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

#221

Post by barry-cotter » Sat, Nov 30, 2019, 3:01 PM UTC

keenmaster wrote: post #219

barry-cotter wrote: post #196

Earlier quoted context omitted.

This would be true if we had any idea what makes a good teacher, or could reliably determine who good teachers are. Neither of those are true. TEACHER QUALITY https://faculty.smu.edu/millimet/classes/eco7321/papers/hanu... > Perhaps most remarkable is the finding that a master’s degree has no systematic relationship to teacher quality as measured by student outcomes. This immediately raises a number of issues for pol…

Shouldn’t that study focus on the distribution of types of master’s degrees, and a sub-population analysis showing which ones correlated most with teaching ability? I bet someone with a master’s in math would be better at teaching math than someone with a master’s in teaching theory. Ditto at the undergrad level.

I used to think subject matter expertise helped too. If you find any evidence it does email me, I haven’t found any research to that effect.

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

#222

Post by all2 » Sat, Nov 30, 2019, 3:06 PM UTC

hervature wrote: post #215

billfruit wrote: post #178

Earlier quoted context omitted.

Well if long division is unintuitive, the procedure to compute square-roots by hand is even more mysterious, as if it has transcended dealing with numbers and instead become a symbolic manipulation. Thankfully it is something I never had to apply, even once in adult life till now.

How do you compute square roots by hand? Isn't it just a rudimentary root finding algorithm?

The only by-hand method for finding roots I know is "Newton's Method". I think I learned this in pure calculus?

https://en.m.wikipedia.org/wiki/Newton's_method

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

#223

Post by leetcrew » Sat, Nov 30, 2019, 3:07 PM UTC

nopinsight wrote: post #115

For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels. We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regar…

I always found it amusing that most of my math and cs professors in college seemed to have terrible arithmetic skills. I'm sure part of it is just that it's hard to concentrate on the work when you're also narrating the process to the class, but I suspect it's also that basic arithmetic is a relatively unimportant skill in most advanced research. hiring this sort of person to teach/tutor grade school math might be like hiring a porsche engineer to repair your car. they'll get the job done, but maybe not as efficiently as your local mechanic.

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

#224

Post by barry-cotter » Sat, Nov 30, 2019, 3:10 PM UTC

username90 wrote: post #216

barry-cotter wrote: post #206

Earlier quoted context omitted.

Your ex was correct. https://spaceplace.nasa.gov/seasons/en/ What Causes the Seasons? The Short Answer: Earth’s tilted axis causes the seasons. Throughout the year, different parts of Earth receive the Sun’s most direct rays. So, when the North Pole tilts toward the Sun, it’s summer in the Northern Hemisphere. And when the South Pole tilts toward the Sun, it’s winter in the Northern Hemisphere. It's all about Earth's…

Yes the seasons are due to earths tilt, but the tilt still doesn't change between seasons as his wife thought, only earths position compared to the sun does.

The tilt of the earth relative to the sun does in fact change. That’s what the seasons are. If the earth was tilted but the tilt didn’t change over the course of the year the areas that had longer days due to being tilted towards the sun would be permanently hotter than the areas tilted away. There would be a permanent summer and winter, rather as at the equator it’s always summer.

The changing tilt of the earth relative to the sun is what the seasons are.

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

#225

Post by ausjke » Sat, Nov 30, 2019, 3:10 PM UTC

Absolutely correct, but it's worse, since they don't truly understand math, they taught in such a way that confused/misled students, no wonder USA had to import so many STEM engineers(and graduate students to fill college classrooms) from other countries, and it's getting worse.

The fix is to have specific teacher undergraduate or graduate degree, or education departments or state-funded full-blown normal universities, pay them well, make teacher profession a honorable career, only then the best will seek a position in k-12 schools and our next generation can keep getting better.

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

#226

Post by all2 » Sat, Nov 30, 2019, 3:11 PM UTC

pbhjpbhj wrote: post #194

_bxg1 wrote: post #47

Earlier quoted context omitted.

Yep. I remember in college when I made that connection and realized you could create infinite "levels" of operation, with each repeating the previous one N times.

Up-arrow notation ftw.

I'm missing the context here. The only arrows I'm familiar with are vector notation and ion spin notation.

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

#227

Post by nopinsight » Sat, Nov 30, 2019, 3:14 PM UTC

nopinsight wrote: post #115

For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels. We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regar…

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 challenging part is not arithmetic.

Some problems focus on geometry, logic, patterns, or other kinds of puzzles. More examples can be found at the source below.

"- The edge of a cube is 8 cm. All the faces are painted orange. It is then cut into small cubes of edge 1 cm. How many small cubes have exactly two faces painted?

- What is the greatest possible number one can get by discarding 100 digits, in any order, from the number 1234567891011121314151617…57585960?

- Eleven consecutive positive integers are written on a board. Maria erases one of the numbers. If the sum of the remaining numbers is 2012, what number did Maria erase?

- You must color each square in the figure below in red, green or blue. Any two squares with adjacent sides must be of a different color. In how many different ways can this coloring be done? Figure at question 11 here: https://gato-docs.its.txstate.edu/jcr:450cce10-3b6a-4ddd-a19... "

Source: the Primary Math World Contest (usually held in Hong Kong) https://www.txstate.edu/mathworks/PMWC/previous-pmwc-tests.h...

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

#228

Post by leetcrew » Sat, Nov 30, 2019, 3:14 PM UTC

darkerside wrote: post #139

mavhc wrote: post #81

Earlier quoted context omitted.

What none of them can tell you is why they've been taught long division, when short division is faster. And it's because you need long division to do division in algebra

I've looked at both Wikipedia pages and still can't really understand the difference. Is it anything more than notational? Either way, you're calculating divisors for each component of the problem, and it only seems to matter whether you calculate it on paper or in your head.

the way I learned it, it's just a notational difference. either way, you are dividing the divisor into each place of the dividend (starting with the most significant digit) and carrying over the divisor to the next place. short division is just a more implicit way of doing this that saves space. the shorthand version doesn't really work for divisors with more than one digit though.

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

#229

Post by scruple » Sat, Nov 30, 2019, 3:16 PM UTC

leetcrew wrote: post #223

nopinsight wrote: post #115

For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels. We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regar…

I always found it amusing that most of my math and cs professors in college seemed to have terrible arithmetic skills. I'm sure part of it is just that it's hard to concentrate on the work when you're also narrating the process to the class, but I suspect it's also that basic arithmetic is a relatively unimportant skill in most advanced research. hiring this sort of person to teach/tutor grade school math might be li…

"My degree is in Mathematics, not arithmetic." was a common one that I'd hear from friends with Math degrees or in the Math department.

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

#230

Post by shantly » Sat, Nov 30, 2019, 3:19 PM UTC

nopinsight wrote: post #115

For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels. We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regar…

> The test includes competitive exam questions focused on mathematical understanding and problem solving skills, rather than advanced math knowledge.

Seems like it might be close to a subset of the sorts of questions one encounters on an IQ test.