Math as a habit(kidswholovemath.substack.com)
kidswholovemath.substack.com
Math as a habit
https://kidswholovemath.substack.com/p/math-as-a-habit
58 comments
> How do I get her to love math (or other good things) in the first place? The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
My suggestion; Kids learn by mimicking and playing. Our Education System beats this out of us in favour of formalism/competition/goals/etc. So if you sit and "play" with her using objects/manipulations of objects (set theory/abstract algebra/formal systems), measurements (quantities/units/coordinate systems), walking across the room with even speed vs. sudden acceleration/de-acceleration (calculus) you can teach Abstractions/Mathematics/etc. This will build up their intuition and hook their interest. Then you can teach them the necessary "formal notation" using paper/pencil and textbooks. You always go from concrete to abstract with enthusiasm and a playful attitude i.e. no right/wrong answers but exploring ideas/concepts.
PS: You might find the videos of the famed educationalist Sir Ken Robinson (https://en.wikipedia.org/wiki/Ken_Robinson_(educationalist)) useful in this regard - https://www.youtube.com/results?search_query=ken+robinson
My suggestion; Kids learn by mimicking and playing. Our Education System beats this out of us in favour of formalism/competition/goals/etc. So if you sit and "play" with her using objects/manipulations of objects (set theory/abstract algebra/formal systems), measurements (quantities/units/coordinate systems), walking across the room with even speed vs. sudden acceleration/de-acceleration (calculus) you can teach Abstractions/Mathematics/etc. This will build up their intuition and hook their interest. Then you can teach them the necessary "formal notation" using paper/pencil and textbooks. You always go from concrete to abstract with enthusiasm and a playful attitude i.e. no right/wrong answers but exploring ideas/concepts.
PS: You might find the videos of the famed educationalist Sir Ken Robinson (https://en.wikipedia.org/wiki/Ken_Robinson_(educationalist)) useful in this regard - https://www.youtube.com/results?search_query=ken+robinson
Just to add, building intuition is the same thing as struggling to solve a problem. The process creates solution shaped holes in your brain, in which the formalism and abstract algebra fit naturally.
But it is important to actually give the formalism and abstract algebra at this point. Unless your child is an age defining genius, they will benefit from some handholding, and theres not much of that that can be done without having access to it yourself.
But it is important to actually give the formalism and abstract algebra at this point. Unless your child is an age defining genius, they will benefit from some handholding, and theres not much of that that can be done without having access to it yourself.
> building intuition is the same thing as struggling to solve a problem.
Not necessarily.
Intuition (borne out of Imagination) is for understanding the domain concepts even before there is a problem to solve.
This is the reason i am against the oft repeated advice "solve a lot of problems to learn Mathematics" which merely leads to mechanical "plug and chug problem-solving" with no real understanding. Instead one should spend a lot of time trying to grasp the concepts well, map them to the appropriate notations used and then study a few fully-worked out problems to grasp the "applications".
Not necessarily.
Intuition (borne out of Imagination) is for understanding the domain concepts even before there is a problem to solve.
This is the reason i am against the oft repeated advice "solve a lot of problems to learn Mathematics" which merely leads to mechanical "plug and chug problem-solving" with no real understanding. Instead one should spend a lot of time trying to grasp the concepts well, map them to the appropriate notations used and then study a few fully-worked out problems to grasp the "applications".
The point is that definitions and theorems are learned backwards. First you dig the hole and then you fill it.
Humans are built to explore and discover and be curious in general. The great tragedy of technology is that improperly configured smartphones, computers and videogames give the illusion of exploration while providing nothing of value in return to the user.
It's like someone shoveling a big empty hole for years and years
It's like someone shoveling a big empty hole for years and years
>improperly
On the contrary. They're all properly configured. It's just that, their goals are not the same as our mental health goals.
I used to be a deadbeat 30-something who got his reward of progression and a sense of achievement from winning online arguments and grinding ranks in online games. Just like our brains cannot tell the difference between a picture of a girl that doesn't exist and a girl that does and both evoke some feelings of attraction, or an image of a wild animal that couldn't possible exist and one who does and both evoke some feelings of fear, the same happens when we get upvotes on reddit or platinum rank in Call of Duty.
In healthy and balanced scenarios both are distractions in our free time. For people whose life situation is less than ideal those same tools exploit their need to be appreciated and rewarded, in return for profits from sales or/and advertisements.
