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

latimes.com

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

#271

Post by orbifold »

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 engineers did calculations before computers were common.

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

#272

Post by esmi »

nopinsight wrote: post #253
esmi wrote: post #251

Earlier quoted context omitted.

Is the answer to the second question allowed to be in engineering form? :) What grade level is question 3 considered?

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.

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

#273

Post by monktastic1 »

cecilpl2 wrote: post #266
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…

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 to discard the 3. In general if you have n+...+(n+10) you discard n+3. Now n+...+(n+10) = 5.5*(n+(n+10)) by Gauss' trick, and subtracting (n+3) you have 10n + 52 = 2012.

Very much doubt I could have solved them in elementary school(!) though.

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

#274

Post by Filligree »

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…

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?

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

#276

Post by BeetleB »

chrisseaton wrote: post #119
cjfd wrote: post #104

Earlier quoted context omitted.

Okay, we have deviations from the mean. They are (0.1, 0.1, -0.1, -0.1). Or we have deviations from the mean (0.2, 0, 0, -0.2). I think is is pretty intuitive that in the second case the deviation is larger. In the first case there are only two differing values that are 0.2 apart. In the second case there are three differing values and some are 0.2 apart and others are 0.4 apart. Also, in the first case there are two…

I still don’t understand why we pick a metric because it’s easy to work with. Isn’t it either the right metric or not?

> Isn’t it either the right metric or not?

There are many "right" metrics - this is one of them. The big picture is we want a measure/idea of how spread out the data is. One can come up with many ways to do this, and absolute value and root mean square are two of the most common. They correspond to L0 and L2 norms. There is also the L-infinity norm (just use the farthest point).

The L2 norm is the most complicated of the 3, but as people pointed out, it is one of the easiest to use analytically because of its nice mathematical properties.

Have a look at https://en.wikipedia.org/wiki/Statistical_dispersion for other measures.

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

#277

Post by gdsimoes »

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…

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.

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

#278

Post by rocqua »

zamfi wrote: post #269
rocqua wrote: post #187

Earlier quoted context omitted.

Its weird that education is payed for completely by property taxes in the US. The benefits of education go to more than just the (parents of) the recipients of that education. You also get weird incentives for people to reduce these taxes if they send their children to private schools.

> The benefits of education go to more than just the (parents of) the recipients of that education. I think this is exactly the intent — get the whole county / district to pay, not just the parents, right? And these payments are usually compulsory regardless of whether you have children or send them to private school...

It should be spread to the state / country level rather than being based on districts is my point.

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

#279

Post by eropple »

Filligree wrote: post #274
orbifold wrote: post #271

Earlier quoted context omitted.

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…

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?

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

#280

Post by shotashotshota »

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…

They are practical only to the one using them. I don't care about fluid dynamics when I stir my coffee with my well-designed spoon.

Perhaps the problem is that there is no difference between 2x + 1 = 0 and 3x + 3 = 0, they are the same kind of question but in my school days we have to do all these similar tasks for ... whatever reasons.

Then again, practice is a really good way to solidify one's understanding of a concept so its a hard thing to balance.

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