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> Without realizing it, he was doing algebra. A friend of mine taught remedial math at UW to incoming freshmen. She would write: x + 2 = 5 on the blackbo

> Without realizing it, he was doing algebra. A friend of mine taught remedial math at UW to incoming freshmen. She would write: x + 2 = 5 on the blackboard and ask a student "what is the value of x?" The student would see the x, and immediately respond with x means algebra, algebra is hard, I cannot do algebra. So she started writing: _ + 2 = 5 and ask the student to fill in the blank. "Oh, it's 3!"

zmgsabst 2y ago
I’ve always found that an indictment of math education — and spent many, many hours discussing it. When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?” Pedagogy is hard.
- Buttons840 2y ago
  Go from "[ ] + 2 = 5" to writing it "box + 2 = 5--what is box?". Then "b + 2 = 5--what is b?" then "x + 2 = 5--what is x?".
  - sublinear 2y ago
    I agree. I think the actual problem is that the student is trying to comprehend what it means for anything to have mathematical value other than explicit numbers. Numbers and letters are taught together, but not as symbols. Letters are taught with sounds and numbers are taught with counting. The notion of a symbol isn't really emphasized much. I would explain it more like after [ ] + 2 = 5 what happens if you need more than one box for a complicated problem? Teach the idea that saying box #3 is equivalent to assigning an arbitrary letter for whatever reason you want, but that people more familiar with math prefer letters because they stand in for words that describe what the number is for. You might want to use 'c' for the number of cats you're trying to figure out. In a room of five animals two are dogs. How many cats? a = 5, c = ?, d = 2 a = c + d so... 5 = c + 2 what is c? Light bulb goes off: "You can do that?" Yes, you can do whatever you want and it's not all about carrying the one or whatever other rote teaching they've been given. They can get creative and be engaged, and then you let them know that actually there are some conventions people like to use for what they're trying to do. They might even believe they've invented a new idea. At least they're having fun.
    - dr_kiszonka 2y ago
      I agree with you. To me, a lot of pre-college math education could be summarized as "In this class I will show you a bunch of abstract problems, a bunch of ways to solve them, and I will test if you have learned them." Learning in these classes is often limited to memorizing a sequence of steps. That's why I would frequently ask "You can do that?" myself when talking to those whom I considered mathematically gifted (math olympiad winners and such). I think they realized that as a problem-solving tool math could be used creatively. I saw it as a largely useless hammer that to work had to be held in a very specific way. I remember connecting sets in, I think, Pascal to what I had learned in school and realizing that all that math was perhaps not as useless as I had thought : - )
  - Jensson 2y ago
    That is what math books already do.
    - Viliam1234 2y ago
      Some of them do it better than others.
  - Viliam1234 2y ago
    Basically, don't teach the new concept and the new syntax both at the same time. New things should be introduced one by one.
  - Izkata 2y ago
    You skipped a step. One of the problems is more obvious with a different operator we learn when in the "box" stage: > Go from "[ ] x 2 = 10" to writing it "box x 2 = 10--what is box?". Then "b x 2 = 10--what is b?" then "x x 2 = 10--what is x?". From memory, we didn't switch from "x" to dot for multiplication until at the exact same time we started using symbols. If we'd done it earlier (or even right from the start) it might not have been as much of a problem.
- uwagar 2y ago
