May 11, 2020: Why learn math?
The Monday Letter, May 11,2020
Dear A2T Parents,
Students often ask about the relevance of mathematics. "When Are We Ever Gonna Use This?" is a question math teachers the world 'round train themselves to answer, repeating different possible responses, depending upon the student or situation.
No one, not-a-one, has asked me this question since January.
The cynic in me thinks that perhaps this is because of this interesting characteristic of humans: studies suggest that we'd rather have pain -- receive electrical shocks, for example -- than be "left alone with our thoughts." Indeed, the internet is rife with similar studies:
People would rather be electrically shocked than left alone with their thoughts | Science | AAAS
https://www.bbc.com/news/science-environment-28130690
https://www.ncbi.nlm.nih.gov/pubmed/26847946
https://www.theguardian.com/science/2014/jul/03/electric-shock-preferable-to-thinking-says-study
Are my students happier subjecting themselves to the "pain" of math than to the discomfort of boredom?
<insert audible moan of deep sadness here>
I like to think otherwise. A parable for all time is about Pythagoras paying a young man with no interest in math to learn geometry. After a short time, the young man became so interested in his studies that he began paying Pythagoras to learn instead of receiving money from Pythagoras in order to be taught. Who knows, of course, if the legend is true, but there does seem to be some truth to the statement that the more you learn, the more you want to learn.
And thus is the transition seen by these students, your children, this year. One young woman (who has been working ahead of schedule) said today she "Cried because she just finished the last Mariner assignment." (I told her that I would certainly oblige her with more if she wanted; she assured me that was not necessary.) I just worked with a young man during my "office hours" on a problem that included the tangent sum formula (a brand new idea). As we progressed through the problem, he noted with glee that we were using some of the algebra skills that we learned last August -- we had certainly come full circle and had, in part, answered the question, "When Are We Gonna Use This?" I noted that the possible answer, "With the tangent sum formula in May," would have clearly been insufficient to my students last August. The student didn't ask "When Are We Gonna Use This?" about the tangent sum formula.
So all this really begs a question for which you might like to hear the answer. What are my responses when a student asks me, "When Are We Ever Gonna Use This?" I answer the question as "Why do we study math?" Here's a "top ten" list of some of my responses in the past.
1. "Because math is beautiful," I say. The Grand Canyon is beautiful, but no one ever says, "What good is it?" or "When are we ever gonna use this?" Student response: eye rolling.
2. "Why do you even ask?" is what I've sometimes asked in response. I then ask if they ever ask their English teachers why they'd need Shakespeare. (The answer is always "NO, I've never asked." Somehow, they see Shakespeare as relevant but math not.) So the student response is, again, eye rolling or simply stunned silence.
3. If I'm pressed for time and need a quick and effective answer, I'll say either, "Because 90% of the careers available to you will require higher math," or "Because the highest paying careers are those that require higher math." (One student this year had the best response to this: "Shouldn't you follow your passion?" and I had to say yes to that question! Then a second student found data that suggested that humanities majors may not make as much money as the math or science majors in the first 5-10 years after college graduation, but that their income exceeded that of their counterparts at 20 years post college graduation. This is why I love AA students! Data! Passion! The irony is that they used data and math to support the cause of majoring in humanities.)
4. "Because I want you to have choices in your life and now is too early for you to close doors," is the parent in me speaking. This is when someone in the room says, "I'm going to med school and don't need this math." And the doctors among you parents would be the first to likely remember that one of the MCAT tests is calculus. Even the GRE (Graduate Record Exams) for any graduate school has a math portion. There's a reason for this; math helps you understand the world.
5. "Because math teaches you to organize and think clearly." Then it's easy to come up with examples.
6. "Because this is a time in your life when your brain is developing rapidly; you want to take advantage of that growth. Like language acquisition which is clearly tied to age, you lose the ability to develop a skill if you miss the window." https://www.brainfacts.org/thinking-sensing-and-behaving/childhood-and-adolescence/2015/hormones-and-the-adolescent-brain-120915 and https://www.pbs.org/wgbh/pages/frontline/shows/teenbrain/work/adolescent.html
7. "Because I want you, as an adult, to be a success at cocktail parties. I mean, everyone talks calculus over a martini." Student response: "That would be just you, Ms M."
