Many elementary teachers don’t understand math, and it makes them anxious • Hacker News Board

Re: Many elementary teachers don’t understand math, and it makes them anxious

#281

Post by r00fus » Sat, Nov 30, 2019, 5:00 PM UTC

BeetleB wrote: post #270

GordonS wrote: post #267

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 (logarithm…

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…

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.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#282

Post by monktastic1 » Sat, Nov 30, 2019, 5:00 PM UTC

esmi wrote: post #272

nopinsight wrote: post #253

Earlier quoted context omitted.

What do you mean by 'engineering form'? Using variables in the answer? It would be suitable for students between grades 4 and 6 (the highest level we currently teach), depending on how talented the kid is. To be clear to other readers, these are hard questions that most people, including older kids and adults, probably can't answer without proper learning and practice.

In the US we call this engineering form. https://en.m.wikipedia.org/wiki/Scientific_notation#E-notati... I misread the question though and now realize it’s not needed.

I'm also from the US but I've never heard the term "engineering form." FWIW, Wikipedia thinks it's something a little different: https://en.wikipedia.org/wiki/Engineering_notation.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#283

Post by m3kw9 » Sat, Nov 30, 2019, 5:01 PM UTC

Or they think there is actually more to elementary math than meets the eye

Re: Many elementary teachers don’t understand math, and it makes them anxious

#284

Post by asdffdsa » Sat, Nov 30, 2019, 5:06 PM UTC

monktastic1 wrote: post #273

cecilpl2 wrote: post #266

Earlier quoted context omitted.

72? 99999785960? 199?

FWIW, I got the same answers. 1. 12 edges * 6 non-corner pieces per edge. 2. There are 111 digits there. You can't keep six nines and have enough digits left. So you keep five (from 9, 19, 29, 39, 49), and now have six digits to keep from 5051525354555657585960. It can't start with 8 (or you still won't have enough digits left), so you choose 785960. 3. First notice that 0+...+10 = 55. To make it end in 2, you have t…

Could you explain why you can't just do 99999988888? 100 digits in any order, what am I missing?

Re: Many elementary teachers don’t understand math, and it makes them anxious

#285

Post by nopinsight » Sat, Nov 30, 2019, 5:08 PM UTC

Shivetya wrote: post #259

nopinsight wrote: post #227

Earlier quoted context omitted.

For those curious, below are some kinds of primary math questions we model after to test teacher applicants. In my experience, many kids are much more enthusiastic about this kind of "challenging" problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well. Note that although they do require a little arithmetic to solve, the ch…

and here I sit totally flummoxed by the questions yet later on you state these were suitable to grades up to sixth? So for those who have let their math skills lapse or need help to get back in the right frame of mind to learn, where online is the best resource? Khan Academy?

To be clear, these are hard contest questions that most people, including older kids and adults, probably can't answer them without proper learning and practice.

I have not checked them out in detail, but it appears that https://artofproblemsolving.com/ is a good resource. They also have interesting online and physical book series: https://artofproblemsolving.com/store (I have no affiliation.)

Re: Many elementary teachers don’t understand math, and it makes them anxious

#286

Post by flafla2 » Sat, Nov 30, 2019, 5:11 PM UTC

orbifold wrote: post #271

GordonS wrote: post #267

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 (logarithm…

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 engin…

Of course we all know this, so you’re preaching to the choir. However I think it would be quite demoralizing to tell a young student who is struggling with logarithms (to follow your example) that “it’s so elementary that there must be a practical use!” Indeed, middle and high school math is, to many, the most intellectually challenging thing they’ve ever had to deal with at the time these classes are taken. Considering they haven’t even taken higher order maths yet, students likely don’t have the context to realize that “elementary ≠ easy to understand”

I’ve taught at a number of “nerd camps”, generally in the fields of Gamedev and 3D modeling. I found that, more than anything else, showing young students what they can use a tool directly for triggers the imagination and inspires them to engage further with the field. These students were able to produce Google Cardboard VR content, which at the time was impressively close to the state of the art.

Anecdote: I’ve personally seen a 10-12 year old student tinker with and research the shadow settings in Unity3D [1], which is quite complicated! And she was willing and excited to put in the work because she could see with her eyes how the options affected the shadows directly. She wanted to match the shadows with a drawing she brought in.

Too bad Logarithms are not as engaging to look at as video games...

[1] https://docs.unity3d.com/Manual/ShadowOverview.html

Re: Many elementary teachers don’t understand math, and it makes them anxious

#287

Post by sologoub » Sat, Nov 30, 2019, 5:12 PM UTC

eropple wrote: post #279

Filligree wrote: post #274

Earlier quoted context omitted.

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?

Because you did not have a * button?

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.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#288

Post by 6gvONxR4sf7o » Sat, Nov 30, 2019, 5:15 PM UTC

spodek wrote: post #174

Or: why do so few people who understand math teach elementary school? Once someone learns math, what incentives do they have to choose teaching elementary school over alternatives? I could imagine that the skills to learn math don't overlap with the skills to teach elementary school and that time spent one detracts from the other. If mastery in each takes a decade or so and few people dedicate themselves to double ti…

The fewer people who are capable at something, the more lucrative it is to know that thing. The more lucrative it is to know something, the more of a pay cut it takes to teach it, assuming teacher pay at this level isn't subject dependent. The more of a pay cut it takes to teach, the fewer the skilled people willing to take a pay cut, and the fewer teachers there are with those skills. The fewer teachers there are with this skill, the worse the students turn out at it, leading to fewer people who are capable at it.

It's a vicious cycle. I'm a data scientist in SF and I'd make 5-10x less if I taught grade school.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#289

Post by stjohnswarts » Sat, Nov 30, 2019, 5:25 PM UTC

ikeyany wrote: post #75

pjscott wrote: post #16

Earlier quoted context omitted.

It's almost never explained with such lucidity. If you find a hundred people who can perform long division, I would be surprised if twenty of them have any idea how it works.

Multiplication tables are the most lucid way to explain long division. In order to get from 5 to 40, you need to keep adding 5s until you can't. So to divide 40 by 5, keep subtracting 5s until you can't any longer.

Exactly, I find it far easier to explain LD as just fast subtraction combined with multiplication to my kid than common core methods which I had to stare at for a while. The most critical method here is how to break up components of a number into addition "parts" as well as decimal positions.

Re: Many elementary teachers don’t understand math, and it makes them anxious

#290

Post by jointpdf » Sat, Nov 30, 2019, 5:26 PM UTC

barry-cotter wrote: post #182

v64 wrote: post #57

Earlier quoted context omitted.

This comment surprised me, as I have a BS in math and Laplace transforms were not something I was required to learn for the degree (although I had the option to take courses as electives that covered them). My university offers a math degree intended for those who want to go into teaching that doesn't get any hairier than Number Theory for required courses.

Your school had a special fake Math degree for aspirant teachers? What was it called, Math for Educators? Was there any indication on the transcript or diploma that it wasn’t a real Math degree?

Damn, what a toxic and misguided comment. I have a MS in Applied Mathematics and there are many areas of math (especially “pure” math) that I’ve never touched. Same goes for my professors. The field is so vast and so deep that it’s impossible to learn even a negligible portion of it (unless you’re immortal). Are our degrees fake?

It makes perfect sense that prospective educators would specialize in different areas of math than those with a pure math (or engineering, or physics, or statistics, etc) degree.