I like your argument, but — how far does this kind of argument extend? For example: Should everyone be able – at least to some degree – to see the physical universe as known by physics? Here's a possible test for threshold physics-think actualization: I hand you a cheap, simple (by 2023 standards) telescope, and ask you to show me a sequence of phenomena with it that make the universality of classical gravitation at least plausible.
Aug 26, 2023·edited Aug 26, 2023Liked by Holly MathNerd
Unless new research has come up in the 35 years since I was in college demonstrating otherwise, the part of your brain responsible for language is the same part of your brain responsible for math. IOW, if a person can speak a language as complicated as English, there's zero reason they can't be competent at least through high school algebra.
When I was a cop, I used to work a security job at a high school in Houston that was about 95% Latino. I knew a lot of the kids by sight and name, and talked to them quite a lot. "I'm not a math person" was a common refrain, even 30 years ago.
"But you speak English AND Spanish fluently?!?!?"
"Yeah, so?"
"Math is just another language. You learned English and Spanish, now learn the language of numbers."
No idea how many, if any at all, took that to heart. I am hopeful that some did. "How many licks to get to the center of a Tootsie Pop?" The world may never know.
I have plenty of experience with students who use this very excuse, but I find that with a little explanation, they get it. If I had a nickel for every time I heard, "Why can't my teacher explain it like this?"
Poor instruction is endemic.
Another issue is emotional. Actually I think that emotional issues impede academic performance more than any other cause. Those are rough to deal with effectively.
And, it drives me nuts when I hear students say, "I'm a visual learner." Or, "I'm an auditory learner." Or something equally inane. And I wonder what idiot teacher or counsellor told them that and caused an ossification of their identity. I have to continually tell these students not to put themselves in a box, that all of that crap is on a continuum and therefore is crap, and that they can learn in multiple ways. I mix up letters and numbers all the time, but I don't consider myself lysdexic. But of course, when I was a kid, that wasn't a thing.
I had a professor in community college who said that the secret to success in math is persistence. I think that's true of life generally.
Excellent piece, Holly. I tried making this point many, many times to colleagues at several schools I've taught at over the years. I've had some success, but I've never really been able to convince people that so-called "non-math people" are confessing to a form of illiteracy, and not with some degree of embarrassment and desire to not be illiterate, but with a sort of "well, them's the breaks" kind of attitude.
Interestingly, I've only really encountered opposition within a math department at a community college (which says something about higher ed). It's a somewhat long story, but the upshot is that I encountered an Emeritus Professor who advocated for turning a significant portion of basic college math classes into instruction for how to interface with technology rather than on learning and practicing essential mathematical skills (ChatGPT was fairly new at the time, and he wasn't familiar with it). However, it did lead me to try and steel-man his position and I'm curious what you think of it, and how you'd respond:
Maybe knowledge of mathematics is passing out of the required skill set for everyday life. We've seen other bodies of knowledge that used to be common become relegated to a smaller subset of specialists as technology has advanced (an example might be animal husbandry or the use of farm tools). Perhaps that's what happening to math, as large language models continue to improve and interfacing with computers becomes more and more seamless, is mathematics going to be important to leading a productive, flourishing life in tomorrow's technological society?
I think you're answer (and mine) is summarized in your statement that: "...the logic and discipline imposed by mathematics makes a person better at critical thinking."
I think this is going to be a point that we (those who argue for the value of mathematics in education) will need to continue to flesh out and argue very strongly in the coming years because we are going to continue to see people being comfortable, even proud of their innumeracy. And with the tools for doing math problems without thought becoming more and more accessible what remains of the shame and embarrassment is going to continue to wither away.
I immediately thought of baking, the attitude of "I'm just not a ____ person." Many, many years ago a bunch of us in my office job were being trained to use a new program. Lots of people were confused, as people don't handle change will. The instructor, in an attempt to assuage insecurity, asked, kindly:
"What happens when you're baking and you follow a recipe?"
"It turns out bad," one woman humbly responded.
Cute line, which got a laugh from the room, but inaccurate. (I had an internal "actually" moment, even though I was years from pastry school.) When you follow instructions it comes out as desired because baking is first and foremost math and science. Understanding the how and why is necessary to perfect or replicate a recipe, and as you say, not easy. A couple years ago I translated into painstaking detail a souffle recipe for a nonbaker friend--in a wheelchair--and I'm proud of both of us that it mostly turned out good. (Laziness kept it from perfection.) But writing it was a slog. You need the nuts and bolts, THEN you can be creative and toss flour in the air like pixie dust. Now, bad recipes exist; I am skeptical of home baker bloggers without professional education and industry experience. Granting that the author is competent the laws of physics and chemistry are consistent. So when "it turns out bad" happens it's likely user error. One of the best things about immutable rules is that you learn to troubleshoot. The rules require that there is solution, even if you haven't yet found it. Applied knowledge is produced.