  back when we was new in programming it was similarly difficult to grok X = X + 1 once we got it, it was a like new world!
  - 5- 2y ago
    most likely this very unfortunate misnomer started with fortran, where it was deemed lucrative to point out "how much programs look like mathematic formulas!". not only is this overloading a symbol (equality) with a completely different meaning (assignment), it is also a poor choice typographically, as it represents a directional operation with a directionless symbol. using an arrow for assignment is much better. it's also worth pointing out that unlike most others, logic programming languages (e.g. prolog) have actual variables, not references to mutable or immutable memory cells.
    - uwagar 2y ago
      arrow for assignment is cool, but the backspace key is the only closest arrow-like key on the keyboard but it has a different purpose. plus the arrow key should be laid out such that u dont have to press a SHIFT/CTRL/ALT to produce it. for this reason, i felt C a breath of fresh air cos u could just assign using = instead of what we was doing in pascal which was the horrible := where u had to press SHIFT for the : things like this matter.
      - dr_kiszonka 2y ago
        Right. If we went more in the direction of APL, we would have had way more symbols. https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keybd.svg https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keyb...
sublinear 2y ago
The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'. People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.
- GodelNumbering 2y ago
  thank Descartes
  - ckolkey 2y ago
    I thank, therefore I am...
- raverbashing 2y ago
  > nobody is really teaching the concept of a symbol in a math class. This was what? 5th grade? What kind of crap teachers never taught that
  - mschuster91 2y ago
    > What kind of crap teachers never taught that It's rarely the fault of the teachers. The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue). The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies. And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.
deleted 2y ago
[deleted]
RobinL 2y ago
There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.
- sethammons 2y ago
  My kids all lived dragonbox games; the algebra and geometry one
  - sethammons 2y ago
    edit: loved*
- gnubison 2y ago
  As a senior in high school, I devoured this game in elementary school and got way better at math than my peers. Now taking differential equations and multivariable calculus through our college in the high school (CHS) program. When I looked for it out of curiosity I was sad to see it transformed into a subscription service.
ozgrakkurt 2y ago
There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time. Even if the system was better the person still has to be able to motivate themselves and put in the time.
jand 2y ago
As we are sharing anecdotes: One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones. Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter. So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.
- Viliam1234 2y ago
  I saw a textbook that used a picture of a box in the equation. The number is hidden in the box, and you are supposed to figure out which number it is.
deleted 2y ago
[deleted]
danenania 2y ago
I got my daughter (just turned 6) this little hand held math game for her birthday: https://www.amazon.com/your-orders/pop?ref=ppx_yo2dv_mob_b_pop__np_2_pp&orderId=112-7222392-8361050&lineItemId=jimgtvprsqknxops&shipmentId=B4Nky4jJL&packageId=1&asin=B0BZWPDGK3 https://www.amazon.com/your-orders/pop?ref=ppx_yo2dv_mob_b_p... She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.
- dr_kiszonka 2y ago
  Is this the game? You linked to your order history. https://www.amazon.com/Educational-Insights-Math-Electronic-Handheld/dp/B0BZWPDGK3 https://www.amazon.com/Educational-Insights-Math-Electronic-...
  - danenania 2y ago
    Oops, yes that’s the one.

