Response to "The Math Formula"
[Editor's Note: While I was a full-timed released mentor to new teachers in Ventura County I worked with a 1st and 2nd year Math teacher at Newbury Park High School named Michael Weingarden. I recently sent him the article "The Math Formula" for his review. Below is his considered response]:
I read your article and you and I share similar perspectives on where math education is and where it should go. When I first considered teaching math, I began to watch every teacher movie and I began to read all sorts of books about math- including Fermat's Enigma which you referenced in your article. I was reading books like Fermat's Enigma, Fermat's Last Theorem, God's Equation, Mystery of the Aleph, and other books by Amir Aczel. Because my degree was in Electrical Engineering and not math, I also had to take 3 CSET Math Exams including the history of math! Yes, believe it or not, at that time, teachers who wanted to teach AP math classes were required to learn and answer questions about the history of math. So, although, Fermat's Enigma and some of the others above did a good job of covering that subject, I did buy and read a book called A History of Mathematics and it is still sitting on a bookshelf in my classroom. So, like you, I was fascinated by the history of math.
And, like you, I question the reasonableness of clinging so tightly to the 7 step lesson plan. And, I like the idea of integrating more reading in the math class. However, my ideas on what students should read have evolved since I started to teach statistics. Years ago, our district had only AP Statistics classes. And at that time, only 50% of our seniors were taking math classes! Can you believe that was true in Conejo Valley? I learned this at one of the district math articulation meetings. At the time, I was just teaching my first AP Stats class and I hated it. It was more of the same rush, rush, rush through too many topics in too little time just like most of the core math subjects. So, I proposed a non-AP statistics class. Everyone who heard the idea loved it, so I created course proposal and took it all the way through the approval process. I will admit that I had some ulterior motives. The class would target seniors, there would be no AP test and no follow on high school math class. In other words, I could sculpt the class anyway that I wanted to.
The summer before I taught my first stats class, I began to read non-fiction books that were related to statistics. Drunkard's Walk: How Randomness Rules Our Lives, Proofiness: How You're Being Fooled by the Numbers (by Charles Seife, one of the authors from your list) and A Mathematician Reads the Newspaper. I found the reading to be fascinating. Practical applications of math that kids will encounter every day in the news. Math regarding elections and sports and gambling and risk and reward. After reading these books, I got a grant to get a class set of Drunkard's Walk and Proofiness. Drunkard's Walk is excellent because it's half history of probability and half modern day anecdotes, both woven in a spiral thread throughout the book. And when the school year started, I began to have my students read Drunkard's Walk in class. We would do silent sustained reading on some days. I tried a variety of ways to hold kids accountable for the reading, but I'll admit, the whole process was a mess. Not the book's fault, all mine. The kids that took my stats class were decent students, they just weren't calculus students. And only some of them loved reading. Some really considered it a burden.
As an aside, I had a conversation with an Economics teacher at NPHS one day. I asked him how much math he does with the kids. He told me, "none, I took all the math out, the kids didn't get it." I hated that response, but after a few years of trying to force kids to read Drunkard's Walk- and later The Signal and The Noise by Nate Silver- I began to feel the same way about reading in statistics class. Some kids read fast, some kids read slow, some kids will read through the text and respond to writing prompts with their newfound knowledge. Others would avoid reading and paraphrase their classmates work. And, as you well know, grading student writing is hard work.
Over the years of teaching stats, I consumed news from the radio and internet like a Baleen whale consumes krill. I enjoyed listening to audio books while driving or exercising and then podcasts came along. I became addicted to NPR radio and the podcasts that came from NPR. I was listening to Science Friday, Freakonomics, Radiolab, Planet Money and others. I read the book Freakonomics and then I read several books by Malcolm Gladwell (an economist whose books have a strong statistical component). And then I put two and two together. I realized that it's hard for kids to sit still and think for long periods of time. And I was listening to topical podcasts while going on long walks for exercise. So, I picked out some podcasts and got permission to take the kids on a hike from NPHS to the Starbucks near the Albertsons on Reino Rd. The kids and I would put in our earbuds and hike and listen to informative podcasts that provided real world examples of math and statistics. I didn't have to worry about the different reading speeds. Everyone could listen at the same pace. Focus is still and issue, but over the past few years I have been working on refining the process.
The first year I started the class, I also wanted to include some appropriate movies and shows that would convey statistical concepts in interesting ways. There is a series of videos called Against All Odds: Inside Statistics with a Computational Geneticist as the host. We watch her videos every week. We watch the movie Moneyball (baseball and statistics) and 21 (probability and gambling). And because of a predominance of infotainment shows, I regularly show clips from John Oliver, Stephen Colbert, Neil DeGrasse Tyson, Bill Nye and others because they present science and the news in such entertaining ways.