And we're all pretending that these people just lack willpower, and if only they had willpower they could break away from the software whose parts are deliberately designed after consultation with psychologists specialized in behavioral addiction.
On the contrary. They're all properly configured. It's just that, their goals are not the same as our mental health goals.
I used to be a deadbeat 30-something who got his reward of progression and a sense of achievement from winning online arguments and grinding ranks in online games. Just like our brains cannot tell the difference between a picture of a girl that doesn't exist and a girl that does and both evoke some feelings of attraction, or an image of a wild animal that couldn't possible exist and one who does and both evoke some feelings of fear, the same happens when we get upvotes on reddit or platinum rank in Call of Duty.
In healthy and balanced scenarios both are distractions in our free time. For people whose life situation is less than ideal those same tools exploit their need to be appreciated and rewarded, in return for profits from sales or/and advertisements.
And we're all pretending that these people just lack willpower, and if only they had willpower they could break away from the software whose parts are deliberately designed after consultation with psychologists specialized in behavioral addiction.
Go on then. How did you beat it?
They used to be a deadbeat 30-something. Now they're a deadbeat 40-something. Time eventually solves all problems.
I can't speak for them, but my own case was similar. For me it was a long process of making the bad habits harder and good habits easier. I deleted my League of Legends account (this improved my life by far the most of these changes) and blocked a bunch of sites on my browser. I started taking more walks, began getting up at a set time which I gradually shifted earlier and earlier, and started working more.
It sounds cliche, but it has worked exactly that way for me. A little more good habits, a little less bad habits, repeat x1000 and you're a whole new person in a whole new place.
It sounds cliche, but it has worked exactly that way for me. A little more good habits, a little less bad habits, repeat x1000 and you're a whole new person in a whole new place.
For me: getting better at delayed gratification by exploiting habit-forming.
I stay mindful of what it is I want, and am certain I want, and create reminders for myself to prevent my auto-pilot from going off track.
I stay mindful of what it is I want, and am certain I want, and create reminders for myself to prevent my auto-pilot from going off track.
We love the things that we are good at.
If you start with easy math problems (but not labelling them as "math problems", but as logic, smart puzzles) you can build up from there.
Consistency and frugality of options is important.
If you start with easy math problems (but not labelling them as "math problems", but as logic, smart puzzles) you can build up from there.
Consistency and frugality of options is important.
We love the things that we feel good at. Even if we are objectively better than most peers playing an instrument, if the teacher (parent) gives the impression that we are not good all motivation might dwindle.
On the other hand if the approach of the author gives a slight competitive edge, this might snowball for the reason you've given.
On the other hand if the approach of the author gives a slight competitive edge, this might snowball for the reason you've given.
This may be just an insignificant anecdote, but as a gen-z person, what helped me as a kid was a sense of community. In my case specifically our parents bought us ipod touches and that sense of community was the early jailbreak community. It didn't get me into math but into computer science which got me into math.
But this could extend to many things, e.g. the kid who likes Minecraft may get into "logic puzzles" through red stone while the kid who likes Roblox may get into creating roblox games.
Then, they will get into math once they actually need math as something useful for their "logic based hobby" as I will call it. Of course it is very hard when a kid is just hit with theoretical math and there is no real association with something they are already interested in. But there are actually countless associations, now you just need to find them and bridge your kids interests with math through them.
But this could extend to many things, e.g. the kid who likes Minecraft may get into "logic puzzles" through red stone while the kid who likes Roblox may get into creating roblox games.
Then, they will get into math once they actually need math as something useful for their "logic based hobby" as I will call it. Of course it is very hard when a kid is just hit with theoretical math and there is no real association with something they are already interested in. But there are actually countless associations, now you just need to find them and bridge your kids interests with math through them.
And I'll give an anecdote from the other side. I loved math as a kid, as well as logic puzzles, Erector sets, Legos, computers, video games, the whole pre-engineering shebang. My birthday present when I turned 11 was a copy of one of those home design CAD suites. I coded simple websites (helped along by a neighbor who, unfortunately, moved away). I had good grades in advanced courses; seemed on track for some sort of career in some STEM-related field. But I was very much alone in my passion. I couldn't seem to get anyone around me interested in this stuff, nor could I find anyone to share that interest with. I remember once, when I was in middle school, programming a very basic Pokemon battle simulator on my TI-83+. There was a software engineer who went to our church, and I was so excited to show him and get feedback, but he just kind of blew me off.
