place for math that is disciplinarily arrogant and willfully ignorant (or even insulting) of the intellectual rigors in every other discipline. Discussions of the utility of skills such as factoring polynomials, solving inequalities, and calculating the volume of a frustum (much as I enjoy these topics) are unconvincing and potentially disingenuous.
It is our job to do better. And from my experience, when we do a better job of connecting what we’re doing in class to something the students want to know, the students respond with curiosity and engagement — the kind of engagement that leads to empowerment, learning, and a new attitude toward math.
And when that happens, people no longer have feel that sinking feeling inside when they see some numbers in an article they’re reading, they no longer have to cringe when they meet a math teacher, and my social life gets a little less awkward.
(*Big ups to the work of the California Acceleration Project and its founders Myra Snell and Katie Hern – my work and the assumptions it’s based on could not have happened without their leadership, intelligence, and support. Snell and Hern are among the finest educators I know.)
The Art of Immersion: How the Digital Generation Is Remaking Hollywood, Madison Avenue, and the Way We Tell Stories (by Frank Rose) is an interesting journalistic look at media and its interaction with humans. Whether in the context of video games, movies, education, or advertising, the book is all about blending the virtual and the real to create immersive experiences. In all cases, the goal is to establish reward systems that motivate us – or manipulate us, depending on your perspective.
As a teacher, the book was thought-provoking and stimulating. The classroom is a reward system and I’m learning to use online tools to improve the immersive educational experience. It made me think more about all the different kinds of rewards to which people respond — affirmation; recognition; artificially created game points; status – not just grades, and how I can use them to help students learn and grow.
Stress is good for humans. It helps us grow and develop, get stronger and adapt in ways we never would be able to without it. Most of us experience healthy stress throughout our lives: dealing with parents and siblings; navigating school; dating; serious relationships—all these and more are sometimes painful, but always rich, opportunities to realize our full potentials.
Of course, stress can also harm if it is too intense or if we don’t have the capacity and/or support to deal with the level of stress with which we are faced. Children who are abused or neglected or who witness violent crimes are often overwhelmed and unable to process the trauma. The results are dramatic, especially if the trauma occurs in the first few years of life, because crucial cognitive and psychological growth can be interrupted causing serious gaps in brain development. It is a testament to the human animal’s resilience that such damage is mostly reparable—but only if the child is treated appropriately within the structure of a loving, stable home and a knowledgeable therapeutic environment.
Bruce D. Perry is a therapist and researcher who can provide the appropriate therapies and he has done so for many children. From sexual abuse, to profound neglect, to former Branch Davidians, Perry has worked with a lot of kids and has collected some of the stories in a book, The Boy Who Was Raised As a Dog: And Other Stories from a Child Psychiatrist’s Notebook: What Traumatized Children Can Teach Us About Loss, Love and Healing (2007), written with journalist and science writer, Maia Szalavitz. Along the way, Perry educates us about trauma, its effects on children, and what he and his team have learned about successful intervention.
Reading this book as a teacher thinking about the trauma that my students may have endured before they came to my classroom gave me pause. If they have undergone such stresses, then helping them to learn means helping them deal with all that. It also means acknowledging that students’ reactions to what seem like an ordinary situations may not be at all ordinary to them because they trigger traumatic memories. Providing a consistent, caring environment for them becomes all the more important.
As teachers, we have to be careful not to approach our students from a deficit perspective. What students lack is less important than what they have, which is always more than we can know. At the same time, understanding some of the environmental stresses can help us deal with them. For me, Perry’s work provides some more understanding of the brain’s development and gives me yet another reason to meet my students where they are. If, sometimes, that means teaching fractions to Calculus students, so be it; if it means helping students over emotional blocks, that’s fine, too. I’m a teacher; I teach, doing whatever is needed to help my students toward their goals. This book helps me think about my work in new ways and for that I am grateful.
Uri Treisman, already well-known for his work improving the success of Calculus students, continues to impress me. (And—I had the chance to meet him last summer—he’s a nice guy.) In this talk at the WestEd Board of Directors’ 2010 Forum, Treisman talks about the work Carnegie is doing on developmental math at the college level. He makes many smart points, often backed by research and data. One of my favorite parts of his talk is that he frequently refers to actual student feedback—a radical notion, by definition.
Good teaching is as difficult to define as other arts and the debate over how teachers should be evaluated and what it should mean is raging all over the country. While reading a paper on teacher evaluation put out by Accomplished California Teachers, I realized that, though the study is useful and the recommendations good, it misses a fundamental issue. Too often, in the discussion among professionals about teaching and learning, we neglect the voice of students.