So, I am still interested in getting the kids to read, but I've been trying to get the knowledge into the kids' brains using every weapon in the arsenal. Certainly, the podcasts and movies make it easier for the kids to swallow their medicine. I don't want to give up on reading, but these days if we do read, I pick out several pages that relate to a particular topic rather than asking them to read a whole chapter or book.
With everything that I've said so far, I am not against reading to help supplement the learning of math. But I do have a problem with the reading being about the history of math. The problem is that the history of math is inherently misogynistic. And if not misogynistic, at least mostly male based. And it's mostly Caucasian based. When you read the history of math, it's all men, men, men and it's mostly European men. Don't get me wrong. Other cultures have their own history of math, the Mayans, the Aztecs, arabic numerals, Indian Vedic math and Chinese math. But the books you described tend to focus on white male European math. And my view of math education is that I want it to be more inclusive.
There is a famous actress who is also a mathematician and she has written several books on math for girls. Her name is Danica McKellar- she was Winny in The Wonder Years. I don't know that she is doing anything revolutionary with math pedagogy, but she has written books on math that target girls.
A step up from there is the work of Jo Boaler who is leading a wave in math education reform. It would be worthwhile to read the Kindle samples of her books about growth mindset in math education. She's an inspiration to girls who want to learn math and she's an inspiration to math teachers who want to try new things to reach more students.
I also just purchased a new book called Necessary Conditions which has some new and intriguing ideas about how to improve math pedagogy.
Last year, I added the movies The Martian and Hidden Figures to my stats class. With the Martian, I read the book and watched the movie and enjoyed both. If I thought I wanted to get more reading into math class, I think a book like The Martian would get way more buy in from today's audience than the history of math. The same could be said of Hidden Figures which is less mathy, but way more inspirational for young women and minorities.
I've meandered about a bit here and I'll try to bring it all together in this last paragraph. I like your idea of asking kids to read about the history of math to get them to think about the bigger picture, to think beyond the computations. But, I think we now have way better material to accomplish that goal than books about the history of math. I'd much rather have kids read books like Moneyball or The Martian or almost anything by Malcolm Gladwell where they can get exposed to the bigger picture in a way that is modern and relevant and exciting. And, although I love the idea of having more reading across the curriculum, I suspect that the future is heading toward well produced podcasts and videos. And, lastly, I look forward to more material that inspires more girls and minorities with role models they can relate to (like Danika McKellar and John Urschel and Jaime Escalante).
Sorry for the tome. Hope that this helps in some small way.
I read your article and you and I share similar perspectives on where math education is and where it should go. When I first considered teaching math, I began to watch every teacher movie and I began to read all sorts of books about math- including Fermat's Enigma which you referenced in your article. I was reading books like Fermat's Enigma, Fermat's Last Theorem, God's Equation, Mystery of the Aleph, and other books by Amir Aczel. Because my degree was in Electrical Engineering and not math, I also had to take 3 CSET Math Exams including the history of math! Yes, believe it or not, at that time, teachers who wanted to teach AP math classes were required to learn and answer questions about the history of math. So, although, Fermat's Enigma and some of the others above did a good job of covering that subject, I did buy and read a book called A History of Mathematics and it is still sitting on a bookshelf in my classroom. So, like you, I was fascinated by the history of math.
And, like you, I question the reasonableness of clinging so tightly to the 7 step lesson plan. And, I like the idea of integrating more reading in the math class. However, my ideas on what students should read have evolved since I started to teach statistics. Years ago, our district had only AP Statistics classes. And at that time, only 50% of our seniors were taking math classes! Can you believe that was true in Conejo Valley? I learned this at one of the district math articulation meetings. At the time, I was just teaching my first AP Stats class and I hated it. It was more of the same rush, rush, rush through too many topics in too little time just like most of the core math subjects. So, I proposed a non-AP statistics class. Everyone who heard the idea loved it, so I created course proposal and took it all the way through the approval process. I will admit that I had some ulterior motives. The class would target seniors, there would be no AP test and no follow on high school math class. In other words, I could sculpt the class anyway that I wanted to.
The summer before I taught my first stats class, I began to read non-fiction books that were related to statistics. Drunkard's Walk: How Randomness Rules Our Lives, Proofiness: How You're Being Fooled by the Numbers (by Charles Seife, one of the authors from your list) and A Mathematician Reads the Newspaper. I found the reading to be fascinating. Practical applications of math that kids will encounter every day in the news. Math regarding elections and sports and gambling and risk and reward. After reading these books, I got a grant to get a class set of Drunkard's Walk and Proofiness. Drunkard's Walk is excellent because it's half history of probability and half modern day anecdotes, both woven in a spiral thread throughout the book. And when the school year started, I began to have my students read Drunkard's Walk in class. We would do silent sustained reading on some days. I tried a variety of ways to hold kids accountable for the reading, but I'll admit, the whole process was a mess. Not the book's fault, all mine. The kids that took my stats class were decent students, they just weren't calculus students. And only some of them loved reading. Some really considered it a burden.
