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A friend of mine used Mathematica in a high school math classroom. I've also met some of his former students who think he was their best teacher. Something tha

A friend of mine used Mathematica in a high school math classroom. I've also met some of his former students who think he was their best teacher. Something that occurs to me is that most of us have a poor grasp of why we even teach school math: It's treated as some kind of tournament to get into college, or a general IQ building exercise, or even a form of obedience training. The math that is "real" to them is just what they happened to learn, the way they learned it. But most people admit that they forgot all of their math immediately upon finishing school. And school math isn't even how "math people" do math. I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel. I'm not too worried about Mathematica being proprietary. Like with programming, if you learn one language, you can usually learn another in a jiffy.

foobarian 5y ago
> Something that occurs to me is that most of us have a poor grasp of why we even teach school math I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.
- dhosek 5y ago
  Some of it comes down to insufficient grounding in math education preparation. In Illinois at least, K5 teachers are required to take a class that's effectively high school algebra, but at least where I got my credential, the class was taught as if it were just a remedial math class (which, to be honest, it was for more than a few of these would-be K5 teachers), rather than making it clear that the math that they would be teaching would be preparatory for the later class. Similar situations occur with 6-12 mathematics education preparation. This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why. In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.
pacbard 5y ago
I 100% agree with you that math is real and that there is real benefit from learning it. With that out of the way, > It's treated as some kind of tournament to get into college and > But most people admit that they forgot all of their math immediately upon finishing school. in those 2 quotes, you summarize the current issues with school mathematics. There is no real benefit in learning school math as most people will just use up to 6th/7th grade math in their daily work. Even professions that "do math" daily (like carpenters) have, most of the time, figured out ways to do it "quickly" without really doing math (see, for example, the diamonds on a measuring tape and how they are used to solve the Pythagorean theorem). That leaves school math as "the great sorter" of students. Students that "can" take advanced math classes and use those as leverage in college admissions. To see this process in motion, look up parents' concerns with California's new math sequence and how those usually involve college readiness (as in, college admission advantage) over career readiness (as in, calculus II is needed for whatever profession my kid will do after high school).
- GrinningFool 5y ago
  I thought those diamonds were placed at common stud/joist intervals for construction, and some searching doesn't find any connection to the Pythagorean theorem. What did you mean?
  - mywittyname 5y ago
    I'm not sure what the OP is getting at, because you're right, they indicate stud centers for 16" on-center. He might be talking about the 3-4-5 trick (pythagorean triples). But the only place I can think of where that is really useful (roofing) has other, better, tricks for figuring out lengths of hypotenuses.
- abdullahkhalids 5y ago
  My school had mandatory art class till 5th grade, and I imagine more schools had some mandatory art class. Yet, I have not really practiced any sort of coloring or painting since my last art class. I am not sure what this similarity with mathematics means for either mandatory art or math classes, but perhaps there is something to consider in our arguments.
contravariant 5y ago
> I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel. Doing mathematics on a computer is pretty darn tricky. It's not impossible but tools like Mathematica tend to lack the flexibility that pen and paper grant you. Of course computers are better at computation, but I don't think that counts as 'doing math'. That would be like saying a loudspeaker composes music.
- randomdata 5y ago
  > Doing mathematics on a computer is pretty darn tricky. Sounds like a case of: "The math that is "real" to them is just what they happened to learn, the way they learned it" Programming is doing mathematics, and computers do a great job of enabling one to program.
  - hansvm 5y ago
    Programming is <<shudder>> _applied_ mathematics.
    - Turing_Machine 5y ago
      Nah. Programming is its own thing. Math is lovely and all, but programming isn't applied mathematics any more than playing the cello is applied physics.
      - analog31 5y ago
        Sadly as a good physicist and terrible cellist I have to agree.
    - randomdata 5y ago
      The execution of the code is applied mathematics. The creation of the code is doing mathematics.
  - contravariant 5y ago