8. The most potent answer I've given is something like the following: "I don't know when you'll use it; it's your job to figure that out." I then tell the story of a former student in the 1980's who said, "When are we going to use this?" in regard to polar graphing. He then called me 10 years later and said, "Remember that useless polar graphing? I'm using it to create an analog clock on a website." Remember, there were no websites in the 1980's.
9. The most emotional answer I've given is: "So you can always entertain yourself with powerful thoughts." I then tell the story of a friend's father who was a POW at the "Hanoi Hilton" in solitary confinement for nearly eight years. He found a small piece of wood in his cell and entertained himself doing math in his head to create a slide rule. He emerged from isolation much stronger than those who did not have the ability to entertain themselves. Indeed, Vice-Admiral James Stockdale was a candidate for U.S. President.in 1992.
10. One reason I've not shared with my classes but I'm sure would resonate with you, as parents: Literacy in the home is an enormous predictor of future success for the children in the home. There is no greater joy than helping your own children succeed in life.
I've not had to pull out my arguments for taking math recently. I'd like to think your sons and daughters have found a purpose and a pleasure in their studies this spring (or they've pulled the rug over my eyes). I daresay, something happened to many of your children this year. They began to change. And these last couple weeks, math became relevant because they started to enjoy how the subject made their minds work. In one of the last office hours of the year, a student with a long-professed distaste of math recognized how trigonometry connects so many different areas of math so beautifully. Her facial expression concerned me, so I asked how she was. She said, "My mind is kinda blown right now." A second student said earlier, "I just discovered that trigonometry is the Frankenstein of math. It's made of all these different parts put together to make a whole beast."
There are no sweeter parting words.
Be safe, be strong, be well.
In Kindness,
Jean Mariner
PS. On the website of The Monday Letters (in addition to in canvas) I've posted links to about 3 hours of videos that I have made for your children to watch and enjoy over the summer. They each discuss an "advanced" topic in trigonometry in a manner familiar to them and in a manner that is an outgrowth of our studies this year. So if your sons or daughters are bored this summer in quarantine, encourage them to watch a Mariner Math Movie with Ms Mariner as the movie star.
Dear A2T Parents,
Students often ask about the relevance of mathematics. "When Are We Ever Gonna Use This?" is a question math teachers the world 'round train themselves to answer, repeating different possible responses, depending upon the student or situation.
No one, not-a-one, has asked me this question since January.
The cynic in me thinks that perhaps this is because of this interesting characteristic of humans: studies suggest that we'd rather have pain -- receive electrical shocks, for example -- than be "left alone with our thoughts." Indeed, the internet is rife with similar studies:
People would rather be electrically shocked than left alone with their thoughts | Science | AAAS
https://www.bbc.com/news/science-environment-28130690
https://www.ncbi.nlm.nih.gov/pubmed/26847946
https://www.theguardian.com/science/2014/jul/03/electric-shock-preferable-to-thinking-says-study
Are my students happier subjecting themselves to the "pain" of math than to the discomfort of boredom?
<insert audible moan of deep sadness here>
I like to think otherwise. A parable for all time is about Pythagoras paying a young man with no interest in math to learn geometry. After a short time, the young man became so interested in his studies that he began paying Pythagoras to learn instead of receiving money from Pythagoras in order to be taught. Who knows, of course, if the legend is true, but there does seem to be some truth to the statement that the more you learn, the more you want to learn.
And thus is the transition seen by these students, your children, this year. One young woman (who has been working ahead of schedule) said today she "Cried because she just finished the last Mariner assignment." (I told her that I would certainly oblige her with more if she wanted; she assured me that was not necessary.) I just worked with a young man during my "office hours" on a problem that included the tangent sum formula (a brand new idea). As we progressed through the problem, he noted with glee that we were using some of the algebra skills that we learned last August -- we had certainly come full circle and had, in part, answered the question, "When Are We Gonna Use This?" I noted that the possible answer, "With the tangent sum formula in May," would have clearly been insufficient to my students last August. The student didn't ask "When Are We Gonna Use This?" about the tangent sum formula.
So all this really begs a question for which you might like to hear the answer. What are my responses when a student asks me, "When Are We Ever Gonna Use This?" I answer the question as "Why do we study math?" Here's a "top ten" list of some of my responses in the past.