Probably a few months later, I was watching The Screensavers (remember that?), and they mentioned that users on the TechTV forums were drawing free art requests. The guy who took mine mentioned that he was posting it to deviantArt. "What's that?" I thought. Long story short, I hold a BFA instead of a BS now.
Community takes most people from hobby to passion. It is very difficult, if not impossible, to go it alone.
Probably a few months later, I was watching The Screensavers (remember that?), and they mentioned that users on the TechTV forums were drawing free art requests. The guy who took mine mentioned that he was posting it to deviantArt. "What's that?" I thought. Long story short, I hold a BFA instead of a BS now.
Community takes most people from hobby to passion. It is very difficult, if not impossible, to go it alone.
> There was a software engineer who went to our church, and I was so excited to show him and get feedback, but he just kind of blew me off.
I'm sorry to hear that you had this experience. I'm sure your Pokemon battle simulator was cool!
I'm sorry to hear that you had this experience. I'm sure your Pokemon battle simulator was cool!
This is the reason why I’m very restrictive with my kids access to any digital devices. Not because they are inherently bad, but because they take valuable time where they should be out playing in nature, practicing social interactions with other kids, learn to play music, or read books.
We have some time limits on games specifically but it really is mostly Roblox (an hour a day). What stops me from limiting this further is social interaction, ironically. A lot of the current elementary school class meets up there in lieu of a playground, and removing that would limit the kid's social life.
They like to run a voice chat in the background while they play, so it's not just a silent in-game chat interaction.
If removing this I don't know how we would replace the social aspect. Would probably need to find an in-person after-school program which would have its own problems.
They like to run a voice chat in the background while they play, so it's not just a silent in-game chat interaction.
If removing this I don't know how we would replace the social aspect. Would probably need to find an in-person after-school program which would have its own problems.
> What stops me from limiting this further is social interaction, ironically. A lot of the current elementary school class meets up there in lieu of a playground, and removing that would limit the kid's social life.
This is such sad commentary on modern life. Why is this acceptable at all?
This is such sad commentary on modern life. Why is this acceptable at all?
I follow this but part of this attitude has always struck me as slightly off. Parents and others deciding what is valuable versus what isn’t. Granted draining full days in Roblox for the average kid is likely a net loss, but I recall similar attitudes parents had for video games. There’s a fair number of people out there who played lots of video games as children and grew up to do great things because they were inspired by games. Guess I am saying it’s hard to know where inspiration can emerge from. I don’t think teaching our kids some skill is always about its benefits to them but the befits we have perceived from it, regardless of what it is and if the kid likes it. I recall having to go on lots of morning hunts as a kid because my dad enjoyed it and wanted me to enjoy it too, even though I did not.
And we decide that they aren't allowed to eat candy for breakfast, lunch, and dinner, because we know that if they do they will feel like crap, even though it might be immediately rewarding.
And while there are people who might have grown up to do great things after playing video games, or reading comic books or watching television, or whatever thing has horrified any given generation, I'm convinced that knowing to play an instrument, have the patience to read to a book or walk in nature, know how to approach a science paper, or dance, give much more chances to live a fulfilling life.
And if you have those things the day you become an adult, you can still choose to play video games with all your free time. But if you have spent your childhood and adolescence playing video games, it is really hard to get started with any of all those other things that life offers.
And while there are people who might have grown up to do great things after playing video games, or reading comic books or watching television, or whatever thing has horrified any given generation, I'm convinced that knowing to play an instrument, have the patience to read to a book or walk in nature, know how to approach a science paper, or dance, give much more chances to live a fulfilling life.
And if you have those things the day you become an adult, you can still choose to play video games with all your free time. But if you have spent your childhood and adolescence playing video games, it is really hard to get started with any of all those other things that life offers.
I want to think that kids today would be able to balance life and tech, because I was able to growing up in the nineties. In the same summer I would spend 8 weeks in the woods working camp staff, and dumping dozens of late nights into MMOs, and think I turned out alright. Surely there were many other factors, but those are the ones focused on here.
It was a very different internet and world though. The thought of giving a child access to YouTube terrifies me. Content is engineered extremely well to prey on children (and adults who are still children), what if they find and get tricked by this? Absolutely terrifies me.
