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I struggled with maths as a kid, but gained a much better grasp as an adult, when I had to use it for practical applications. I really think the abstract natur

I struggled with maths as a kid, but gained a much better grasp as an adult, when I had to use it for practical applications. I really think the abstract nature of the way maths is taught (at least in the UK) is a big problem that holds people back - kids don't understand the point of the more complex stuff. I recall asking my secondary school maths teacher what the point of learning about some concept was (logarithmic equations, I think), what practical applications it had - he couldn't answer that. If I'd understood how such concepts could be used in the real world for interesting things, I'm certain I and others in the class would have been better able to "get it", and would certainly been more enthused.

BeetleB 7y ago
It's a double edged sword. I loved math because I liked physics, and calculus text books had plenty of physics examples. Then I tutored people doing "business math" - calculus but using finance for all its applications. Most people struggled not because of the math but because of the difficulty in understanding the finance part. And it was hard for me to give help because I had to learn the financial aspects to help them with their HW. If the application doesn't click with you, then you now have two problems.
- r00fus 7y ago
  Exactly - the applicability has to mean something for the person. It could require several regressions before you get to a core interest of any specific student.
orbifold 7y ago
I never understood people that questioned the practical applicability of math. Surely they must realize that these things are so elementary that there is no way there was no practical use for them. Logarithms specifically allow you to multiply values quickly by looking up their logarithm in a table, add the values and do a reverse lookup in the same table. This is the foundation of slide rules, which is the way engineers did calculations before computers were common.
- deleted 7y ago
  [deleted]
- Filligree 7y ago
  I have never once in my life used logarithms in that fashion. I've used them in other ways, but why would you do it that way instead of just hitting the "*" button?
  - eropple 7y ago
    Because you did not have a * button?
    - sologoub 7y ago
      I this sums up my first math experience in the US high school. Learning before moving to the US, we were not allowed any calculators. My first class the teach wrote something basic like quadratic equation to solve. To my shock, out went the TI-83 graphing calculators. I was done with the problem before my peers even hit the right keys in their pocket computers (TI-83 is not a calculator, but a computer pretending to be a calculator). I still think the non-calculator way of teaching math gave me better skills down the road.
    - Filligree 7y ago
      You don't have a calculator, so you're calculating logarithms by hand?
      - eropple 7y ago
        You understand that slide rules existed before calculators, yeah?
- gdsimoes 7y ago
  I only learned about this application of logarithms years after learning the definition. Usually the applications are not obvious to students and this goes on even at the university level.
dan-robertson 7y ago
I sympathise with you. It certainly seems that those people who do best at mathematics in school are just those who are best at abstract manipulation of symbols. The example you give is an interesting one. Logarithms are quite hard to motivate[+]. Once they could be introduced as analogous to a slide rule as something to speed up multiplication (indeed that was their actual original motivation). But that isn’t convincing these days. Perhaps a motivation could be found in science (something about gradients and log-log plots). The problem is that the real reason you learn about logs is because they are related to exponential and exponential are important. Consider the differential equation: dy/dx = k y This kind of equation comes up a lot in modelling things in science and other parts of the real world (eg compound interest). We can solve it: k dx/dy = 1/y k x = log(y) + C log(y) = k x - C y = exp(k x - C) y = A exp(k x) (where A = exp(-C) is chosen to fit initial conditions) But this motivation isn’t much use when one doesn’t have differential equations or calculus. When I was in school I think differential equations where only in A-level further maths (age 16-18). I’m not sure whether we had logarithms at GCSE (14-16) but I think they were in A level maths which included calculus up to integration by parts and integrals/derivatives of various trig functions. [+] By motivate I mean “put into context of some practical application”. In the “real world” such mathematical things aren’t necessarily well motivated either. It may be that one has to calculate certain weird things because that is what clients/customers/taxes/regulations/circumstances dictate. In applied mathematics things aren’t so well motivated. Either “we see these equations in physics sometimes” or for fluids you mumble something about boats or planes. In pure mathematics the motivation basically always boils down to “we need this crazy thing to solve a certain problem to tell if two objects are the same/different/somehow interesting because we are interested in this sort of object and in particular how to classify the different kinds of it.

BeetleB 7y ago

It's a double edged sword. I loved math because I liked physics, and calculus text books had plenty of physics examples. Then I tutored people doing "business math" - calculus but using finance for all its applications. Most people struggled not because of the math but because of the difficulty in understanding the finance part. And it was hard for me to give help because I had to learn the financial aspects to help them with their HW. If the application doesn't click with you, then you now have two problems.

r00fus 7y ago
Exactly - the applicability has to mean something for the person. It could require several regressions before you get to a core interest of any specific student.

orbifold 7y ago

I never understood people that questioned the practical applicability of math. Surely they must realize that these things are so elementary that there is no way there was no practical use for them. Logarithms specifically allow you to multiply values quickly by looking up their logarithm in a table, add the values and do a reverse lookup in the same table. This is the foundation of slide rules, which is the way engineers did calculations before computers were common.

deleted 7y ago
[deleted]
Filligree 7y ago
I have never once in my life used logarithms in that fashion. I've used them in other ways, but why would you do it that way instead of just hitting the "*" button?
- eropple 7y ago
  Because you did not have a * button?
  - sologoub 7y ago
    I this sums up my first math experience in the US high school. Learning before moving to the US, we were not allowed any calculators. My first class the teach wrote something basic like quadratic equation to solve. To my shock, out went the TI-83 graphing calculators. I was done with the problem before my peers even hit the right keys in their pocket computers (TI-83 is not a calculator, but a computer pretending to be a calculator). I still think the non-calculator way of teaching math gave me better skills down the road.
  - Filligree 7y ago
    You don't have a calculator, so you're calculating logarithms by hand?
    - eropple 7y ago
      You understand that slide rules existed before calculators, yeah?
gdsimoes 7y ago
I only learned about this application of logarithms years after learning the definition. Usually the applications are not obvious to students and this goes on even at the university level.

dan-robertson 7y ago

I sympathise with you. It certainly seems that those people who do best at mathematics in school are just those who are best at abstract manipulation of symbols. The example you give is an interesting one. Logarithms are quite hard to motivate[+]. Once they could be introduced as analogous to a slide rule as something to speed up multiplication (indeed that was their actual original motivation). But that isn’t convincing these days. Perhaps a motivation could be found in science (something about gradients and log-log plots). The problem is that the real reason you learn about logs is because they are related to exponential and exponential are important. Consider the differential equation: dy/dx = k y This kind of equation comes up a lot in modelling things in science and other parts of the real world (eg compound interest). We can solve it: k dx/dy = 1/y k x = log(y) + C log(y) = k x - C y = exp(k x - C) y = A exp(k x) (where A = exp(-C) is chosen to fit initial conditions) But this motivation isn’t much use when one doesn’t have differential equations or calculus. When I was in school I think differential equations where only in A-level further maths (age 16-18). I’m not sure whether we had logarithms at GCSE (14-16) but I think they were in A level maths which included calculus up to integration by parts and integrals/derivatives of various trig functions. [+] By motivate I mean “put into context of some practical application”. In the “real world” such mathematical things aren’t necessarily well motivated either. It may be that one has to calculate certain weird things because that is what clients/customers/taxes/regulations/circumstances dictate. In applied mathematics things aren’t so well motivated. Either “we see these equations in physics sometimes” or for fluids you mumble something about boats or planes. In pure mathematics the motivation basically always boils down to “we need this crazy thing to solve a certain problem to tell if two objects are the same/different/somehow interesting because we are interested in this sort of object and in particular how to classify the different kinds of it.