zmgsabst 2y ago

I’ve always found that an indictment of math education — and spent many, many hours discussing it. When teaching addition, workbooks commonly use a box, eg, “[ ] + 2 = 5” — and first graders have no conceptual problem with this. Somehow, we lose people by the time we’re trying to formalize the same concept in algebra. There’s been many times I’ve written a box around letters in a problem and asked students “what’s in the box labeled x?” Pedagogy is hard.

Buttons840 2y ago
Go from "[ ] + 2 = 5" to writing it "box + 2 = 5--what is box?". Then "b + 2 = 5--what is b?" then "x + 2 = 5--what is x?".
- sublinear 2y ago
  I agree. I think the actual problem is that the student is trying to comprehend what it means for anything to have mathematical value other than explicit numbers. Numbers and letters are taught together, but not as symbols. Letters are taught with sounds and numbers are taught with counting. The notion of a symbol isn't really emphasized much. I would explain it more like after [ ] + 2 = 5 what happens if you need more than one box for a complicated problem? Teach the idea that saying box #3 is equivalent to assigning an arbitrary letter for whatever reason you want, but that people more familiar with math prefer letters because they stand in for words that describe what the number is for. You might want to use 'c' for the number of cats you're trying to figure out. In a room of five animals two are dogs. How many cats? a = 5, c = ?, d = 2 a = c + d so... 5 = c + 2 what is c? Light bulb goes off: "You can do that?" Yes, you can do whatever you want and it's not all about carrying the one or whatever other rote teaching they've been given. They can get creative and be engaged, and then you let them know that actually there are some conventions people like to use for what they're trying to do. They might even believe they've invented a new idea. At least they're having fun.
  - dr_kiszonka 2y ago
    I agree with you. To me, a lot of pre-college math education could be summarized as "In this class I will show you a bunch of abstract problems, a bunch of ways to solve them, and I will test if you have learned them." Learning in these classes is often limited to memorizing a sequence of steps. That's why I would frequently ask "You can do that?" myself when talking to those whom I considered mathematically gifted (math olympiad winners and such). I think they realized that as a problem-solving tool math could be used creatively. I saw it as a largely useless hammer that to work had to be held in a very specific way. I remember connecting sets in, I think, Pascal to what I had learned in school and realizing that all that math was perhaps not as useless as I had thought : - )
- Jensson 2y ago
  That is what math books already do.
  - Viliam1234 2y ago
    Some of them do it better than others.
- Viliam1234 2y ago
  Basically, don't teach the new concept and the new syntax both at the same time. New things should be introduced one by one.
- Izkata 2y ago
  You skipped a step. One of the problems is more obvious with a different operator we learn when in the "box" stage: > Go from "[ ] x 2 = 10" to writing it "box x 2 = 10--what is box?". Then "b x 2 = 10--what is b?" then "x x 2 = 10--what is x?". From memory, we didn't switch from "x" to dot for multiplication until at the exact same time we started using symbols. If we'd done it earlier (or even right from the start) it might not have been as much of a problem.
uwagar 2y ago
back when we was new in programming it was similarly difficult to grok X = X + 1 once we got it, it was a like new world!
- 5- 2y ago
  most likely this very unfortunate misnomer started with fortran, where it was deemed lucrative to point out "how much programs look like mathematic formulas!". not only is this overloading a symbol (equality) with a completely different meaning (assignment), it is also a poor choice typographically, as it represents a directional operation with a directionless symbol. using an arrow for assignment is much better. it's also worth pointing out that unlike most others, logic programming languages (e.g. prolog) have actual variables, not references to mutable or immutable memory cells.
  - uwagar 2y ago
    arrow for assignment is cool, but the backspace key is the only closest arrow-like key on the keyboard but it has a different purpose. plus the arrow key should be laid out such that u dont have to press a SHIFT/CTRL/ALT to produce it. for this reason, i felt C a breath of fresh air cos u could just assign using = instead of what we was doing in pascal which was the horrible := where u had to press SHIFT for the : things like this matter.
    - dr_kiszonka 2y ago
      Right. If we went more in the direction of APL, we would have had way more symbols. https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keybd.svg https://upload.wikimedia.org/wikipedia/commons/9/94/APL-keyb...

sublinear 2y ago

The semantic meaning of a blank is much better understood to everyone than an arbitrary letter like 'x'. People just want to know why it's x and not something else or how a letter can have value. They might even think how can 24 + 2 = 5? They just want something to grab onto and nobody is really teaching the concept of a symbol in a math class.