Not allowing access is obviously wrong, they will just resent you and watch even more of it at school, a friends house, etc. So you have to allow access but teach them enough to not fall for it. It’s your parenting vs their extremely well rehearsed, metrics backed, full-time, for-profit, well disguised content, which can either be completely harmless or fuck them up for life.
So, I get it.
It was a very different internet and world though. The thought of giving a child access to YouTube terrifies me. Content is engineered extremely well to prey on children (and adults who are still children), what if they find and get tricked by this? Absolutely terrifies me.
Not allowing access is obviously wrong, they will just resent you and watch even more of it at school, a friends house, etc. So you have to allow access but teach them enough to not fall for it. It’s your parenting vs their extremely well rehearsed, metrics backed, full-time, for-profit, well disguised content, which can either be completely harmless or fuck them up for life.
So, I get it.
Maybe we shouldn't be forcing kids to do what they don't love in the first place. Well, I don't mean we shouldn't get them to understand basic math, but shove it down their throats? Why not just let them explore what they like?
Oh yeah, it's because we want them to get jobs. But trust me, if you make a child do a lot of something they don't love, they might get a job with it and then just quit because they hate it.
Oh yeah, it's because we want them to get jobs. But trust me, if you make a child do a lot of something they don't love, they might get a job with it and then just quit because they hate it.
Too much of anything is poison, and a harsh upbringing is certainly counterproductive, but so is the opposite. Limiting yourself to doing only what you love goes against yours and you children self-realization and leaves the door open to marketing and fads.
I find that people who do this to their children regret it later, life is short and the time we have to help our children forge a good foundation is even shorter.
You can very well give them a balance between a carefree, happy childhood full of love, while at the same time forcing them to discover lots of things they don't like at first sight.
It's better to fail at raising children by trying to pass something on to them than to let others do it all for you.
I find that people who do this to their children regret it later, life is short and the time we have to help our children forge a good foundation is even shorter.
You can very well give them a balance between a carefree, happy childhood full of love, while at the same time forcing them to discover lots of things they don't like at first sight.
It's better to fail at raising children by trying to pass something on to them than to let others do it all for you.
Yes, and all I advocate is giving children the opportunity to learn lots of things, but not necessarily choosing one very specific one like "math" and making them learn it.
I don't disagree with a little pushing, but some children will just never be good at math....
I don't disagree with a little pushing, but some children will just never be good at math....
My mother forced me to practice classical string instruments from a very young age, and as a child, I fought her viciously over it.
Because she pushed through my complaints and bore my abuse, I now have deeply embedded musical skills that have changed the trajectory of my life experience for the better.
As an adult, I try to thank her for this whenever I can. I don’t know if I’ll be strong enough to give my own future children this gift.
Because she pushed through my complaints and bore my abuse, I now have deeply embedded musical skills that have changed the trajectory of my life experience for the better.
As an adult, I try to thank her for this whenever I can. I don’t know if I’ll be strong enough to give my own future children this gift.
> Oh yeah, it's because we want them to get jobs
Interesting, I thought we're doing it because we don't want them to be stupid.
Interesting, I thought we're doing it because we don't want them to be stupid.
You're right, but this is a different problem. Often people like doing certain things, but have trouble getting to them. I love boardgames, and I'd love to introduce my kids to some of my favorite games, but I need to set up the game, relearn the rules, explain them etc. The "cost to entry" (in terms of energy/motivation) is pretty high even though I know I'm going to like it.
I'm working on convincing my kids that maths is just cheat codes.
Once you know the cheat code for figuring out a math problem the actual working out is fast and easy... (like turning on creative mode in minecraft)
Its a work in process...
Its a work in process...
This reminded me of how I cheesed a lot of advanced math in high school.
I'd memorize the formulas we were being tested on right before the tests were handed out. Then I'd write them in the top of the test immediately and before I forgot them. Then I'd ace the test. Lol.
I'd memorize the formulas we were being tested on right before the tests were handed out. Then I'd write them in the top of the test immediately and before I forgot them. Then I'd ace the test. Lol.
There's a reason that most my my Mechanical Engineering courses allowed note sheets during exams. The Fundamentals of Engineering exam comes with a large book of formulae.
The test is really about how to apply the formula, not a test of remembering it.
