Out of curiosity -- did he memorize the multiplication tables at any point? If yes, was it required in school? Did you suggest it? Or did he decide to do so on his own?
Some people have trauma when it comes to the multiplication table. Math was my weakest subject as a child and I was forced to do extra work at home and I was made to memorize the multiplication. My father was an accountant, so, ummm, yeahhhhh. I have such trauma that it is extremely difficult for me to remember anything above 7times and I usually resort to my calculator when I have to recall something like 8x7.
Truth be told. His third grade teacher, when this would have happened normally, sucked. (I knew she would when she started talking about racist book collections.) Won't call it trauma, but despite our best efforts he's never been quick at that.
According to his tests, he also messes up signs a lot.
Teachers have told him to practice more, but he frequently makes those mistakes, which he has to check, which cost him time, which....
Good thought. Even if it's just enough to understand what probabilities and statistics are and how they differ from simple facts, and how to apply that understanding to everyday things like weather forecasts, marketing claims, common (and especially political) use of statistical and scientific studies, etc.
I am math challenged, to say the least, and took only as much as I needed to graduate high school. I am actually very good at simple math (ie giving change, tips or cooking calculations), but truly cannot comprehend geometry type math. As an adult, I finally realized that most people are able think in 3D, while I apparently cannot. Putting together ikea type furniture is a lesson in futility for me. Thankfully my son got my husband’s math abilities and graduated with a degree in mathematics like you.
I'm like Carole. My answer to those questions are 3 minor accidents (no injuries), during 65 years of driving: 1)backing out of a parking spot, 2)slow approach rear-ending the car in front of me, and 3)entering traffic from an exit perpendicular to the street, and getting t-boned. Ha! covered all sides! I don't play any musical instruments. Musical notes on sheet music might as well be hieroglyphs when I look at them. Basic math is about it for me, and I'm not even very good at that.
I had 3 accidents (I am 52) before I turned 21….all minor and I rear ended people. Failure to pay attention and maintain assured clear distance. 🤣 That caused me to become a crazy careful driver. I played flute and piccolo, but struggled and gave up piano.
I taught my son to play the flute, friends taught him piano and drums, and he taught himself trumpet.
These are interesting questions. Now that I think about it, besides an amazing 3rd grade teacher I mentioned in a previous comment, the summer before my daughter started 3rd grade, she started taking piano lessons. Her math skills seemed to really blossom from that point. She took lessons for 7 years - then high school activities/homework necessitated dropping something. She just played for enjoyment after that.
Son took guitar lessons for 6 years and "fiddled" with drums, violin... and an ocarina, thank you Legend of Zelda, lol.
How to calculate percentage. On Twitter I like to look at followers/following. For instance, Elon Musk has 410 following and 152.7M followers. So that's 152,700,000 followers, right? And I couldn't remember how to get the ratio, the percentage.
This will sound weird but teach parents how common core actually works. It's like mental math. We home school and, being along for the ride, it makes so much more sense and the kidsike it.
Ahhhhh THANK YOU! I have a 20 yr old that didn’t get a good groundwork in math and so is struggling w college math. And really wants to improve his basic understanding so he can go farther in his education. Would love to have a course of some sort that isn’t grade dependent and values comprehension. Would definitely pay for this!
I don't struggle with math at the level you are describing (I have a degree in it, although I've probably forgotten most of what I learned by now). I've had to explain basic fractions, specifically as used in unit conversions, to coworkers in shipping jobs way too many times, so I suspect that may be something that's taught poorly.
I've worked as an engineer a long time. Most useful to me has been a training in grasping orders of magnitude by direct "seeing", as one used to have to do when one used a slide rule. The kind of thing I have in mind is "crap detecting" like "Would this putative blood pressure burst arteries with millimeter-thick steel walls?" I think this is one of the simpler parts of having math as one of one's "languages" for thinking about phenomena in the world.
Holly, I am big fan. Loved your recent piece on Sam Harris, spot on. I am an engineer and math is an important part of my life, though I don't appreciate math of its beauty, for me it is more functional, for problem solving. My fav part of math was 3D calculus, I loved differential equations, and quite recently (I am 58) have come to really appreciate the Euler equation and harmonic motion. My most recent investigations have been to properly understand the Poisson Distribution and its use. I would love to properly understand quantum mechanics and the math behind it, but alas I probably do not have enough time in my lifetime to do so (given all my other priorities).
My main issue at the moment is helping my 9 year old daughters overcome her burgeoning math anxiety. She is competent for her age, though not a math star, but she doesn't like math and gets extremely stressed now even doing basic homework. Her 7 year old sister is fine, and my wife is a teacher. How can a 9 year old girl overcome math anxiety? Thanks. Keep up the great work.