That’s one of the reasons I like the draft study done by James W. Stigler, Karen B. Givvin, and Belinda J. Thompson, “What Community College Developmental Mathematics Students Understand About Mathematics.” In it, they try to eplore what students get wrong and what they don’t and why. They listen carefully and respectfully to students, thoughtfully writing about what they find.
One of the most profound questions that students pose when asked to solve a problem during the interview is, “Am I supposed to do it the math way, or just do what makes sense?” The question reveals a fundamental disconnect between what students experience in their lives and what they experience in the classroom. Not a revelation: the disconnect is completely consistent with my experience listening to community college students in developmental math classes. Any teacher paying attention is aware of it. However, as I read this question and the rest of the study, I began asking a series of different questions:
- Is the math we teach connected to students’ lives?
- Is the math we teach connected to our own lives?
- Are we, as math teachers, so indoctrinated into a mathematical perspective that we force the connections between math and our lives?
- Would it be beneficial to math students for teachers to call out the cultural framing that we are bringing to the subject and that we are trying to help them assume?
Clearly, I’m not going to answer the first three questions here. People make variously good and bad arguments about math’s “utility” that are usually circular, starting from the assumption that math applies to most, if not all, the natural world. Rather, I think we must continue to ask them of ourselves and of our curriculum. The question of perspective and acculturation is complex and probably unanswerable. Philosophers of science, much smarter and more capable than I (e.g., Karl Popper, Imre Lakatos, Thomas Kuhn, and Paul Feyerabend) have been arguing about it for years without full resolution.
But the last question is easier for me. Cultures around the world do math, so math seems to be a fundamentally human activity. However, that math is not usually what we’re teaching. As such, I firmly believe it is helpful for students to see that the math we teach in our classrooms is a cultural construct and not necessarily “natural”; in fact, the math in our modern textbooks is a carefully contrived version of math. It is made to appear smooth, a straight line of development from numeration, to fractions, to factoring, to graphing, to functions, to differentiation, to integration, and beyond. If students don’t see how smooth and “obvious” it all is, then it is their fault. And when the story isn’t quite so smooth, we just pretend it is — “don’t you see?”
Acknowledging the culture of math and its interplay with the other parts of our culture is an important step to demystifying math and to being intellectually honest, toward having students realize that they can bring all their intuitions, experience, and knowledge to bear on problems, both in and out of math class. At the same time, it helps remind us, as teachers, to listen to students, because their experience of math is part of what math is in our classrooms. More, their experience of math will survive us, long after we’re retired, helping to create the culture of math in the world to come.
As teachers, we have spent years mastering our content and working to be better teachers. Yet, students still sometime disparage our work and/or our chosen field of study. Working with as many students as we do, it is often hard to see what we can learn from the next batch. Truly listening to our students takes effort and focus. I frequently fail to do it well, but every time I do, I am rewarded with a better connection and a better class. Listening to our students is part of the art of teaching. We fail to listen at our own, our profession’s, and our culture’s peril.
I find TED talks slightly annoying, bastions of self-satisfied, white (how many people of color do you notice in the audience?), upper-middle class intellectualism (I’m using the term intellectualism as a form of oppression practiced on those deemed uneducated, unthinking, and uninterested in “Ideas”).
Still, there are some good talks in the series. If you haven’t seen the one entitled “Do schools kill creativity?“, by Sir Ken Robinson, then you should, especially if you’re a teacher. One of my favorite bits in the talk is his story about a now-famous dancer, who as a fidgety, irresponsible girl was taken to the doctor to see what was wrong. The doctor reputedly said to the mother, “Your daughter’s not sick; she’s a dancer.” That doctor recognized the talent and ability in that child and helped bring it out, if only by referring her to the right place. The more we, as teachers, can do that, instead of forcing all our students into the same boxes, the more we will be happy as teachers, the more our students will succeed, and the more our society will benefit from the wealth of contributions we all have to bring.
But there’s another piece to this issue. The answer is not just to say that all poor students are studying the wrong thing. I’ve seen too many math students, who appear destined to fail, turn their difficulties into success to think that all struggling students should be referred to another field of study. Rather, I see it as my job to help my students use the skills and abilities and experiences they bring to the classroom to become successful math students. When we do that, we are achieving the highest goals of democratic education by fostering people that bring their whole selves to the collective issues we face. Considering the complexity of the problems in the global society, we need all the help we can get.