The skills you say come from learning a hard skill like math or science translate anywhere, even on a broad, personal level. The concept of mis-en-place made me a better person. Mis-en-place is literally "put in place", meaning have everything ready when production begins. No searching for things (or reading the recipe!!) *as you go*. The recipe has been read all the way through at least once. All ingredients, tools, hardware are out on the table or counter when you start. "Oops, I forgot one thing" does not happen. (In pastry school our chefs taught us that if you screw up in culinary you can still fix, alter, or re-purpose. If you screw up in baking you start over from square one.) I've never been a total slob but for sure an eager, easily distracted scatterbrain. Baking made me a much better organizer. I tolerate far less mess in my living spaces. I've slowly become more structured, though still far from where I want to be. But I am measurably an improved, less inefficient person.
You can have a growth mindset or a fixed mindset. With a fixed mindset you think things like, "I'm not a math person" (and will never be one because that 'fact' cannot change). With a growth mindset you think things like, "This is hard, but with enough study and asking for help I can figure it out."
I think some people may have growth mindsets on all subjects, but some others have a mix depending on the subject.
For some reason society has decided that we are "fixed" on Math skills and can be a math person or not. I never viewed people who were not good at math as "stupid" at it. I knew they could figure it out with time, patience, and study. But so many did not seem to want to do it. I enjoyed it, because I thought of them as puzzles, like Sudoku. To me it was a game. With enjoyment it wasn't difficult to do the work.
But that is not to say it wasn't challenging. I remember in college Calculus we were give two class periods to get an assignment done. After class on Monday, I would get to working on all of the problems (that would be due in 2 classes from then, Friday). I would go into the next class, Wednesday, with my problems that I couldn't figure out. The teacher would ask if anyone had any problems. So few people raised their hands. You could tell people were not working on their homework yet (procrastination). Because I worked ahead I asked questions on all of my tough areas. It was sometimes like a private tutoring session since no one else had issues they wanted help on. I would wait and see, then raise my hand if no one else was. We were all given the opportunity to get help but so few chose to take up the offer.
Thank you so much -- in one essay you hit on two of my pedagogic pet peeves!
When I was in my 20s (so, grad school into my first professional job) you heard this saying all the time: “I’m not a numbers person -- I’m a *people* person.” It managed to turn what should have been a rueful or embarrassing admission about one’s substandard education or lack of any drive for self-improvement not just to a neutral but a *positive* statement: I’m not like those soulless number-crunchers and I’m proud of it! And on at least one occasion I snapped and spit out exactly as you did: “If you couldn’t read you wouldn’t announce to the whole world that you were a ‘people person, not a words person’.”
The other peeve is the “you’re so talented...I don’t have any of [that kind of] talent.” My daughter, now 29, is a graphic artist and designer. She often sits in public places sketching, and invariably someone approaches, looks at her work, and says some variant of “you have such talent” in the same way they would comment on the color of her eyes or the blouse she was wearing. She is too polite to ever say anything less mild than “Oh, do you like it?” But it inwardly enrages me, because that kid from the age of eight had a pencil in her hand every waking moment she wasn’t being forced to do something else. She *still* spends time every day practicing new techniques in addition to the 8-10 hours she is doing commercial work. The way she became so talented was she worked at it in the same way a professional athlete works at speed, agility, and strength.
In a softball quiz at the start of last year's fall semester, students were asked to subtract eight from negative six, recalls Jessica Babcock. “I graded a whole bunch of papers in a row. No two papers had the same answer, and none of them were correct.”
Thank You so very much for the "Excuses vs Explanations" bit, mega Thanks!
. . . my personal note, there are people, not as extreme as "Rainman" who poses unique abilities in varying degrees, I have been blessed with special powers over hardware ( it was said that I could repair Apple][ computers by the laying on of hands . . ) and in all too many other areas, serious deficiencies.
I agree with everything you wrote. Especially the bit about teachable skills, and the difference between explanations and excuses.
But the funny part is, that I actually was that person who didn't want to learn to drive in high school. In my defense, I didn't make the excuse that I wasn't a "driving person." I just didn't like driving. I still don't. I took driver's ed in high school because I had to, got my driver's license, and let it lapse. In the mean time, I actually did travel a lot, including taking trains all over Germany, and studying in the then USSR, without being able to drive.
Then, when I got my first assignment as an officer in the Air Force, they told me I had to be able to drive, so I refreshed my driver's ed and got my license.
"This imagined parental response probably sounds reasonable to you."
What scares me is how many--perhaps the majority-- parents do not perceive that as reasonable.
You're so, so correct. The analogy to what it would be like if people bragged about verbal illiteracy is exactly, 100 percent, the same thing.