Hey, Steven. I identify with a lot of what you say. Funny about mentioning the Euler equation. There are more than a few. I've spent the last 15+ years tutoring kids primarily for math and standardized tests. Anxiety comes from uncertainty. If you can eliminate the uncertainty, the anxiety will fade. Also, familiarity with the physical test situation is helpful. Good luck!
Dan thank you. I was referring to the Euler identity and its breakdown into sin/cos and its use in harmonic motion, especially in AC power system engineering. I believe you when you say they are more than one notable equations named after Euler. Thx for the input on anxiety.
Many 9 year old girls are readers. The young readers' edition of Kathryn Johnson's autobiography is a fantastic book. As Dan mentioned, finding the source of the anxiety is the best approach. With kids her age, the analogy I use is a staircase. Math is a staircase and if she's stumbling, it's because there's a loose board on a step (something she didn't fully understand before moving on). Finding it and nailing down the board is how to prevent future stumbling. Unfortunately, common core is a disorganized mess and if she's in a cc-based school, it may take some hunting to find where the loose board is.
Thanks for the input. I will look into that book. I think the issue is partly that she simply does not have an interest in math. I do think there is an issue with maybe missing some boards too. Keep up your great work.
If lack of interest is part of the problem, that's very lucky, since you can make infinite math lessons out of money and money buys anything and everything a kid might be interested in. Offer to pay her interest on her savings towards a goal once she can understand the math of interest calculation well enough. Make the interest payment high enough that she gets something she really wants inside of two weeks after she understands it. That'll go far, LOL.
That is an excellent idea, I will seriously consider this. Agree that math is everywhere, and getting into a context that matters to her is a great idea.
Many firstborns, especially girls, are *highly* motivated by being treated like adults (which is damaging if you treat them like an adult for real, of course, but teaching them something that only adults typically know is a harmless version of such). Having her help you make the mortgage payment one month after she understands interest would likely be a powerful and interesting "teachable moment".
The destruction of education must be intentional; the problem is people don’t know what they themselves and their kids don’t know to demand better. I am a retired engineer who tried to get involved in schools as a math teacher. I gave up. The ‘system’ doesn’t encourage learning…
Spot on! Two observations about the public school system. 1) It is territorial and hierarchical. Kind of like a troop of baboons. 2) It is a funnel to mediocrity. No one should fall behind, and no one should excel. Both are either forbidden or denied. And that is true for the teachers as well as the students. Truly a dysfunctional system.
I got confused at math starting with long division, and everything beyond that was extremely difficult. I was much better at things with words, and awful at things with numbers. (I don't remember having problems with super simple math, and long division was do-able, but when it got anywhere near complex, I found it confusing, but I don't remember details of why.)
I also was turned off by math because I thought (at the time), that beyond the basics, add/subtract / multiplication, percentages, simpler division, there was no use for it, if there was no chance of becoming an engineer or something like that. (That was my thinking in high school and college, where I was able to get away with hardly any math).
Many years later I was at the ocean with a friend, admiring a stone with a beautiful spiral. He explained that spirals in rocks have the same proportions of something that appear in nature many times. I remember thinking if I had known that in math classes, I may have been more interested, and put more effort in.
Are you in touch with Mathew Crawford (Rounding the Earth)? (Mathew with one T) (I heard of both of you from Dark Horse Podcast). https://roundingtheearth.substack.com/s/rte-education-zonehttps://metaprep.net/about/ Seems like potential for collaboration, both of you are math nerds and passionate about healing the world by empowering nuanced, independent thought.
Holly. I've been tutoring kids for math and standardized tests for over 15 years now. I've noticed quite a number of issues.
1) Some kids have emotional issues that impede learning significantly. These are beyond my pay grade, and require intensive psychological counseling. Tough to find someone competent for that task.
2) The transition from elementary school to high school is interesting. In third and fourth grade, the kid gives an answer to a simple question such as what is 5 x 3? But for some reason, many kids are unable to learn to work multistep problems. They continue to think that they should be able to spout an instant answer, even to a difficult trig question, for example. I chalk it up to poor instruction. Once it's explained to them that they don't need to, can't, come up with an instant answer, they do much better.
3) Fractions. High school kids who can't do fractions. I find it helpful to do fractions, ratios, percents all together to show how they are all the same thing. Also, it works to point out that every fraction is a division problem.
4) Geometry. After Chemistry, this is the most complained of subject. These both seem to be the result of poor instruction.
5) Algebra. There seems to be difficulty distinguishing terms from factors, which confusion leads to consistent errors in algebraic manipulation. Often, using concrete examples with numbers is necessary to show why certain moves don't work.