1. "Because math is beautiful," I say. The Grand Canyon is beautiful, but no one ever says, "What good is it?" or "When are we ever gonna use this?" Student response: eye rolling.
2. "Why do you even ask?" is what I've sometimes asked in response. I then ask if they ever ask their English teachers why they'd need Shakespeare. (The answer is always "NO, I've never asked." Somehow, they see Shakespeare as relevant but math not.) So the student response is, again, eye rolling or simply stunned silence.
3. If I'm pressed for time and need a quick and effective answer, I'll say either, "Because 90% of the careers available to you will require higher math," or "Because the highest paying careers are those that require higher math." (One student this year had the best response to this: "Shouldn't you follow your passion?" and I had to say yes to that question! Then a second student found data that suggested that humanities majors may not make as much money as the math or science majors in the first 5-10 years after college graduation, but that their income exceeded that of their counterparts at 20 years post college graduation. This is why I love AA students! Data! Passion! The irony is that they used data and math to support the cause of majoring in humanities.)
4. "Because I want you to have choices in your life and now is too early for you to close doors," is the parent in me speaking. This is when someone in the room says, "I'm going to med school and don't need this math." And the doctors among you parents would be the first to likely remember that one of the MCAT tests is calculus. Even the GRE (Graduate Record Exams) for any graduate school has a math portion. There's a reason for this; math helps you understand the world.
5. "Because math teaches you to organize and think clearly." Then it's easy to come up with examples.
6. "Because this is a time in your life when your brain is developing rapidly; you want to take advantage of that growth. Like language acquisition which is clearly tied to age, you lose the ability to develop a skill if you miss the window." https://www.brainfacts.org/thinking-sensing-and-behaving/childhood-and-adolescence/2015/hormones-and-the-adolescent-brain-120915 and https://www.pbs.org/wgbh/pages/frontline/shows/teenbrain/work/adolescent.html
7. "Because I want you, as an adult, to be a success at cocktail parties. I mean, everyone talks calculus over a martini." Student response: "That would be just you, Ms M."
8. The most potent answer I've given is something like the following: "I don't know when you'll use it; it's your job to figure that out." I then tell the story of a former student in the 1980's who said, "When are we going to use this?" in regard to polar graphing. He then called me 10 years later and said, "Remember that useless polar graphing? I'm using it to create an analog clock on a website." Remember, there were no websites in the 1980's.
9. The most emotional answer I've given is: "So you can always entertain yourself with powerful thoughts." I then tell the story of a friend's father who was a POW at the "Hanoi Hilton" in solitary confinement for nearly eight years. He found a small piece of wood in his cell and entertained himself doing math in his head to create a slide rule. He emerged from isolation much stronger than those who did not have the ability to entertain themselves. Indeed, Vice-Admiral James Stockdale was a candidate for U.S. President.in 1992.
10. One reason I've not shared with my classes but I'm sure would resonate with you, as parents: Literacy in the home is an enormous predictor of future success for the children in the home. There is no greater joy than helping your own children succeed in life.
I've not had to pull out my arguments for taking math recently. I'd like to think your sons and daughters have found a purpose and a pleasure in their studies this spring (or they've pulled the rug over my eyes). I daresay, something happened to many of your children this year. They began to change. And these last couple weeks, math became relevant because they started to enjoy how the subject made their minds work. In one of the last office hours of the year, a student with a long-professed distaste of math recognized how trigonometry connects so many different areas of math so beautifully. Her facial expression concerned me, so I asked how she was. She said, "My mind is kinda blown right now." A second student said earlier, "I just discovered that trigonometry is the Frankenstein of math. It's made of all these different parts put together to make a whole beast."
There are no sweeter parting words.
Be safe, be strong, be well.
In Kindness,
Jean Mariner
PS. On the website of The Monday Letters (in addition to in canvas) I've posted links to about 3 hours of videos that I have made for your children to watch and enjoy over the summer. They each discuss an "advanced" topic in trigonometry in a manner familiar to them and in a manner that is an outgrowth of our studies this year. So if your sons or daughters are bored this summer in quarantine, encourage them to watch a Mariner Math Movie with Ms Mariner as the movie star.
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