In keeping with my Week 1 emphasis in Algebra 1 on activating prior knowledge of how to translate words into mathematical expressions, equations, or inequalities (or at least gelling some of it back into place), I've also created a "Block" game for practicing 'Words into Math' in my Algebra 1 classes. There are two levels of game cards that correspond to Lessons 1.3 and 1.4 in McDougall Littell Algebra 1 California edition (for those of you playing along at home).
This is a variation on Maria Anderson's wonderful, tic-tac-toe-style "blocking games" (Antiderivative Block, Factor Pair Block, and Exponent Block — using her generic gameboard, rules, and my own game cards for each of these first three games of hers on her web site).
The game can be played in any number of ways — either competitive or collaborative. Students can compete against each other — tic-tac-toe style — to get four of their counters in a row. Or they can simply take turns choosing the problem and working on solving each problem on the whole board.
I've created two levels of "Words into Math Block": Level 1 (purple problem cards) and Level 2 (green problem cards). I use Maria's generic PDF gameboard and print or copy them on colored cardstock or paper. I have learned the hard way to give each level its own color ID as soon as I create the game cards so I can easily recreate the card sets later whenever I need to.
I allow students to use whatever resources they need to during practice activities, so I expect to see those nifty Troublesome Phrase Translator slider sleeves flying during these two days. :-)
All of my materials, plus the photo above (in case you need a model) are on the Math Teacher Wiki.
Students really love these block games! I have a bunch of different "counters" that they can use as their game board markers: little stars (Woodsies from Michael's), circles, and hearts, colorful foam planet/star clusters, and various kinds of beans.
I'm hoping to get my students to be less flummoxed by mathematical language by giving them practice in using it early and often. Enjoy!
cheesemonkey wonders

Showing posts with label writing in math class. Show all posts
Showing posts with label writing in math class. Show all posts
Monday, August 6, 2012
Saturday, July 7, 2012
On choosing sanity, and on modeling this choice for our students
I want to talk a bit about sanity — not because I think I'm an expert (I'm not; no one is) but because I have come to understand sanity as a choice we make moment by moment, and because, in so doing, I have seen how we either model — or do not model — it for our students in our classrooms and in our lives. And this is an enormous part of the social and emotional life training they either receive or do not receive in this crucial part of their lives.
I teach middle schoolers, or rather, I should confess that they teach me. Every student and every class is a mirror in which I can see what I am teaching them. Perhaps because their access to it is new, middle school students have a finely tuned hypocrisy detector. More so than any of the high school or university students I've ever taught, middle school students want to see who "walks their talk." Do so, I have learned, and they will follow you anywhere. Fail to do so at your own peril.
So a big part of this year's learning, for me, has been learning how to tune in to what I am actually doing and checking in on whether this is consistent with the social and emotional lessons on appropriate self-care I am trying to teach. Sometimes that has meant being the adult in their lives who tells them to stop the madness. The only way to stop the war is to stop fighting, stop struggling, stop efforting. There really are only so many hours of the day, and for middle schoolers, about eight of those need to be spent sleeping. That means every piece of homework can't always get done every day all the time. Sometimes a person has to choose sanity. So I try to understand that and allow for it, because learning to allow space for all of life is something they are going to have to learn if they are going to do better in running this world than we have done so far.
I've also had to learn how to trust my training and my gut. I was blessed to study for over ten years with a pioneer in integrating social and emotional intelligence and mindfulness into learning environments ranging from special education to mainstream classrooms to therapy situations. You probably haven't heard of him because he has spent his life being what I think of as a guerrilla bodhisattva — a pioneering educational psychologist and an undercover evangelist for social and emotional health in daily life. His name is Dr. Fred Joseph Orr, and I am blessed to count myself among his students. Actually, we think of ourselves as his disciples, though he would undoubtedly discourage that characterization. But it's a fair one. He taught us to integrate teachings from whatever sources might be beneficial to ourselves and our communities — teachings from Adlerian psychology, spiritual development, meditation, yoga, Buddhism, his own mischievous sense of humor and spirit of adventure, writing as a practice, the practice of joy and creativity in whatever form they might take, and environmental restoration and ecological rebalancing. I came to him as a writer, writing teacher, and longtime meditation practitioner, but I quickly became much more than that under his mentorship. And it was the kind of mentorship that is a true spiritual gift — the kind you can only repay by sharing it with others. In his life, he suffered in ways that most of us would find unimaginable, and yet he remains the most radiant and joyful person I have ever known. And although his active teaching practice has been cut short by a medical condition that has become the focus of his own personal life practice, his students carry on his great efforts, sharing the learning and the gifts we received from his teachings. His teaching of us was an investment in the future and a labor of love. I wake up every morning determined to be worthy of the effort, love, and energy he poured into teaching me.