6) Calculators. If only we could throw away all the calculators. Of course, they're really useful for Stats, and other tedious calculations. But they become such a crutch; I have high school kids who can't do simple arithmetic with two-digit numbers, and sometimes one-digit numbers.
I was always good at math from before I went to kindergarten, and I've been playing music since a young child. It seems to me that math and music occupy the same space in my brain, but that's just my subjective experience. I've tried to identify why math is so easy for me, and how to convey that ease to my students, but it's an elusive thing. The best I can guess is that I visualize numbers in my mind's eye, mostly from 1 to 100, but focused on 1 to 20. And different numbers have different shading to them. I don't know where that came from, but it forms a firm foundation for everything else. I also see calendars like that. I wonder what other people see.
💬 math and music occupy the same space in my brain
Quadrivium of classical curriculum—arithmetic, geometry, music, and astronomy—might provide a clue 🙂 Arithmetic is about numbers as such; geometry = numbers in space; music = numbers in time; astronomy = numbers in both space and time.
Currently homeschooling a 7th grader. Open to any ideas, books, websites etc. that might spark interest. It's a beautiful mathematical world out there, I'm just not sure how to initiate the wonder.
I was good at math -- 99th percentile on (then) SAT scores (98th on college-bound) -- because my father, who was earning his PhD from Math Department at UW, insisted in teaching me and drilling me in math tables: both "the old way" (7x1=7, 7x2=14, 7x3=21, . . . 7x11-77, 7x12=84) and "the new way" (7, 14, 21, 18 . . . 77, 84), from 1 through 12. My students at the Tribal (Native American Indian) college where I taught, in contrast, were in general terrible at math because they had not been taught this. I don't know who benefits from students' NOT being taught this, but it isn't American students.
I don't know about any of this. Can you tell us more about why?
I asked my rising 9th grader...he said inefficiency w quick calculations...direct quote
Out of curiosity -- did he memorize the multiplication tables at any point? If yes, was it required in school? Did you suggest it? Or did he decide to do so on his own?
Some people have trauma when it comes to the multiplication table. Math was my weakest subject as a child and I was forced to do extra work at home and I was made to memorize the multiplication. My father was an accountant, so, ummm, yeahhhhh. I have such trauma that it is extremely difficult for me to remember anything above 7times and I usually resort to my calculator when I have to recall something like 8x7.
Truth be told. His third grade teacher, when this would have happened normally, sucked. (I knew she would when she started talking about racist book collections.) Won't call it trauma, but despite our best efforts he's never been quick at that.
According to his tests, he also messes up signs a lot.
Teachers have told him to practice more, but he frequently makes those mistakes, which he has to check, which cost him time, which....
Send me an email? I'll reply with three PDFs I made for a tutoring student recently that really helped her with signs.
Will do.
hollymathnerd at gmail dot com.
I think covering some basic probability and statistics would be helpful.
Seconded. IMHO statistics is where the most BS is generated by the media.
Good thought. Even if it's just enough to understand what probabilities and statistics are and how they differ from simple facts, and how to apply that understanding to everyday things like weather forecasts, marketing claims, common (and especially political) use of statistical and scientific studies, etc.
I am math challenged, to say the least, and took only as much as I needed to graduate high school. I am actually very good at simple math (ie giving change, tips or cooking calculations), but truly cannot comprehend geometry type math. As an adult, I finally realized that most people are able think in 3D, while I apparently cannot. Putting together ikea type furniture is a lesson in futility for me. Thankfully my son got my husband’s math abilities and graduated with a degree in mathematics like you.
Tell me about your experiences with driving and music. How many accidents have you had where you were at fault? What if any instruments do you play?
I'm like Carole. My answer to those questions are 3 minor accidents (no injuries), during 65 years of driving: 1)backing out of a parking spot, 2)slow approach rear-ending the car in front of me, and 3)entering traffic from an exit perpendicular to the street, and getting t-boned. Ha! covered all sides! I don't play any musical instruments. Musical notes on sheet music might as well be hieroglyphs when I look at them. Basic math is about it for me, and I'm not even very good at that.
I had 3 accidents (I am 52) before I turned 21….all minor and I rear ended people. Failure to pay attention and maintain assured clear distance. 🤣 That caused me to become a crazy careful driver. I played flute and piccolo, but struggled and gave up piano.
I taught my son to play the flute, friends taught him piano and drums, and he taught himself trumpet.