Maybe the difficulty is not for the kids, but for the parents to allocate time to do the activity the kids like. Maybe kids doing math by themselves without any adult support would not work? Don't know which problems to choose, don't know how to get unstuck, things like that. Or at least the parents think so.
Roblox and reading seem different from this perspective.
Roblox and reading seem different from this perspective.
> Math? That’s about as easy to form a habit with as running 5 miles. How do I get her to love math (or other good things) in the first place?
> The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
Step 1 is defining your goal. Assume you will not change the fact that your daughter doesn't like math. What capabilities do you want her to have that will come from studying it?
Focus on those, not on trying to build a habit of math-for-its-own-sake.
(If you don't think there are any particular capabilities that she will need, then I would suggest having her study math is probably not a good use of her time.)
> The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
Step 1 is defining your goal. Assume you will not change the fact that your daughter doesn't like math. What capabilities do you want her to have that will come from studying it?
Focus on those, not on trying to build a habit of math-for-its-own-sake.
(If you don't think there are any particular capabilities that she will need, then I would suggest having her study math is probably not a good use of her time.)
Just like "habit stacking" worked for the author, maybe you should try what might be called "interests or hobby stacking". Let them do what they love after completing something that they don't love doing.
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>The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
Easy. Give her access to Roblox only after she does her math for the day.
Easy. Give her access to Roblox only after she does her math for the day.
The hard part is getting your kids to love things they don't love yet.
Sounds like something the kids will drop as soon as they'll become independent enough.
I count stuff(so "do math") as a habit and it's like that because my mother was slipping it into daily activities in an unstructured way.
Some examples:
When we were back from doing groceries we would sometimes weigh the bags and see how heavy they were. We would also keep track of our own weights and heights.
I could play with things like measuring tape.
She would give me and my sister coins and ask what can be bought with them, so that we could get the thing.
If I wanted a learning toy that taught me about numbers, I could have it.
I was allowed to set the time on the microwave when I was like four.
After some pestering she crafted a "counter" for me out of plastic caps, carboard and one of those sticks that you use to check if whatever is in the oven is done.
We also read every number we saw.
This is all stuff that happened before I went to school, at which point I was already ahead of most of the class without even seeing it as much of an effort.
I count stuff(so "do math") as a habit and it's like that because my mother was slipping it into daily activities in an unstructured way.
Some examples:
When we were back from doing groceries we would sometimes weigh the bags and see how heavy they were. We would also keep track of our own weights and heights.
I could play with things like measuring tape.
She would give me and my sister coins and ask what can be bought with them, so that we could get the thing.
If I wanted a learning toy that taught me about numbers, I could have it.
I was allowed to set the time on the microwave when I was like four.
After some pestering she crafted a "counter" for me out of plastic caps, carboard and one of those sticks that you use to check if whatever is in the oven is done.
We also read every number we saw.
This is all stuff that happened before I went to school, at which point I was already ahead of most of the class without even seeing it as much of an effort.
The biggest challenge in this kind of parenting appears to be the psychology of puberty: At some age kids start to actively seek interests in fields their parents do NOT encourage or approve of. There was a post a while ago suggesting ways to make undesirable traits (like taking drugs) "uncool" but that might backfire too.
> the moment we fell off the streak, it broke completely
This sounds strange to me. I used the streak method for several physical activities. At first I was worried I would not keep it up, so it was very important to not miss any single day. But after 100 days? A miss does nothing. I have proof I can keep it up, and that motivates me to continue. Besides, life happens, it's impossible to _never_ miss a day of anything.
The first weeks are harder, but after that, I look more for a moving average. If I have 95 of the last 100 days, I'm doing great.
This sounds strange to me. I used the streak method for several physical activities. At first I was worried I would not keep it up, so it was very important to not miss any single day. But after 100 days? A miss does nothing. I have proof I can keep it up, and that motivates me to continue. Besides, life happens, it's impossible to _never_ miss a day of anything.
The first weeks are harder, but after that, I look more for a moving average. If I have 95 of the last 100 days, I'm doing great.
The language-learning app Drops gives you "free passes" which regenerate every 5 days of actual streak & get automatically applied if you miss a day. I think this is a really nice way to get a streak system to work if you are super focused on a big number; if you miss 1 day you are suddenly extra incentivized to not miss the next several days so you can regain your now-used-up free pass, and theres some flexibility added to the streak so life can interfere occasionally and you get to keep your large number.