There's an urban fable Fred used as a teaching tale. It's known as The Hundredth Monkey principle. It began in the 1950s as a call to end the escalating nuclear arms race, but Fred believes it has broader applicability as a model for how human awareness and sanity can be activated too, and I have come to believe this too. The idea is simple, yet profound: when a critical mass of individuals' consciousness gets raised, it inevitably triggers a paradigm shift in the dominant culture. So this turns out to be a more leveraged model for social change than the conventional wisdom tends to think, for when we direct the focus of our daily efforts on helping individuals and small groups to shift their energies, awareness, and attention, we are doing our part to put our culture on the path that leads toward greater sanity, in addition to greater achievement.
So what does all this squishy-sounding woo-woo stuff have to do with teaching and learning mathematics?
I believe it provides us with an on-ramp, a way to reach the hearts and minds of the students who are most discouraged and shut down in the math classroom. It's differentiated for the most capable students because most of them have never been given tools to cultivate self-awareness and other-awareness as a part of their learning. And by learning — and by teaching these discouraged students how — to cultivate their social and emotional intelligence in how they engage in mathematical practice in our classrooms, we can change their relationship with mathematical studies to one based on what the American Tibetan Buddhist teacher Pema Chodron describes as "unconditional friendliness."
Over the last couple of days, as I've begun my yearly summer rituals of cooking and storing school lunches in the freezer for days when I need the loving self-care of hand-made soup in the middle of my day, I have realized that this is the heart of my Twitter Math Camp talk. My topic is Dan Pink's book, Drive: The Surprising Truth About What Motivates Us, and how to use his ideas about intrinsic motivation to reach the discouraged math learners in our classrooms. I've begun to understand how Fred's work with me is an arrow that flies straight to the bullseye of this target, and it's given me some hopefully valuable insight into how to create the toughest of Pink's three pillars of intrinsic motivation. That pillar is autonomy, and I'll write more about it in an upcoming post as I flesh out my talk with ideas and activities.
In the meantime, I'm going to let my subconscious mind work on the problems while my conscious mind takes a nap.
I teach middle schoolers, or rather, I should confess that they teach me. Every student and every class is a mirror in which I can see what I am teaching them. Perhaps because their access to it is new, middle school students have a finely tuned hypocrisy detector. More so than any of the high school or university students I've ever taught, middle school students want to see who "walks their talk." Do so, I have learned, and they will follow you anywhere. Fail to do so at your own peril.
So a big part of this year's learning, for me, has been learning how to tune in to what I am actually doing and checking in on whether this is consistent with the social and emotional lessons on appropriate self-care I am trying to teach. Sometimes that has meant being the adult in their lives who tells them to stop the madness. The only way to stop the war is to stop fighting, stop struggling, stop efforting. There really are only so many hours of the day, and for middle schoolers, about eight of those need to be spent sleeping. That means every piece of homework can't always get done every day all the time. Sometimes a person has to choose sanity. So I try to understand that and allow for it, because learning to allow space for all of life is something they are going to have to learn if they are going to do better in running this world than we have done so far.
I've also had to learn how to trust my training and my gut. I was blessed to study for over ten years with a pioneer in integrating social and emotional intelligence and mindfulness into learning environments ranging from special education to mainstream classrooms to therapy situations. You probably haven't heard of him because he has spent his life being what I think of as a guerrilla bodhisattva — a pioneering educational psychologist and an undercover evangelist for social and emotional health in daily life. His name is Dr. Fred Joseph Orr, and I am blessed to count myself among his students. Actually, we think of ourselves as his disciples, though he would undoubtedly discourage that characterization. But it's a fair one. He taught us to integrate teachings from whatever sources might be beneficial to ourselves and our communities — teachings from Adlerian psychology, spiritual development, meditation, yoga, Buddhism, his own mischievous sense of humor and spirit of adventure, writing as a practice, the practice of joy and creativity in whatever form they might take, and environmental restoration and ecological rebalancing. I came to him as a writer, writing teacher, and longtime meditation practitioner, but I quickly became much more than that under his mentorship. And it was the kind of mentorship that is a true spiritual gift — the kind you can only repay by sharing it with others. In his life, he suffered in ways that most of us would find unimaginable, and yet he remains the most radiant and joyful person I have ever known. And although his active teaching practice has been cut short by a medical condition that has become the focus of his own personal life practice, his students carry on his great efforts, sharing the learning and the gifts we received from his teachings. His teaching of us was an investment in the future and a labor of love. I wake up every morning determined to be worthy of the effort, love, and energy he poured into teaching me.