These are interesting questions. Now that I think about it, besides an amazing 3rd grade teacher I mentioned in a previous comment, the summer before my daughter started 3rd grade, she started taking piano lessons. Her math skills seemed to really blossom from that point. She took lessons for 7 years - then high school activities/homework necessitated dropping something. She just played for enjoyment after that.
Son took guitar lessons for 6 years and "fiddled" with drums, violin... and an ocarina, thank you Legend of Zelda, lol.
How to calculate percentage. On Twitter I like to look at followers/following. For instance, Elon Musk has 410 following and 152.7M followers. So that's 152,700,000 followers, right? And I couldn't remember how to get the ratio, the percentage.
This will sound weird but teach parents how common core actually works. It's like mental math. We home school and, being along for the ride, it makes so much more sense and the kidsike it.
Ahhhhh THANK YOU! I have a 20 yr old that didn’t get a good groundwork in math and so is struggling w college math. And really wants to improve his basic understanding so he can go farther in his education. Would love to have a course of some sort that isn’t grade dependent and values comprehension. Would definitely pay for this!
I don't struggle with math at the level you are describing (I have a degree in it, although I've probably forgotten most of what I learned by now). I've had to explain basic fractions, specifically as used in unit conversions, to coworkers in shipping jobs way too many times, so I suspect that may be something that's taught poorly.
I've worked as an engineer a long time. Most useful to me has been a training in grasping orders of magnitude by direct "seeing", as one used to have to do when one used a slide rule. The kind of thing I have in mind is "crap detecting" like "Would this putative blood pressure burst arteries with millimeter-thick steel walls?" I think this is one of the simpler parts of having math as one of one's "languages" for thinking about phenomena in the world.
Holly, I am big fan. Loved your recent piece on Sam Harris, spot on. I am an engineer and math is an important part of my life, though I don't appreciate math of its beauty, for me it is more functional, for problem solving. My fav part of math was 3D calculus, I loved differential equations, and quite recently (I am 58) have come to really appreciate the Euler equation and harmonic motion. My most recent investigations have been to properly understand the Poisson Distribution and its use. I would love to properly understand quantum mechanics and the math behind it, but alas I probably do not have enough time in my lifetime to do so (given all my other priorities).
My main issue at the moment is helping my 9 year old daughters overcome her burgeoning math anxiety. She is competent for her age, though not a math star, but she doesn't like math and gets extremely stressed now even doing basic homework. Her 7 year old sister is fine, and my wife is a teacher. How can a 9 year old girl overcome math anxiety? Thanks. Keep up the great work.
Hey, Steven. I identify with a lot of what you say. Funny about mentioning the Euler equation. There are more than a few. I've spent the last 15+ years tutoring kids primarily for math and standardized tests. Anxiety comes from uncertainty. If you can eliminate the uncertainty, the anxiety will fade. Also, familiarity with the physical test situation is helpful. Good luck!
Dan thank you. I was referring to the Euler identity and its breakdown into sin/cos and its use in harmonic motion, especially in AC power system engineering. I believe you when you say they are more than one notable equations named after Euler. Thx for the input on anxiety.
Many 9 year old girls are readers. The young readers' edition of Kathryn Johnson's autobiography is a fantastic book. As Dan mentioned, finding the source of the anxiety is the best approach. With kids her age, the analogy I use is a staircase. Math is a staircase and if she's stumbling, it's because there's a loose board on a step (something she didn't fully understand before moving on). Finding it and nailing down the board is how to prevent future stumbling. Unfortunately, common core is a disorganized mess and if she's in a cc-based school, it may take some hunting to find where the loose board is.
Thanks for the input. I will look into that book. I think the issue is partly that she simply does not have an interest in math. I do think there is an issue with maybe missing some boards too. Keep up your great work.
If lack of interest is part of the problem, that's very lucky, since you can make infinite math lessons out of money and money buys anything and everything a kid might be interested in. Offer to pay her interest on her savings towards a goal once she can understand the math of interest calculation well enough. Make the interest payment high enough that she gets something she really wants inside of two weeks after she understands it. That'll go far, LOL.
That is an excellent idea, I will seriously consider this. Agree that math is everywhere, and getting into a context that matters to her is a great idea.
Many firstborns, especially girls, are *highly* motivated by being treated like adults (which is damaging if you treat them like an adult for real, of course, but teaching them something that only adults typically know is a harmless version of such). Having her help you make the mortgage payment one month after she understands interest would likely be a powerful and interesting "teachable moment".
The destruction of education must be intentional; the problem is people don’t know what they themselves and their kids don’t know to demand better. I am a retired engineer who tried to get involved in schools as a math teacher. I gave up. The ‘system’ doesn’t encourage learning…
Spot on! Two observations about the public school system. 1) It is territorial and hierarchical. Kind of like a troop of baboons. 2) It is a funnel to mediocrity. No one should fall behind, and no one should excel. Both are either forbidden or denied. And that is true for the teachers as well as the students. Truly a dysfunctional system.