    As a counterpoint I'd like to claim that pen and paper is a massively underrated tool for programming, and furthermore that the parts that you can do on pen and paper are more mathematically interesting than the parts that can't be done without a computer.
Jap2-0 5y ago
> Something that occurs to me is that most of us have a poor grasp of why we even teach school math One of my favorite math courses was a college class that focused on concepts - technically not an education class but intended for those in education majors. It covered 5th-8th grade math and showed me the why of so many things I had just taken for granted previously, and I'm sure if math was taught that way it would be much better remembered. Of course, it could still be argued over whether math should be intended for practical use or not, but I think it's important that math be taught from (at least one of) a conceptual basis, or a historical basis (eg. [0] on the creation/discovery of imaginary numbers - it explains why they were needed, as well as interesting historical background). (This was typed in a hurry, sorry if it's not entirely cohesive.) [0] https://www.youtube.com/watch?v=cUzklzVXJwo https://www.youtube.com/watch?v=cUzklzVXJwo
someguydave 5y ago
It is impossible to “build IQ”, you have the IQ you were born with minus whatever brain damage you might have endured.
- jonsen 5y ago
  "New Evidence for a Way to Raise Your IQ": https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/new-evidence-way-raise-your-iq https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/...
  - someguydave 5y ago
    I doubt this will replicate
frankbreetz 5y ago
I wholeheartedly agree, I used to tutor calculus in college and getting students to focus on the fact that the derivative was the slope of the curve or the rate of change and the integral was the area under the curve and the significance of that made calculus so much easy. Drawing the unit circle to explain the cos, sin, and tan was also so enlightening to students. Most students just see a list of characters when the see math problem, but "math people" understand what is going on underneath and become excited to solve a problem and see multiple paths of potentially solving it. If you can unleash that excitement the problem solves itself. Once you understand the why, the how becomes so much easier.
- LeifCarrotson 5y ago
  > Once you understand the why, the how becomes so much easier. The interesting thing is how each student has a different path to understand the "how". It sounds like you have particularly vivid mental imagery, and gravitate towards visualizations for solving problems. This isn't true for everyone; it's not necessarily aphantasia but a unit circle or slope/area curve just isn't as useful for some as it is for you, others might prefer to think in terms of limits or series or patterns or a myriad of other techniques. You can repeat "The derivative is the slope of the curve" until you're blue in the face but some people just won't 'get it', finding the means by which they can get it is the fun part.
  - monkeywork 5y ago
    https://www.youtube.com/watch?v=rhgwIhB58PA https://www.youtube.com/watch?v=rhgwIhB58PA
    - jiriro 5y ago
      What’s the TL;DR?
      - AStrangeMorrow 5y ago
        I watched it a while ago, but the TLDR is more or less that the learning styles (ex: visual learners, or auditory, reading/writing, by doing etc...) are a myth. People do not learn better when we use their preferred learning style. But overall, people do learn better with multi-modal (mixed support / style).
tacomansteve 5y ago
> Like with programming, if you learn one language, you can usually learn another in a jiffy. I actually agree with you in general but, this isn't a guarantee. I've known plenty of people who "only" know how to "program" in Visual Studio. They don't understand how to use git outside of a helper GUI, they didn't understand the distinction between a compiler and a linker, or build options, or pathing issues--at least not down to the bare wires of what's actually going on. I'm not saying "everyone" is like that, but when you give exhaustive encapsulating tools, oftentimes people will only learn what they have to, to get running and never delve deeper. Of course, never delving deeper is the key issue but some frameworks/systems make delving deeper much easier than others, and better yet, encourage it. For an example, it was way easier for me to learn deep aspects of "what is really going on" when I started learning Linux--even immediately when I had to decide how to partition my hard drive correctly just to install it. I "could" just hit auto format but... what are all these buttons? Why is there different types of partitions? Is there a benefit? Not hiding me the inherent complexity allowed me information to better my understanding. Perhaps this applies more to programming than math, as, the core is to do math... right? The rest is just implementation details of "how do I tell this [math thing] to do [thing I want]". So as long as you know what you're asking "I need a line integral" that's a general enough term. You're learning the _techniques_ not only the framework itself.
calderwoodra 5y ago
Also not worried about proprietary since I got started learning programming through a pirated version of Mathematica and solving ProjectEuler problems.