People are often outcome-driven when they should be behaviour-driven. People focus on the actual streak, rather than the intention to maintain the streak. The second is what makes you successful, the former is easy for a lot of people to fall into.
This is pervasive. At both school and work, we tend to incentivise good outcomes rather than the sort of behaviour that leads to good outcomes. The result is less than optimal.
This is pervasive. At both school and work, we tend to incentivise good outcomes rather than the sort of behaviour that leads to good outcomes. The result is less than optimal.
> the moment we fell off the streak, it broke completely. […] Going back to having a 1-day streak compared to a 10-day, 50-day, 100-day, etc. streak is so daunting that most people (us included) find it hard to start again. […] We didn’t do math for a while.
I find this super interesting, a fantastic example of how weird our brains are and how good they are at tricking us out of effort. I always liked the idea of the Seinfeld chain for habit forming, but never tried it long enough to experience the breaking of a super long chain. I bet a lot of people who try it have a similar experience to the author, which is really funny in a way because it totally worked amazingly well for a long time. The chain isn’t supposed to be the ultimate reward, except that if the mental hack for doing it every day is make a chain, it’s easy to see why this happens. But still funny that our brains will let one tiny slip become more important than months and months of progress, even when it’s not. Clearly a way to handle inevitable breaks should be built in and provide motivation to start again, maybe an anti-chain for misses, or a progress meter, or something else. Maybe if I try this I’ll force myself to have some breaks early on, to practice restarting. This kind of subconscious battle with ourselves is what makes diets and exercise hard… all habits we wish we had but don’t, and it’s fascinating what different mental tricks work for different people.
I find this super interesting, a fantastic example of how weird our brains are and how good they are at tricking us out of effort. I always liked the idea of the Seinfeld chain for habit forming, but never tried it long enough to experience the breaking of a super long chain. I bet a lot of people who try it have a similar experience to the author, which is really funny in a way because it totally worked amazingly well for a long time. The chain isn’t supposed to be the ultimate reward, except that if the mental hack for doing it every day is make a chain, it’s easy to see why this happens. But still funny that our brains will let one tiny slip become more important than months and months of progress, even when it’s not. Clearly a way to handle inevitable breaks should be built in and provide motivation to start again, maybe an anti-chain for misses, or a progress meter, or something else. Maybe if I try this I’ll force myself to have some breaks early on, to practice restarting. This kind of subconscious battle with ourselves is what makes diets and exercise hard… all habits we wish we had but don’t, and it’s fascinating what different mental tricks work for different people.
One thing I've seen to help with this is the idea of "recovering" a streak. For example there's an online puzzle site (puzzmo.com) that tracks how many days in a row you completed a puzzle. If you miss a day the streak counter resets to zero, but if you then complete it seven days in a row, the counter goes back to whatever your old longest streak was.
Of course, this is completely arbitrary and silly, but it does take the sting out of losing a super-long streak. A new goal of seven consecutive days feels reasonable; a new goal of 300 consecutive days feels impossible.
Of course, this is completely arbitrary and silly, but it does take the sting out of losing a super-long streak. A new goal of seven consecutive days feels reasonable; a new goal of 300 consecutive days feels impossible.
I thought I loved math as a kid. My mother encouraged and supported me in an everyday sense and I considered myself quite well versed as a kid.
This completely broke down with highschool and university math. The teachers, for the love of God, simply could not teach and were indulging themselves on a whiteboard. I felt helpless and at some point merely looking at equations caused anxiety.
Basic arithmetic is not math.
This completely broke down with highschool and university math. The teachers, for the love of God, simply could not teach and were indulging themselves on a whiteboard. I felt helpless and at some point merely looking at equations caused anxiety.
Basic arithmetic is not math.
>The teachers, for the love of God, simply could not teach and were indulging themselves on a whiteboard.
At the university level, I found math professors to be the worst instructors I encountered, without a doubt. Was your experience the same?
The first time I took Calc 3, the professor would say "Now anyone can look at the example in the book on their own and work through it. I'm going to put a little twist on it to show you another concept."
The premise of this is fine, but execution was awful. He would then on-the-fly decide what variables he was going to change and start writing on the chalkboard. After filling all 3 sections, he'd erase and fill the first and second sections. That was ~40 minutes into the 50 minute class. Then something wouldn't look right as he studied the 3/5 of the problem still on the board. The class would finish, and sometimes he'd spend the first 5-10 minutes of the next class showing where he messed up and completing the example. My 5 pages of notes were of no value because somewhere they were very wrong.