It's not an "analogy". It is that very thing itself.
I like your argument, but — how far does this kind of argument extend? For example: Should everyone be able – at least to some degree – to see the physical universe as known by physics? Here's a possible test for threshold physics-think actualization: I hand you a cheap, simple (by 2023 standards) telescope, and ask you to show me a sequence of phenomena with it that make the universality of classical gravitation at least plausible.
Unless new research has come up in the 35 years since I was in college demonstrating otherwise, the part of your brain responsible for language is the same part of your brain responsible for math. IOW, if a person can speak a language as complicated as English, there's zero reason they can't be competent at least through high school algebra.
When I was a cop, I used to work a security job at a high school in Houston that was about 95% Latino. I knew a lot of the kids by sight and name, and talked to them quite a lot. "I'm not a math person" was a common refrain, even 30 years ago.
"But you speak English AND Spanish fluently?!?!?"
"Yeah, so?"
"Math is just another language. You learned English and Spanish, now learn the language of numbers."
No idea how many, if any at all, took that to heart. I am hopeful that some did. "How many licks to get to the center of a Tootsie Pop?" The world may never know.
Great article, Holly. All true.
I have plenty of experience with students who use this very excuse, but I find that with a little explanation, they get it. If I had a nickel for every time I heard, "Why can't my teacher explain it like this?"
Poor instruction is endemic.
Another issue is emotional. Actually I think that emotional issues impede academic performance more than any other cause. Those are rough to deal with effectively.
And, it drives me nuts when I hear students say, "I'm a visual learner." Or, "I'm an auditory learner." Or something equally inane. And I wonder what idiot teacher or counsellor told them that and caused an ossification of their identity. I have to continually tell these students not to put themselves in a box, that all of that crap is on a continuum and therefore is crap, and that they can learn in multiple ways. I mix up letters and numbers all the time, but I don't consider myself lysdexic. But of course, when I was a kid, that wasn't a thing.
I had a professor in community college who said that the secret to success in math is persistence. I think that's true of life generally.
Excellent piece, Holly. I tried making this point many, many times to colleagues at several schools I've taught at over the years. I've had some success, but I've never really been able to convince people that so-called "non-math people" are confessing to a form of illiteracy, and not with some degree of embarrassment and desire to not be illiterate, but with a sort of "well, them's the breaks" kind of attitude.
Interestingly, I've only really encountered opposition within a math department at a community college (which says something about higher ed). It's a somewhat long story, but the upshot is that I encountered an Emeritus Professor who advocated for turning a significant portion of basic college math classes into instruction for how to interface with technology rather than on learning and practicing essential mathematical skills (ChatGPT was fairly new at the time, and he wasn't familiar with it). However, it did lead me to try and steel-man his position and I'm curious what you think of it, and how you'd respond:
Maybe knowledge of mathematics is passing out of the required skill set for everyday life. We've seen other bodies of knowledge that used to be common become relegated to a smaller subset of specialists as technology has advanced (an example might be animal husbandry or the use of farm tools). Perhaps that's what happening to math, as large language models continue to improve and interfacing with computers becomes more and more seamless, is mathematics going to be important to leading a productive, flourishing life in tomorrow's technological society?
I think you're answer (and mine) is summarized in your statement that: "...the logic and discipline imposed by mathematics makes a person better at critical thinking."
I think this is going to be a point that we (those who argue for the value of mathematics in education) will need to continue to flesh out and argue very strongly in the coming years because we are going to continue to see people being comfortable, even proud of their innumeracy. And with the tools for doing math problems without thought becoming more and more accessible what remains of the shame and embarrassment is going to continue to wither away.
I immediately thought of baking, the attitude of "I'm just not a ____ person." Many, many years ago a bunch of us in my office job were being trained to use a new program. Lots of people were confused, as people don't handle change will. The instructor, in an attempt to assuage insecurity, asked, kindly:
"What happens when you're baking and you follow a recipe?"
"It turns out bad," one woman humbly responded.
Cute line, which got a laugh from the room, but inaccurate. (I had an internal "actually" moment, even though I was years from pastry school.) When you follow instructions it comes out as desired because baking is first and foremost math and science. Understanding the how and why is necessary to perfect or replicate a recipe, and as you say, not easy. A couple years ago I translated into painstaking detail a souffle recipe for a nonbaker friend--in a wheelchair--and I'm proud of both of us that it mostly turned out good. (Laziness kept it from perfection.) But writing it was a slog. You need the nuts and bolts, THEN you can be creative and toss flour in the air like pixie dust. Now, bad recipes exist; I am skeptical of home baker bloggers without professional education and industry experience. Granting that the author is competent the laws of physics and chemistry are consistent. So when "it turns out bad" happens it's likely user error. One of the best things about immutable rules is that you learn to troubleshoot. The rules require that there is solution, even if you haven't yet found it. Applied knowledge is produced.