foobarian 5y ago

> Something that occurs to me is that most of us have a poor grasp of why we even teach school math I had this experience myself. Math during grade school was delivered kind of like a set of unquestionable facts. Much of which was valuable but I wish it didn't take me until college and some random tangential exercise to realize i didnt really understand how real numbers work.

dhosek 5y ago
Some of it comes down to insufficient grounding in math education preparation. In Illinois at least, K5 teachers are required to take a class that's effectively high school algebra, but at least where I got my credential, the class was taught as if it were just a remedial math class (which, to be honest, it was for more than a few of these would-be K5 teachers), rather than making it clear that the math that they would be teaching would be preparatory for the later class. Similar situations occur with 6-12 mathematics education preparation. This continues well into 200-level and even 300-level college mathematics. Gallian's Contemporary Abstract Algebra spends a lot of time exploring groups of the form a + b√n without explaining why. In general, it seems like math education should step back and read John Dewey and stop teaching mathematics as inert knowledge.

pacbard 5y ago

I 100% agree with you that math is real and that there is real benefit from learning it. With that out of the way, > It's treated as some kind of tournament to get into college and > But most people admit that they forgot all of their math immediately upon finishing school. in those 2 quotes, you summarize the current issues with school mathematics. There is no real benefit in learning school math as most people will just use up to 6th/7th grade math in their daily work. Even professions that "do math" daily (like carpenters) have, most of the time, figured out ways to do it "quickly" without really doing math (see, for example, the diamonds on a measuring tape and how they are used to solve the Pythagorean theorem). That leaves school math as "the great sorter" of students. Students that "can" take advanced math classes and use those as leverage in college admissions. To see this process in motion, look up parents' concerns with California's new math sequence and how those usually involve college readiness (as in, college admission advantage) over career readiness (as in, calculus II is needed for whatever profession my kid will do after high school).

GrinningFool 5y ago
I thought those diamonds were placed at common stud/joist intervals for construction, and some searching doesn't find any connection to the Pythagorean theorem. What did you mean?
- mywittyname 5y ago
  I'm not sure what the OP is getting at, because you're right, they indicate stud centers for 16" on-center. He might be talking about the 3-4-5 trick (pythagorean triples). But the only place I can think of where that is really useful (roofing) has other, better, tricks for figuring out lengths of hypotenuses.
abdullahkhalids 5y ago
My school had mandatory art class till 5th grade, and I imagine more schools had some mandatory art class. Yet, I have not really practiced any sort of coloring or painting since my last art class. I am not sure what this similarity with mathematics means for either mandatory art or math classes, but perhaps there is something to consider in our arguments.

contravariant 5y ago

> I still enjoy doing a pencil and paper derivation for fun sometimes, but mostly I do math at a computer. The world does math in Excel. Doing mathematics on a computer is pretty darn tricky. It's not impossible but tools like Mathematica tend to lack the flexibility that pen and paper grant you. Of course computers are better at computation, but I don't think that counts as 'doing math'. That would be like saying a loudspeaker composes music.

randomdata 5y ago
> Doing mathematics on a computer is pretty darn tricky. Sounds like a case of: "The math that is "real" to them is just what they happened to learn, the way they learned it" Programming is doing mathematics, and computers do a great job of enabling one to program.
- hansvm 5y ago
  Programming is <<shudder>> _applied_ mathematics.
  - Turing_Machine 5y ago
    Nah. Programming is its own thing. Math is lovely and all, but programming isn't applied mathematics any more than playing the cello is applied physics.
    - analog31 5y ago
      Sadly as a good physicist and terrible cellist I have to agree.
  - randomdata 5y ago
    The execution of the code is applied mathematics. The creation of the code is doing mathematics.
- contravariant 5y ago
  As a counterpoint I'd like to claim that pen and paper is a massively underrated tool for programming, and furthermore that the parts that you can do on pen and paper are more mathematically interesting than the parts that can't be done without a computer.