Had he taken 15 minutes to work it out on his own ahead of class, I might not have dropped the class. The next time I took it, I had a lecturer who was really amazing and I earned a A. That was the only A from the math department I earned in college across 4 difference classes and 5 instructors.
At the university level, I found math professors to be the worst instructors I encountered, without a doubt. Was your experience the same?
The first time I took Calc 3, the professor would say "Now anyone can look at the example in the book on their own and work through it. I'm going to put a little twist on it to show you another concept."
The premise of this is fine, but execution was awful. He would then on-the-fly decide what variables he was going to change and start writing on the chalkboard. After filling all 3 sections, he'd erase and fill the first and second sections. That was ~40 minutes into the 50 minute class. Then something wouldn't look right as he studied the 3/5 of the problem still on the board. The class would finish, and sometimes he'd spend the first 5-10 minutes of the next class showing where he messed up and completing the example. My 5 pages of notes were of no value because somewhere they were very wrong.
Had he taken 15 minutes to work it out on his own ahead of class, I might not have dropped the class. The next time I took it, I had a lecturer who was really amazing and I earned a A. That was the only A from the math department I earned in college across 4 difference classes and 5 instructors.
> I found math professors to be the worst instructors I encountered, without a doubt
Same. If this weren't common I think memes like "this is left as exercise to the reader" wouldn't exist.
I'm convinced most of them find math intuitive to a point where they can't indentify at all with people who struggle with it and have no idea where to even start explaining things. And it also takes patience to try and bridge that gap. Not to mention a lot of maths concepts depend on understanding other ones and education in general just assumes that each person is proficient in everything from previous classes.
It's similar with technology as well, some people know immediately how to rule out problems or google a solution while others struggle to come up with the right question.
Same. If this weren't common I think memes like "this is left as exercise to the reader" wouldn't exist.
I'm convinced most of them find math intuitive to a point where they can't indentify at all with people who struggle with it and have no idea where to even start explaining things. And it also takes patience to try and bridge that gap. Not to mention a lot of maths concepts depend on understanding other ones and education in general just assumes that each person is proficient in everything from previous classes.
It's similar with technology as well, some people know immediately how to rule out problems or google a solution while others struggle to come up with the right question.
The problem is simple: The kind of person who can understand Calc 3 enough to teach it, cannot possibly know what it is like to be the average student in the Calc 3 class who don't magically just "get" it like someone who became a math professor definitely did.
Teaching is a really difficult skill that most people are not born with. If you can easily understand high level math, you usually aren't going to decide to spend your life teaching, rather than making good money.
The best math professor I ever had in college was an adjunct from the local community college, because they were a teacher first, and a mathematician second.
Teaching is a really difficult skill that most people are not born with. If you can easily understand high level math, you usually aren't going to decide to spend your life teaching, rather than making good money.
The best math professor I ever had in college was an adjunct from the local community college, because they were a teacher first, and a mathematician second.
had a similar experience where i got frustrated out of maths when i had to switch to study it in three different regions, each using different notations and terms for the same thing.
once you are off the train it is hard to self-motivate to get back on. the university lecturers i learnt from do not seem to have any incentive to help you get back up to speed.
once you are off the train it is hard to self-motivate to get back on. the university lecturers i learnt from do not seem to have any incentive to help you get back up to speed.
Interest and competence is a feedback loop that drive each other. I really had it with the reductionist views that "don't force kids to learn things they don't like" and "keep up the practice and the rest will come". On one hand, kids have fleeting interests and they are easily frustrated. On the other hand, there is nothing more demoralizing than being forced to do busy work you are not interested in.
Teachers need to sparkle and be protective of their students curiosity. Amazing things happen when a student is eager to learn. It is also true that deliberate practice and spaced repetition are very effective at building competence and then confidence. Confidence drives further interest.
Teachers need to sparkle and be protective of their students curiosity. Amazing things happen when a student is eager to learn. It is also true that deliberate practice and spaced repetition are very effective at building competence and then confidence. Confidence drives further interest.
Teachers have the most important job I think
When parents start pressurizing kids with too much planning and excessively focused expectations, IMHO, they risk the kids rebelling-- especially as the kids start developing their own interests and tastes.