There's an urban fable Fred used as a teaching tale. It's known as The Hundredth Monkey principle. It began in the 1950s as a call to end the escalating nuclear arms race, but Fred believes it has broader applicability as a model for how human awareness and sanity can be activated too, and I have come to believe this too. The idea is simple, yet profound: when a critical mass of individuals' consciousness gets raised, it inevitably triggers a paradigm shift in the dominant culture. So this turns out to be a more leveraged model for social change than the conventional wisdom tends to think, for when we direct the focus of our daily efforts on helping individuals and small groups to shift their energies, awareness, and attention, we are doing our part to put our culture on the path that leads toward greater sanity, in addition to greater achievement.
So what does all this squishy-sounding woo-woo stuff have to do with teaching and learning mathematics?
I believe it provides us with an on-ramp, a way to reach the hearts and minds of the students who are most discouraged and shut down in the math classroom. It's differentiated for the most capable students because most of them have never been given tools to cultivate self-awareness and other-awareness as a part of their learning. And by learning — and by teaching these discouraged students how — to cultivate their social and emotional intelligence in how they engage in mathematical practice in our classrooms, we can change their relationship with mathematical studies to one based on what the American Tibetan Buddhist teacher Pema Chodron describes as "unconditional friendliness."
Over the last couple of days, as I've begun my yearly summer rituals of cooking and storing school lunches in the freezer for days when I need the loving self-care of hand-made soup in the middle of my day, I have realized that this is the heart of my Twitter Math Camp talk. My topic is Dan Pink's book, Drive: The Surprising Truth About What Motivates Us, and how to use his ideas about intrinsic motivation to reach the discouraged math learners in our classrooms. I've begun to understand how Fred's work with me is an arrow that flies straight to the bullseye of this target, and it's given me some hopefully valuable insight into how to create the toughest of Pink's three pillars of intrinsic motivation. That pillar is autonomy, and I'll write more about it in an upcoming post as I flesh out my talk with ideas and activities.
In the meantime, I'm going to let my subconscious mind work on the problems while my conscious mind takes a nap.
Saturday, May 28, 2011
Getting students writing and reflecting in math class
I used this idea in Algebra 2 during our polynomial graph sketching unit to support their conceptual understanding of end behavior, and it worked surprisingly well.
Most of my students had not had much truck with the idea of infinity, much less with the idea of approaching it, so we started by talking about how the graph of a function is a representation of a specific story — like a novel — or like the life story of a human being. Every person's life story is completely unique, yet everyone has an experience of both birth and death (the beginning and end being like end behavior). Everyone's birth story may be different -- some people are born in a taxi cab, some are born at home, some are born in a hospital, some are born under water, and yet every single one of these births has the very fact of having gone through birth in common. Similarly, death is the ultimate "end behavior" of life. We cannot know exactly how or when a specific person's death may come, but we do know that it is going to happen some time after they have been born and have lived for some duration of time.
We also talked about the movement of a function graph across the axis at its x-intercepts — how at certain key transformative moments, a person's life crosses from negative into positive territory -- or it may move in the opposite direction.
Most of my students had not had much truck with the idea of infinity, much less with the idea of approaching it, so we started by talking about how the graph of a function is a representation of a specific story — like a novel — or like the life story of a human being. Every person's life story is completely unique, yet everyone has an experience of both birth and death (the beginning and end being like end behavior). Everyone's birth story may be different -- some people are born in a taxi cab, some are born at home, some are born in a hospital, some are born under water, and yet every single one of these births has the very fact of having gone through birth in common. Similarly, death is the ultimate "end behavior" of life. We cannot know exactly how or when a specific person's death may come, but we do know that it is going to happen some time after they have been born and have lived for some duration of time.
We also talked about the movement of a function graph across the axis at its x-intercepts — how at certain key transformative moments, a person's life crosses from negative into positive territory -- or it may move in the opposite direction.
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