Jap2-0 5y ago

> Something that occurs to me is that most of us have a poor grasp of why we even teach school math One of my favorite math courses was a college class that focused on concepts - technically not an education class but intended for those in education majors. It covered 5th-8th grade math and showed me the why of so many things I had just taken for granted previously, and I'm sure if math was taught that way it would be much better remembered. Of course, it could still be argued over whether math should be intended for practical use or not, but I think it's important that math be taught from (at least one of) a conceptual basis, or a historical basis (eg. [0] on the creation/discovery of imaginary numbers - it explains why they were needed, as well as interesting historical background). (This was typed in a hurry, sorry if it's not entirely cohesive.) [0] https://www.youtube.com/watch?v=cUzklzVXJwo https://www.youtube.com/watch?v=cUzklzVXJwo

someguydave 5y ago

It is impossible to “build IQ”, you have the IQ you were born with minus whatever brain damage you might have endured.

jonsen 5y ago
"New Evidence for a Way to Raise Your IQ": https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/new-evidence-way-raise-your-iq https://www.psychologytoday.com/us/blog/iq-boot-camp/201606/...
- someguydave 5y ago
  I doubt this will replicate

frankbreetz 5y ago

I wholeheartedly agree, I used to tutor calculus in college and getting students to focus on the fact that the derivative was the slope of the curve or the rate of change and the integral was the area under the curve and the significance of that made calculus so much easy. Drawing the unit circle to explain the cos, sin, and tan was also so enlightening to students. Most students just see a list of characters when the see math problem, but "math people" understand what is going on underneath and become excited to solve a problem and see multiple paths of potentially solving it. If you can unleash that excitement the problem solves itself. Once you understand the why, the how becomes so much easier.

LeifCarrotson 5y ago
> Once you understand the why, the how becomes so much easier. The interesting thing is how each student has a different path to understand the "how". It sounds like you have particularly vivid mental imagery, and gravitate towards visualizations for solving problems. This isn't true for everyone; it's not necessarily aphantasia but a unit circle or slope/area curve just isn't as useful for some as it is for you, others might prefer to think in terms of limits or series or patterns or a myriad of other techniques. You can repeat "The derivative is the slope of the curve" until you're blue in the face but some people just won't 'get it', finding the means by which they can get it is the fun part.
- monkeywork 5y ago
  https://www.youtube.com/watch?v=rhgwIhB58PA https://www.youtube.com/watch?v=rhgwIhB58PA
  - jiriro 5y ago
    What’s the TL;DR?
    - AStrangeMorrow 5y ago
      I watched it a while ago, but the TLDR is more or less that the learning styles (ex: visual learners, or auditory, reading/writing, by doing etc...) are a myth. People do not learn better when we use their preferred learning style. But overall, people do learn better with multi-modal (mixed support / style).

tacomansteve 5y ago

> Like with programming, if you learn one language, you can usually learn another in a jiffy. I actually agree with you in general but, this isn't a guarantee. I've known plenty of people who "only" know how to "program" in Visual Studio. They don't understand how to use git outside of a helper GUI, they didn't understand the distinction between a compiler and a linker, or build options, or pathing issues--at least not down to the bare wires of what's actually going on. I'm not saying "everyone" is like that, but when you give exhaustive encapsulating tools, oftentimes people will only learn what they have to, to get running and never delve deeper. Of course, never delving deeper is the key issue but some frameworks/systems make delving deeper much easier than others, and better yet, encourage it. For an example, it was way easier for me to learn deep aspects of "what is really going on" when I started learning Linux--even immediately when I had to decide how to partition my hard drive correctly just to install it. I "could" just hit auto format but... what are all these buttons? Why is there different types of partitions? Is there a benefit? Not hiding me the inherent complexity allowed me information to better my understanding. Perhaps this applies more to programming than math, as, the core is to do math... right? The rest is just implementation details of "how do I tell this [math thing] to do [thing I want]". So as long as you know what you're asking "I need a line integral" that's a general enough term. You're learning the _techniques_ not only the framework itself.

calderwoodra 5y ago

Also not worried about proprietary since I got started learning programming through a pirated version of Mathematica and solving ProjectEuler problems.