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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 ...
Justin Skycak's user avatar
26 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 ...
Chris Cunningham's user avatar
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 ...
Tyrannogina's user avatar
17 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'...
kjfdhg's user avatar
  • 187
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 ...
paul garrett's user avatar
  • 14.7k
12 votes

Earliest real-world uses of Calculus and Linear Algebra

I want to find what the earliest real-world applications of Calculus were. By real-world application, I mean a device, instrument or technology which made lives better. Let's assume that: Earliest = ...
Pedro's user avatar
  • 1,800
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 ...
ruferd's user avatar
  • 2,101
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 ...
Amy B's user avatar
  • 8,017
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 ...
Amir Asghari's user avatar
  • 4,438
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 ...
Dave L Renfro's user avatar
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 ...
Dave L Renfro's user avatar
9 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 ...
Daniel R. Collins's user avatar
8 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 ...
Ming Lei's user avatar
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 ...
guest's user avatar
  • 159
8 votes

Earliest real-world uses of Calculus and Linear Algebra

The Mercator projection (1569). This map projection revolutionized naval navigation. The vertical coordinate $y$ depends on the latitude $\varphi$. In modern language, it is the integral of the ...
Gerald Edgar's user avatar
  • 7,607
8 votes

Earliest real-world uses of Calculus and Linear Algebra

By real-world application, I mean a device, instrument or technology which made lives better and would have been simply impossible without Calculus or Linear Algebra. In the case of calculus, I don't ...
kjdfhlkdfjh's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

Maxwell's equations (1861) are a set of coupled partial differential equations. They led to Heinrich Hertz demonstrating radio waves in 1887. Marconi sent messages to British battleships in 1899. I ...
Peter Balch's user avatar
8 votes

Earliest real-world uses of Calculus and Linear Algebra

In the late 18th century, ships leaving Europe for other continents routinely brought with them books such as trigonometrical tables and astronomical almanacs. Those almanacs included ephemerides, a.k....
jpmarinier's user avatar
7 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 ...
Michael's user avatar
  • 195
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 ...
user52817's user avatar
  • 11k
6 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 ...
Mikhail Katz's user avatar
  • 2,238
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: ...
Benjamin Dickman's user avatar
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 ...
Benjamin Dickman's user avatar
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 ...
Daniel R. Collins's user avatar
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 ...
Daniel R. Collins's user avatar
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 ...
Richard Larson's user avatar
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 ...
Dan Fox's user avatar
  • 5,869
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 ...
pjs36's user avatar
  • 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 ...
guest's user avatar
  • 234

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