I find these two examples to be fantastic for challenging students. I am starting to work with some students who have dyslexia and have trouble with patterns and the number line. It will be interesting to see how they would approach these two problems. Is the spiral number line easier for them or harder to understand? It will be interesting to find out.
I experience math joy when I get to work with a student or teacher or class that is struggling to understand. I am comfortable with the struggle. I have learned to listen first, then ask questions to draw out thinking. Often I find I must dig back to identify previous misunderstandings before we can progress with the original issue. My brain loves the sheer challenge of finding a way to help the learner create personal understanding and experience triumph. I know that this is a very complicated task but it feels so natural to me. To see the face of an excited learner is reward enough to urge me back to school for my 41st year as an educator!
As a math coach, I work for the weekend when I am not invited into rooms to help teachers and their students. It makes me sad that teachers settle for what they’ve always done and console themselves with the promise to work harder next year. I believe that we can all work better— and the key is communication with both words and visual means, whether pictures or manipulatives. Most of the words, however, need to come from the learner, not the teacher.
My personal favorite math tool, one that brings me joy, is tape diagrams. I first encountered them with Common Core and MEC workshops presented by Ruth Parker and Patty Lofgren. Tapes have so many uses from fractions to proportions to algebraic relationships. The wonder of using tape diagrams is that they demonstrate mathematical relationships throughout your work in a very intuitive way. I’ve developed a way to teach math equations (and steps) with them. My efforts may stem from the fact that algebra is the branch of mathematics that brings me the most joy.
Thanks for the opportunity to describe mathematical joy. When I meet people who say they’ve never understood math, I want to say, “Let’s sit down and work on that!” I’m not sure that strangers would welcome that opportunity as much as I. 🙂
Math brings me so much joy! I find myself looking at the number spiral and trying to find patterns just as I did with the multiplication table in my Pee Chee folder way back when. For some reason it brings me a sense of peace that the rules of math don’t have exceptions. As someone who’s always struggled with language, it’s ironic that my career path lead me to teach English language learners. However, math is fun! Math is a puzzle just waiting to be solved.
“Math is a puzzle just waiting to be solved.” Love that. Building from Carol 👆 my personal view is that the point of learning math is for people to learn how to puzzle and unpuzzle themselves in increasingly sophisticated ways. I experience joy when my I finish one question and recognize that “wait – I too am an asker of questions” and create a variant of that original question that now interests me more. Just me, my brain, and something to write with and on.
I can get so task-oriented when it comes to my current work with colleagues around improving instructional practice in math classrooms that I can easily lose track of the importance of JOY in doing math (in workshops and on our own).
Cathy Humphreys reminded our leadership team of this last summer when she introduced us to the work of Amy Parks and Anita Wager and a presentation they gave at the 2017 NCTM Research Conference (https://docplayer.net/98572135-Joy-the-zeroth-mathematical-practice-amy-noelle-parks-anita-a-wager.html) Thinking of Joy as the “zeroth mathematical practice” is easy to say but is a worthy and meaty challenge if we take it seriously, especially those of us at higher grades where Parks and Wager saw very little evidence of joy.
As a learner myself, I experience the most joy when I am given time to dig into a problem on my own terms. Group work is massively more tolerable to me if I know I will have the opportunity to also play with the task at hand on my own at some point.
As a student in school, I had to create these opportunities myself and I was motivated to do so a very small number of times. I was rarely asked interesting questions and then asked to explore them. I remember once being told by a student teacher in my geometry class that I was making proofs unnecessarily hard by using more steps than needed. I knew I was still correct though and remember feeling for the first time that I might want to challenge the judgment of a mathematical authority figure, and that I might have something unique to offer math.
It wasn’t until the MEC workshops Lisa mentioned (above) that I experienced a learning environment where I was asked interesting questions AND that my time to explore was not only available, but also fiercely protected.
Not every moment in class needs to be joyful, but creating an environment where joyful interaction with mathematics is seen as necessary and is the primary priority, as opposed to a side activity when there’s time, is something worth continuing to fight for.
And thank you for sharing the number spiral, I can’t remember if I’ve played with it before or not and am excited to jump in and see what I see!
This reminds me of a saying by my friend, Dr. Edmund Harriss of the University of Arkansas, who claims that “homework should be a joyful meditation.” In other words, kids shouldn’t be at home crying w hile their parents complete their homework for them. How do we get there is the question?
