38
votes
Correcting how a student writes symbols
Personally, if I can make up an ordinary math problem where the student's alternate/new/strange symbols lead to an incorrect response, then I think that's grounds for correcting the student. (Of ...
- 1,556
25
votes
Accepted
Why are $m$ and $b$ used in the slope-intercept equation of a line?
This is also borderline not-an-answer, but it might be a nice broadening of your students' worldview to know that the "$m$" and the "$b$" are not universally accepted. Showing them this map (even ...
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22
votes
Accepted
When did US mathematics programs start failing to prepare incoming students for books like "Baby" Rudin?
Opinion.
There never was a generation of high school students in the US who could jump right into Rudin.
There would be (and still is) a small portion of the top high school graduates who could. ...
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19
votes
Accepted
Correcting how a student writes symbols
Not sure if this is the case but: is this student a Spanish speaker? What they write looks like ñ, so if that's the case it could just be that they are interpreting 𝜋 as a letter they know, specially ...
- 306
18
votes
Correcting how a student writes symbols
This isn't a moral conundrum, and your students shouldn't be snowflakes who freak out when they're corrected on something like this. They need your guidance in fixing their incorrect habits while they'...
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15
votes
Correcting how a student writes symbols
I think the real-world operational point is not that there is some sacred correctness to "orthodox" writing/font styles, but that writing in a very unorthodox style will cause one's readers ...
- 14k
13
votes
SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?
Your question is twofold:
(1) Did any school districts actual teach the curriculum as planned and (2) what were the results for the teachers and students?
At the moment, I have an answer for (1): ...
- 18.3k
11
votes
Accepted
What on earth was Old Math?
New math was introduced in the US in the 1960s. Before it was introduced, math was taught very algorithmically with little emphasis on understanding. Student were taught a method to do an arithmetic ...
- 7,929
11
votes
Why are $m$ and $b$ used in the slope-intercept equation of a line?
I taught low level algebra for a bit and those students really struggled with knowing what variables were and that they actually stood for numbers. They would see $y=mx+b$ and just not have any idea ...
- 2,062
10
votes
What female mathematician can I introduce to my High School students?
Thanks to Google Doodle, today I learned about Olga Ladyzhenskaya and her fantastic life.
From Wikipedia. Ladyzhenskaya was born and grew up in Kologriv. She was the daughter of a mathematics ...
- 4,368
10
votes
Accepted
Where can I find primary sources from the New Math movement in the 60s?
The following three books are, I believe, the most significant of the earlier treatments of new math, and I suspect you can find much in them that will direct you towards literature for your questions ...
- 5,698
10
votes
Correcting how a student writes symbols
These kind of syntactical glitches need to be corrected immediately, firmly, and clearly. As others have stated: it's immensely easier to fix these things earlier, rather than later when bad habits ...
- 23.6k
9
votes
Accepted
Why is polynomial factorization over the integers part of secondary school curricula?
"any references pointing in the right direction would be greatly appreciated"
Reference [1] below is probably where you want to look. A few years ago I tried to obtain a copy of [1], but I was not ...
- 5,698
8
votes
When (and why) did geometric means of more than two numbers exit the secondary curriculum?
Your last para was very reasonable. (I was going to give a mean sarcastic answer, but can't now.) We can crowdsource this:
Frank Ayres, First Year College Math (algebra 1 to precalc; Schaum's ...
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7
votes
What was the problem with New Math? Why did it end?
Please refer to Whatever became of the New Math?, a series written by Professor Raimi of the Department of Mathematics of the University of Rochester, and also Whatever Happened To New Math?. Together ...
- 71
7
votes
When did US mathematics programs start failing to prepare incoming students for books like "Baby" Rudin?
My recollection of the Math program at Harvey Mudd College (I was in CS, but lots of math major friends), is as follows:
The core Calc I included a taste of analysis-like material, in building up the ...
- 171
7
votes
Does anyone use the cubic formula these days?
It seems unlikely that the Cardano formula has even been of serious analytic use, i.e., used to approximate roots of a cubic. At least since the inception of calculus, Newton's method can be used to ...
- 9,473
6
votes
What did math educators think about the transition to widespread classroom use of calculators?
Googling "NACOME" 1975 calculators seemingly leads to the report that you mention:
Hill, S. (1975). Overview and analysis of school mathematics, grades K-12 (NACOME Report). In Washington, DC: ...
- 18.3k
6
votes
Why are $m$ and $b$ used in the slope-intercept equation of a line?
I would suggest not focusing on the notation "m" and "b" and just explain why they are different in terms of their relationships to x and y.
What's in a name? That which we call a rose by any ...
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6
votes
Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?
I gave an earlier answer [to a rather different question] in which I pointed to the Regents Exam Archives. One approach that you could take would be to look over a few tests from the 1990s as compared ...
- 18.3k
6
votes
Does anyone use the cubic formula these days?
Here's another computer-graphics example, which may or may not count as "nowadays". When I was in college 25 years ago I started a project to write a ray-trace renderer, which I then continued to ...
- 23.6k
6
votes
How much math would a non-STEM major have studied in 1950?
I'll quote a few short things from the (fantastic!) articles shared in comments by Dan Fox and user1527. Morris Kline in 1954 wrote:
What have we been feeding the liberal arts students? The almost
...
- 23.6k
5
votes
SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?
Just a short addition. Ed Begle published a valuable study through MAA/NCTM entitled "Critical Variables in Mthematics Education", which was an attempt (in part) to sort out some of the lessons of the ...
- 101
5
votes
Historical tidbits to liven up calculus classes
There is a fabulous story that is bound to captivate the students about Cauchy's alleged "error" in claiming that a convergent sequence of continuous functions necessarily converges to a continuous ...
- 2,039
5
votes
What was the problem with New Math? Why did it end?
There is an article by Phillips:
Phillips, C. "In accordance with a `more majestic order': the new math and the nature of mathematics at midcentury." Isis 105 (2014), no. 3, 540--563
that presents ...
- 2,039
5
votes
What female mathematician can I introduce to my High School students?
Karen Uhlenbeck ought to be mentioned. She made deep contributions in the theory of minimal immersions (more generally, harmonic maps), gauge theory of Yang Mills equations (the work of Taubes and ...
- 5,719
5
votes
Why is polynomial factorization over the integers part of secondary school curricula?
If we can do something with integers, we can do it with polynomials too
Things like adding, subtracting, multiplying, dividing, factoring. At least, that's how I framed these kinds of topics when I ...
- 581
5
votes
Accepted
Duodecimal by Stealth
A. Cons:
Distraction from normal topics (which many kids need to work on, are not meeting state standards). Just in that it is "extra material".
Potentially confusing for kids struggling to master ...
- 234
5
votes
Undergraduate Vector Calculus Notation Mess
I think you are being harsh in your criticism of the classical notation. Of course, at the mathematician's end of the spectrum, the notation you promote towards the end of your question has merit. But ...
- 9,473
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