As an aside, I had a conversation with an Economics teacher at NPHS one day. I asked him how much math he does with the kids. He told me, "none, I took all the math out, the kids didn't get it." I hated that response, but after a few years of trying to force kids to read Drunkard's Walk- and later The Signal and The Noise by Nate Silver- I began to feel the same way about reading in statistics class. Some kids read fast, some kids read slow, some kids will read through the text and respond to writing prompts with their newfound knowledge. Others would avoid reading and paraphrase their classmates work. And, as you well know, grading student writing is hard work.
Over the years of teaching stats, I consumed news from the radio and internet like a Baleen whale consumes krill. I enjoyed listening to audio books while driving or exercising and then podcasts came along. I became addicted to NPR radio and the podcasts that came from NPR. I was listening to Science Friday, Freakonomics, Radiolab, Planet Money and others. I read the book Freakonomics and then I read several books by Malcolm Gladwell (an economist whose books have a strong statistical component). And then I put two and two together. I realized that it's hard for kids to sit still and think for long periods of time. And I was listening to topical podcasts while going on long walks for exercise. So, I picked out some podcasts and got permission to take the kids on a hike from NPHS to the Starbucks near the Albertsons on Reino Rd. The kids and I would put in our earbuds and hike and listen to informative podcasts that provided real world examples of math and statistics. I didn't have to worry about the different reading speeds. Everyone could listen at the same pace. Focus is still and issue, but over the past few years I have been working on refining the process.
The first year I started the class, I also wanted to include some appropriate movies and shows that would convey statistical concepts in interesting ways. There is a series of videos called Against All Odds: Inside Statistics with a Computational Geneticist as the host. We watch her videos every week. We watch the movie Moneyball (baseball and statistics) and 21 (probability and gambling). And because of a predominance of infotainment shows, I regularly show clips from John Oliver, Stephen Colbert, Neil DeGrasse Tyson, Bill Nye and others because they present science and the news in such entertaining ways.
So, I am still interested in getting the kids to read, but I've been trying to get the knowledge into the kids' brains using every weapon in the arsenal. Certainly, the podcasts and movies make it easier for the kids to swallow their medicine. I don't want to give up on reading, but these days if we do read, I pick out several pages that relate to a particular topic rather than asking them to read a whole chapter or book.
With everything that I've said so far, I am not against reading to help supplement the learning of math. But I do have a problem with the reading being about the history of math. The problem is that the history of math is inherently misogynistic. And if not misogynistic, at least mostly male based. And it's mostly Caucasian based. When you read the history of math, it's all men, men, men and it's mostly European men. Don't get me wrong. Other cultures have their own history of math, the Mayans, the Aztecs, arabic numerals, Indian Vedic math and Chinese math. But the books you described tend to focus on white male European math. And my view of math education is that I want it to be more inclusive.
There is a famous actress who is also a mathematician and she has written several books on math for girls. Her name is Danica McKellar- she was Winny in The Wonder Years. I don't know that she is doing anything revolutionary with math pedagogy, but she has written books on math that target girls.
A step up from there is the work of Jo Boaler who is leading a wave in math education reform. It would be worthwhile to read the Kindle samples of her books about growth mindset in math education. She's an inspiration to girls who want to learn math and she's an inspiration to math teachers who want to try new things to reach more students.
I also just purchased a new book called Necessary Conditions which has some new and intriguing ideas about how to improve math pedagogy.
Last year, I added the movies The Martian and Hidden Figures to my stats class. With the Martian, I read the book and watched the movie and enjoyed both. If I thought I wanted to get more reading into math class, I think a book like The Martian would get way more buy in from today's audience than the history of math. The same could be said of Hidden Figures which is less mathy, but way more inspirational for young women and minorities.
I've meandered about a bit here and I'll try to bring it all together in this last paragraph. I like your idea of asking kids to read about the history of math to get them to think about the bigger picture, to think beyond the computations. But, I think we now have way better material to accomplish that goal than books about the history of math. I'd much rather have kids read books like Moneyball or The Martian or almost anything by Malcolm Gladwell where they can get exposed to the bigger picture in a way that is modern and relevant and exciting. And, although I love the idea of having more reading across the curriculum, I suspect that the future is heading toward well produced podcasts and videos. And, lastly, I look forward to more material that inspires more girls and minorities with role models they can relate to (like Danika McKellar and John Urschel and Jaime Escalante).
Sorry for the tome. Hope that this helps in some small way.