I find these two examples to be fantastic for challenging students. I am starting to work with some students who have dyslexia and have trouble with patterns and the number line. It will be interesting to see how they would approach these two problems. Is the spiral number line easier for them or harder to understand? It will be interesting to find out.
Fascinating ideas! As a retired math educator I miss the challenges that math problems posed. I will seek these out again.
I experience math joy when I get to work with a student or teacher or class that is struggling to understand. I am comfortable with the struggle. I have learned to listen first, then ask questions to draw out thinking. Often I find I must dig back to identify previous misunderstandings before we can progress with the original issue. My brain loves the sheer challenge of finding a way to help the learner create personal understanding and experience triumph. I know that this is a very complicated task but it feels so natural to me. To see the face of an excited learner is reward enough to urge me back to school for my 41st year as an educator!
As a math coach, I work for the weekend when I am not invited into rooms to help teachers and their students. It makes me sad that teachers settle for what they’ve always done and console themselves with the promise to work harder next year. I believe that we can all work better— and the key is communication with both words and visual means, whether pictures or manipulatives. Most of the words, however, need to come from the learner, not the teacher.
My personal favorite math tool, one that brings me joy, is tape diagrams. I first encountered them with Common Core and MEC workshops presented by Ruth Parker and Patty Lofgren. Tapes have so many uses from fractions to proportions to algebraic relationships. The wonder of using tape diagrams is that they demonstrate mathematical relationships throughout your work in a very intuitive way. I’ve developed a way to teach math equations (and steps) with them. My efforts may stem from the fact that algebra is the branch of mathematics that brings me the most joy.
Thanks for the opportunity to describe mathematical joy. When I meet people who say they’ve never understood math, I want to say, “Let’s sit down and work on that!” I’m not sure that strangers would welcome that opportunity as much as I. 🙂
Math brings me so much joy! I find myself looking at the number spiral and trying to find patterns just as I did with the multiplication table in my Pee Chee folder way back when. For some reason it brings me a sense of peace that the rules of math don’t have exceptions. As someone who’s always struggled with language, it’s ironic that my career path lead me to teach English language learners. However, math is fun! Math is a puzzle just waiting to be solved.
“Math is a puzzle just waiting to be solved.” Love that. Building from Carol 👆 my personal view is that the point of learning math is for people to learn how to puzzle and unpuzzle themselves in increasingly sophisticated ways. I experience joy when my I finish one question and recognize that “wait – I too am an asker of questions” and create a variant of that original question that now interests me more. Just me, my brain, and something to write with and on.
I can get so task-oriented when it comes to my current work with colleagues around improving instructional practice in math classrooms that I can easily lose track of the importance of JOY in doing math (in workshops and on our own).
Cathy Humphreys reminded our leadership team of this last summer when she introduced us to the work of Amy Parks and Anita Wager and a presentation they gave at the 2017 NCTM Research Conference (https://docplayer.net/98572135-Joy-the-zeroth-mathematical-practice-amy-noelle-parks-anita-a-wager.html) Thinking of Joy as the “zeroth mathematical practice” is easy to say but is a worthy and meaty challenge if we take it seriously, especially those of us at higher grades where Parks and Wager saw very little evidence of joy.
As a learner myself, I experience the most joy when I am given time to dig into a problem on my own terms. Group work is massively more tolerable to me if I know I will have the opportunity to also play with the task at hand on my own at some point.
As a student in school, I had to create these opportunities myself and I was motivated to do so a very small number of times. I was rarely asked interesting questions and then asked to explore them. I remember once being told by a student teacher in my geometry class that I was making proofs unnecessarily hard by using more steps than needed. I knew I was still correct though and remember feeling for the first time that I might want to challenge the judgment of a mathematical authority figure, and that I might have something unique to offer math.
It wasn’t until the MEC workshops Lisa mentioned (above) that I experienced a learning environment where I was asked interesting questions AND that my time to explore was not only available, but also fiercely protected.
Not every moment in class needs to be joyful, but creating an environment where joyful interaction with mathematics is seen as necessary and is the primary priority, as opposed to a side activity when there’s time, is something worth continuing to fight for.
And thank you for sharing the number spiral, I can’t remember if I’ve played with it before or not and am excited to jump in and see what I see!
This reminds me of a saying by my friend, Dr. Edmund Harriss of the University of Arkansas, who claims that “homework should be a joyful meditation.” In other words, kids shouldn’t be at home crying w hile their parents complete their homework for them. How do we get there is the question?