GodelNumbering 2y ago
thank Descartes
- ckolkey 2y ago
  I thank, therefore I am...
raverbashing 2y ago
> nobody is really teaching the concept of a symbol in a math class. This was what? 5th grade? What kind of crap teachers never taught that
- mschuster91 2y ago
  > What kind of crap teachers never taught that It's rarely the fault of the teachers. The problem is, in many MANY MANY schools, teachers are more like social workers that have to compensate for utter horrifics outside of school. You got a ton of children so poor they didn't have breakfast which means their first (and all too often: only) meal will be the school-provided lunch (Covid showed that - a bunch of schools were open at least for lunches). You got children that are literally homeless and living with their parents in some car on a Walmart parking lot. You got children whose parents are in and out of jail. You got children living with their siblings in way too small, pest and mold ridden "apartments". You got children whose parents don't have money to pay for basic school supplies. You got children who are dealing with mental, physical and sexual abuse. You got children where the parents are constantly on drugs or seeking for drugs. You got children with a drug dependency on their own - if they're lucky it's just tobacco or weed, if not it's opioids. You got children with parents or siblings with serious mental or physical health issues. Or you got children with their own mental and physical health issues, or if you want it worse, children with these issues but without access to any kind of treatment. You got children that are being weaponized in nasty divorces. You got children that are being weaponized by street gangs. You got children committing crimes from petty theft to dealing drugs just to survive. You got children that have to literally work (and states like FL pushing to have more working children). You got children having their own children already (either from sexual abuse, from under-education about their own bodies, or intentionally because they fell for some stupid challenge/dare). You got children dealing with bullying, you got some who actually are bullies because they have no other way of dealing with their emotions or getting lunch money. You got children with parents with about zero interest in them. You got children who worry that they'll come home and find out their parents got snatched and disappeared by ICE. You got children who worry that ICE will storm their classroom and deport them. You got children who worry they might not survive the school day because someone will shoot at them. You got children who are constantly on the move because their parents' employment/deployment requires absolute mobility. You got children who are LGBT and have to deal with ever increasing hate against them (and LGBT youth already had significantly higher suicide rates than before the GQP made it a culture war issue). The US doesn't have any kind of system to help these children but schools and libraries, both are horribly underfunded (there's some school districts where teachers gotta take up second jobs because the government can only afford paying them for 4 days a week), and all too often teachers have to pay with their own money for students' school supplies. And on top of dealing with these kind of nightmares, they actually have to try and teach these children something - even if the children in question aren't anywhere near a headspace where they can actually learn.

deleted 2y ago

[deleted]

RobinL 2y ago

There is a game called dragonbox algebra which I'm currently working through with my son and is an absolutely fantastic approach to this problem. Sadly its now part of a horrendous subscription service and is hard to access. I find it really sad that we've had computers for decades and there are so few good maths games like this.

sethammons 2y ago
My kids all lived dragonbox games; the algebra and geometry one
- sethammons 2y ago
  edit: loved*
gnubison 2y ago
As a senior in high school, I devoured this game in elementary school and got way better at math than my peers. Now taking differential equations and multivariable calculus through our college in the high school (CHS) program. When I looked for it out of curiosity I was sad to see it transformed into a subscription service.

ozgrakkurt 2y ago

There are two sides to this. The system or method might be bad but also a determined person can go all the way and perform at a decent level if they put in enough time. Even if the system was better the person still has to be able to motivate themselves and put in the time.

jand 2y ago

As we are sharing anecdotes: One of my school math teacher had the same approach in another way: We were expected to use greek letters, not latin ones. Same reasoning: It showed us kiddos that the letter was insignificant compared to the concept expressed by the letter. So my take would be: Your friend taught the students for the first time what they were actually doing while handling equations with "a letter in it". That is no problem of algebra in itself. It just means their previous teachers sucked.

Viliam1234 2y ago
I saw a textbook that used a picture of a box in the equation. The number is hidden in the box, and you are supposed to figure out which number it is.

deleted 2y ago

[deleted]

danenania 2y ago

I got my daughter (just turned 6) this little hand held math game for her birthday: https://www.amazon.com/your-orders/pop?ref=ppx_yo2dv_mob_b_pop__np_2_pp&orderId=112-7222392-8361050&lineItemId=jimgtvprsqknxops&shipmentId=B4Nky4jJL&packageId=1&asin=B0BZWPDGK3 https://www.amazon.com/your-orders/pop?ref=ppx_yo2dv_mob_b_p... She loves it. It uses a ‘?’ for basic algebra style problems and after a few days of playing (if/when she wants to, we don’t make her play it), she was already much better and faster at those problems. It made me think that schools should be giving kids games like these.

dr_kiszonka 2y ago
Is this the game? You linked to your order history. https://www.amazon.com/Educational-Insights-Math-Electronic-Handheld/dp/B0BZWPDGK3 https://www.amazon.com/Educational-Insights-Math-Electronic-...
- danenania 2y ago
  Oops, yes that’s the one.