The skills you say come from learning a hard skill like math or science translate anywhere, even on a broad, personal level. The concept of mis-en-place made me a better person. Mis-en-place is literally "put in place", meaning have everything ready when production begins. No searching for things (or reading the recipe!!) *as you go*. The recipe has been read all the way through at least once. All ingredients, tools, hardware are out on the table or counter when you start. "Oops, I forgot one thing" does not happen. (In pastry school our chefs taught us that if you screw up in culinary you can still fix, alter, or re-purpose. If you screw up in baking you start over from square one.) I've never been a total slob but for sure an eager, easily distracted scatterbrain. Baking made me a much better organizer. I tolerate far less mess in my living spaces. I've slowly become more structured, though still far from where I want to be. But I am measurably an improved, less inefficient person.
You can have a growth mindset or a fixed mindset. With a fixed mindset you think things like, "I'm not a math person" (and will never be one because that 'fact' cannot change). With a growth mindset you think things like, "This is hard, but with enough study and asking for help I can figure it out."
I think some people may have growth mindsets on all subjects, but some others have a mix depending on the subject.
For some reason society has decided that we are "fixed" on Math skills and can be a math person or not. I never viewed people who were not good at math as "stupid" at it. I knew they could figure it out with time, patience, and study. But so many did not seem to want to do it. I enjoyed it, because I thought of them as puzzles, like Sudoku. To me it was a game. With enjoyment it wasn't difficult to do the work.
But that is not to say it wasn't challenging. I remember in college Calculus we were give two class periods to get an assignment done. After class on Monday, I would get to working on all of the problems (that would be due in 2 classes from then, Friday). I would go into the next class, Wednesday, with my problems that I couldn't figure out. The teacher would ask if anyone had any problems. So few people raised their hands. You could tell people were not working on their homework yet (procrastination). Because I worked ahead I asked questions on all of my tough areas. It was sometimes like a private tutoring session since no one else had issues they wanted help on. I would wait and see, then raise my hand if no one else was. We were all given the opportunity to get help but so few chose to take up the offer.
Thank you so much -- in one essay you hit on two of my pedagogic pet peeves!
When I was in my 20s (so, grad school into my first professional job) you heard this saying all the time: “I’m not a numbers person -- I’m a *people* person.” It managed to turn what should have been a rueful or embarrassing admission about one’s substandard education or lack of any drive for self-improvement not just to a neutral but a *positive* statement: I’m not like those soulless number-crunchers and I’m proud of it! And on at least one occasion I snapped and spit out exactly as you did: “If you couldn’t read you wouldn’t announce to the whole world that you were a ‘people person, not a words person’.”
The other peeve is the “you’re so talented...I don’t have any of [that kind of] talent.” My daughter, now 29, is a graphic artist and designer. She often sits in public places sketching, and invariably someone approaches, looks at her work, and says some variant of “you have such talent” in the same way they would comment on the color of her eyes or the blouse she was wearing. She is too polite to ever say anything less mild than “Oh, do you like it?” But it inwardly enrages me, because that kid from the age of eight had a pencil in her hand every waking moment she wasn’t being forced to do something else. She *still* spends time every day practicing new techniques in addition to the 8-10 hours she is doing commercial work. The way she became so talented was she worked at it in the same way a professional athlete works at speed, agility, and strength.
Nice Brett and Heather drawing!
It seems that wuflu plus current school math instruction is failing miserably
https://www.joannejacobs.com/post/math-disaster-in-college-would-be-stem-majors-can-t-add-1-2-1-3
Quote:
In a softball quiz at the start of last year's fall semester, students were asked to subtract eight from negative six, recalls Jessica Babcock. “I graded a whole bunch of papers in a row. No two papers had the same answer, and none of them were correct.”
Thank You so very much for the "Excuses vs Explanations" bit, mega Thanks!
. . . my personal note, there are people, not as extreme as "Rainman" who poses unique abilities in varying degrees, I have been blessed with special powers over hardware ( it was said that I could repair Apple][ computers by the laying on of hands . . ) and in all too many other areas, serious deficiencies.
oops!
I agree with everything you wrote. Especially the bit about teachable skills, and the difference between explanations and excuses.
But the funny part is, that I actually was that person who didn't want to learn to drive in high school. In my defense, I didn't make the excuse that I wasn't a "driving person." I just didn't like driving. I still don't. I took driver's ed in high school because I had to, got my driver's license, and let it lapse. In the mean time, I actually did travel a lot, including taking trains all over Germany, and studying in the then USSR, without being able to drive.
Then, when I got my first assignment as an officer in the Air Force, they told me I had to be able to drive, so I refreshed my driver's ed and got my license.