I got confused at math starting with long division, and everything beyond that was extremely difficult. I was much better at things with words, and awful at things with numbers. (I don't remember having problems with super simple math, and long division was do-able, but when it got anywhere near complex, I found it confusing, but I don't remember details of why.)
I also was turned off by math because I thought (at the time), that beyond the basics, add/subtract / multiplication, percentages, simpler division, there was no use for it, if there was no chance of becoming an engineer or something like that. (That was my thinking in high school and college, where I was able to get away with hardly any math).
Many years later I was at the ocean with a friend, admiring a stone with a beautiful spiral. He explained that spirals in rocks have the same proportions of something that appear in nature many times. I remember thinking if I had known that in math classes, I may have been more interested, and put more effort in.
Are you in touch with Mathew Crawford (Rounding the Earth)? (Mathew with one T) (I heard of both of you from Dark Horse Podcast). https://roundingtheearth.substack.com/s/rte-education-zone https://metaprep.net/about/ Seems like potential for collaboration, both of you are math nerds and passionate about healing the world by empowering nuanced, independent thought.
Holly. I've been tutoring kids for math and standardized tests for over 15 years now. I've noticed quite a number of issues.
1) Some kids have emotional issues that impede learning significantly. These are beyond my pay grade, and require intensive psychological counseling. Tough to find someone competent for that task.
2) The transition from elementary school to high school is interesting. In third and fourth grade, the kid gives an answer to a simple question such as what is 5 x 3? But for some reason, many kids are unable to learn to work multistep problems. They continue to think that they should be able to spout an instant answer, even to a difficult trig question, for example. I chalk it up to poor instruction. Once it's explained to them that they don't need to, can't, come up with an instant answer, they do much better.
3) Fractions. High school kids who can't do fractions. I find it helpful to do fractions, ratios, percents all together to show how they are all the same thing. Also, it works to point out that every fraction is a division problem.
4) Geometry. After Chemistry, this is the most complained of subject. These both seem to be the result of poor instruction.
5) Algebra. There seems to be difficulty distinguishing terms from factors, which confusion leads to consistent errors in algebraic manipulation. Often, using concrete examples with numbers is necessary to show why certain moves don't work.
6) Calculators. If only we could throw away all the calculators. Of course, they're really useful for Stats, and other tedious calculations. But they become such a crutch; I have high school kids who can't do simple arithmetic with two-digit numbers, and sometimes one-digit numbers.
I was always good at math from before I went to kindergarten, and I've been playing music since a young child. It seems to me that math and music occupy the same space in my brain, but that's just my subjective experience. I've tried to identify why math is so easy for me, and how to convey that ease to my students, but it's an elusive thing. The best I can guess is that I visualize numbers in my mind's eye, mostly from 1 to 100, but focused on 1 to 20. And different numbers have different shading to them. I don't know where that came from, but it forms a firm foundation for everything else. I also see calendars like that. I wonder what other people see.
💬 math and music occupy the same space in my brain
Quadrivium of classical curriculum—arithmetic, geometry, music, and astronomy—might provide a clue 🙂 Arithmetic is about numbers as such; geometry = numbers in space; music = numbers in time; astronomy = numbers in both space and time.
Currently homeschooling a 7th grader. Open to any ideas, books, websites etc. that might spark interest. It's a beautiful mathematical world out there, I'm just not sure how to initiate the wonder.
I was good at math -- 99th percentile on (then) SAT scores (98th on college-bound) -- because my father, who was earning his PhD from Math Department at UW, insisted in teaching me and drilling me in math tables: both "the old way" (7x1=7, 7x2=14, 7x3=21, . . . 7x11-77, 7x12=84) and "the new way" (7, 14, 21, 18 . . . 77, 84), from 1 through 12. My students at the Tribal (Native American Indian) college where I taught, in contrast, were in general terrible at math because they had not been taught this. I don't know who benefits from students' NOT being taught this, but it isn't American students.
A few places I've noticed students bottleneck when it comes to mathematical skills:
Arithmetic:
-Negative number arithmetic (sign rules)
-Finding a Least Common Denominator algorithmically
Algebra:
-Combining like terms
-Understanding the relationship between a graph and an equation
-Fluency moving terms in an equation to one side or the other
-Approach to isolating variables in different situations
Trigonometry:
-Overreliance on a written unit circle to find the sin/cos/tan of basic angles
General:
-Ability translate a written statement into a mathematical expression or algebraic equation