Math educations: creating new paths

[Kharakov]

https://www.insidehighered.com/news/2016/04/21/tpsemath-working-reform-math-education

How do you decide what can be trimmed from the curriculum? Certainly can't leave it up to kids...

 

[J842P]

Frankly, my gut says that these sorts of changes won't have much of an effect until high-school math education is improved. The problem isn't the curriculum, it's that students aren't prepared for it, IMO.

 

[ronburgundy]

Sound like their aim is mostly to create undergrad courses for non-math majors that advance math understanding, but within an applied context that is directly relevant to other fields that apply math.

Makes sense, but that should start right at the beginning of math education. A good deal of Algebra could be couched within the context of research statistics and probability that is useful for most empirical fields, not to mention critical thinking in general.

However, a counter-argument is that sound unbiased reasoning requires being able to evaluate logical relationships independent of the conceptual content of what the reasoning is about. Also, knowledge is only useful if it can be applied to other contexts to which it is logically relevant, and that application requires understanding the deep and more abstract principles at work. It is one thing to use an applied context to provide a motivation and a purpose for applying mathematical principles, but another to try and teach those principles only using highly contexualized "real world" presentations of the problems. There is research showing that making math problems more "meaningful", "real world", or "applied", such as with word problems is harmful to students ever learning the principles in way that they can apply to other contexts.

Teachers often use real-world examples in math class, the researchers said. In some classrooms, for example, teachers may explain probability by pulling a marble out of a bag of red and blue marbles and determining how likely it will be one color or the other.
But students may learn better if teachers explain the concept as the probability of choosing one of n things from a larger set of m things, Kaminski said.
The issue can also be seen in the story problems that math students are often given, she explained. For example, there is the classic problem of two trains that leave different cities heading toward each other at different speeds. Students are asked to figure out when the two trains will meet.
“The danger with teaching using this example is that many students only learn how to solve the problem with the trains,” Kaminski said.
“If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn’t seem to transfer,” she said.

 

[Jimmy Higgins]

Personally, calculus seems kind of foreign and Greek. Curves, equations, integration, it just seems like stuff that only applies on paper. But when you apply Calculus to structural engineering (amongst other disciplines), it becomes almost poetic.


Integrating from the load -> shear -> moment -> angular deflection -> physical deflection. The hard part about math and higher level stuff is few teachers are masters at making it obvious, that truly is an art, to take something complicated and boiling it down to something that is meaningful and relatable.

toward each other at different speeds. Students are asked to figure out when the two trains will meet.
“The danger with teaching using this example is that many students only learn how to solve the problem with the trains,” Kaminski said.
“If students are later given a problem using the same mathematical principles, but about rising water levels instead of trains, that knowledge just doesn’t seem to transfer,” she said.

What? Rising water levels is a volumetric problem (3 dimensional) while trains is a velocity problem (2 dimensional).

 

[ronburgundy]

Personally, calculus seems kind of foreign and Greek. Curves, equations, integration, it just seems like stuff that only applies on paper. But when you apply Calculus to structural engineering (amongst other disciplines), it becomes almost poetic.
View attachment 6560

Integrating from the load -> shear -> moment -> angular deflection -> physical deflection. The hard part about math and higher level stuff is few teachers are masters at making it obvious, that truly is an art, to take something complicated and boiling it down to something that is meaningful and relatable.
What? Rising water levels is a volumetric problem (3 dimensional) while trains is a velocity problem (2 dimensional).

That difference is irrelevant to the problems they are given. They don't need to solve for volume in the problems. They are given information about the rates (i.e., velocity) at which different water levels in different containers are rising or falling (i.e. velocity) and asked when the two will be at the same level. It is mathematically identical to the trains problem. Yet, when they do worse at the water level problem after learning the math via a trains problems than if they just learn the math abstractly without any specific relatable context or example.

 

[fromderinside]

So thing, flow rates, do this?