Is There Any Mathematics in Our Mathematics Classes?
I'll return to this question at the end!
I want to begin with a reflection from February's I Love Math Day. We were blessed by the presence of two wonderful visiting mathematicians. After spending the day at Mustard Seed School, each of them wrote a note of thanks and reflected on what they saw:
"I really enjoyed today -- to meet the students, to hear about and celebrate their work, to enjoy the Mustard Seed culture of care and love for kids and their learning and development. It was ..... such a delight to be with you all! So great to enjoy the fruits of [the school's] labors through these years of nurturing a culture of math appreciation and engagement!"
Dr. Jen Knight, computational chemist, Schrödinger, New York
"I can't describe how wonderful today was...in so many ways. I am blessed to .... experience a glimpse of your community of colleagues, parents, and especially students. Today I have felt more in touch with my "math" self and my "spiritual" self than ever. The questions that the kids asked were thought provoking and as much as I hope they enjoyed my answers, I enjoyed reflecting and even understanding more why I do what I do. Their projects were creative and their presentations were very well done. I loved visiting even the youngest of students today, as it shows me how we can shape young minds to truly enjoy math!"
Janine Cuervo, Middle School Math Teacher, Trinity School, New York
Among the many things they experienced, our guests saw amazing student work. They saw us celebrating great middle school problem-solving as seen in submissions like this:
And they saw students bringing joy and wit into the explanations of their work. Here is a paper sculpture of three scoops of strawberry ice cream. A sixth grade team created this to explain their solution to the Strawberry Ice Cream Problem.
One team came up with a three dimensional way to share a proof of this equation:
Now to the title question: Last Friday night I heard Steven Strogatz, Professor of Applied Mathematics at Cornell University speak. He lamented the experiences of his 13 and 15 year old sons in math classes that did not always inspire them. He quoted Paul Lockhart who writes this in his essay A Mathematician's Lament:
I want to begin with a reflection from February's I Love Math Day. We were blessed by the presence of two wonderful visiting mathematicians. After spending the day at Mustard Seed School, each of them wrote a note of thanks and reflected on what they saw:
A student submission for The Missile problem:
"I really enjoyed today -- to meet the students, to hear about and celebrate their work, to enjoy the Mustard Seed culture of care and love for kids and their learning and development. It was ..... such a delight to be with you all! So great to enjoy the fruits of [the school's] labors through these years of nurturing a culture of math appreciation and engagement!"
Dr. Jen Knight, computational chemist, Schrödinger, New York
"I can't describe how wonderful today was...in so many ways. I am blessed to .... experience a glimpse of your community of colleagues, parents, and especially students. Today I have felt more in touch with my "math" self and my "spiritual" self than ever. The questions that the kids asked were thought provoking and as much as I hope they enjoyed my answers, I enjoyed reflecting and even understanding more why I do what I do. Their projects were creative and their presentations were very well done. I loved visiting even the youngest of students today, as it shows me how we can shape young minds to truly enjoy math!"
Janine Cuervo, Middle School Math Teacher, Trinity School, New York
Among the many things they experienced, our guests saw amazing student work. They saw us celebrating great middle school problem-solving as seen in submissions like this:
And they saw students bringing joy and wit into the explanations of their work. Here is a paper sculpture of three scoops of strawberry ice cream. A sixth grade team created this to explain their solution to the Strawberry Ice Cream Problem.
One team came up with a three dimensional way to share a proof of this equation:
(1/4) + (1/4)2 + (1/4)3 + (1/4)4 + … = (1/3)
"If you deny students the opportunity to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs -- you deny them mathematics itself. So no, I'm not complaining about the presence of facts and formulas in our mathematics classes, I'm complaining about the lack of mathematics in our mathematics classes."
Paul Lockhart, Saint Ann's School, Brooklyn, NY (Ph.D. Columbia University)
I think that what our visitors saw on I Love Math Day was a bit of the mathematics in our mathematics classes! I think this is part of what touched them so deeply.
I see the fruit of this work every day in class. Eighth graders are struggling with linear equations right now. They graph them and see a concrete picture of a solution set. Then they move to the abstract process of solving simultaneous equations using substitution. Then they graph again to see the connections between the concrete and the abstract. They do all this fully confident that patterns and beauty will be revealed through the struggle. They have come to know that that is how mathematics works!