The "cues" the author talks about, even the one that's claimed as successful (habit stacking), seem like that. Children need structure of course, but they also need variety and free time. "Stacking" anything seems counter to that.
The "cues" the author talks about, even the one that's claimed as successful (habit stacking), seem like that. Children need structure of course, but they also need variety and free time. "Stacking" anything seems counter to that.
Yeah - I see this approach as being far too “on the nose” to be sustainable. It makes it seem like work.
My approach as a kid, and as an adult, which I hope to instill in my daughter, was just to use mathematics as a lens to examine the world - using the equations of motion to derive how deep a well is or how high a cliff is from dropping a stone, calculating the mass of water in a swimming pool and therefore the force on each support column underneath it, the number of candies in a jar (man, I won so much candy as a kid), estimating the number of people in a crowd from a sample (that got me backstage at Glastonbury!), how much longer will I need to read this book based on my current pace, what my basal metabolic rate is based on the curve I see in my weight loss on a fixed diet, etc. etc. - nothing overly taxing, but plenty of things which answer small “I wonder…” questions, and keep the habit of doing mental arithmetic alive, and various equations and tools alive in my mind.
It also ends up giving insight, and therefore an incentive to keep honing those mental tools.
I generally find the best way to get myself or anyone else to do something is to make it useful and interesting, and to make it not feel like work.
My approach as a kid, and as an adult, which I hope to instill in my daughter, was just to use mathematics as a lens to examine the world - using the equations of motion to derive how deep a well is or how high a cliff is from dropping a stone, calculating the mass of water in a swimming pool and therefore the force on each support column underneath it, the number of candies in a jar (man, I won so much candy as a kid), estimating the number of people in a crowd from a sample (that got me backstage at Glastonbury!), how much longer will I need to read this book based on my current pace, what my basal metabolic rate is based on the curve I see in my weight loss on a fixed diet, etc. etc. - nothing overly taxing, but plenty of things which answer small “I wonder…” questions, and keep the habit of doing mental arithmetic alive, and various equations and tools alive in my mind.
It also ends up giving insight, and therefore an incentive to keep honing those mental tools.
I generally find the best way to get myself or anyone else to do something is to make it useful and interesting, and to make it not feel like work.
Has anyone read the book referenced at the beginning of the blog article, "The Power of Habit"? Or a similar book? If so, would you recommend reading it?
Not really IMO. Like most self help books, the book is around an extremely simple concept with way too much filler to try to make it into a book. Besides being boring and repetitive... Applying them to my own life was way too much of a stretch, felt like a lab rat having science experiments done on it.
Atomic habits is way better, and approachable if you're trying to actually change your behavior
Atomic habits is way better, and approachable if you're trying to actually change your behavior
A similar book, Atomic Habits, is okay.
Like all self-help, buying a book and reading it is the easy part.
What matters is actually _applying_ what you learn. The snippet about building habits at the end of the article represents the core techniques of forming habits.
Like all self-help, buying a book and reading it is the easy part.
What matters is actually _applying_ what you learn. The snippet about building habits at the end of the article represents the core techniques of forming habits.
I used the "don't break the chain" rule to write a book and it was the only thing that kept me going through small kids and the inherent "distractions." It was interesting to read how demoralized the author was when they broke that streak. I suppose it can look like that, but it feels like you can easily game that, and count breaks as OK, and then have a streak with an asterisk by it.
The intuition seems reversed for Math as a Habit. Doing math problems, then tying a reward to it to reinforce a habit is one approach.
I feel like given the broad nature of math, another approach might be to just integrate the math concepts and learning into already things that kids enjoy doing. Whether it's tying it into video games, sports, etc.
I feel like given the broad nature of math, another approach might be to just integrate the math concepts and learning into already things that kids enjoy doing. Whether it's tying it into video games, sports, etc.
My kid loves Roblox. Math not so much. She’ll gladly play Roblox every day with no assistance or structure from me. Math? That’s about as easy to form a habit with as running 5 miles. How do I get her to love math (or other good things) in the first place?
The hard part isn’t getting by kids to do things they love, it’s getting them to do things they DON’T love.
I was able to get her hooked on reading actual paper books but only when she messed up in school and lost access to devices for 9 days. Boredom took over and books were the answer. Now she loves them, thank god.