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Questions tagged [history]

For questions concerning the history of mathematical education and the use of historical topics in teaching mathematics.

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7 votes
11 answers

Earliest real-world uses of Calculus and Linear Algebra

I want to illustrate in class that real-world applications of mathematics might take time to come to fruit. In this context, I want to find what the earliest real-world applications of Calculus and ...
Jaikrishnan's user avatar
24 votes
5 answers

Correcting how a student writes symbols

One of my college students writes the Greek letter $\pi$ as a script n with a bar over it, like $\bar{n}$. [There is actual space between the letter and the bar.] I have never seen this before, and ...
Nick C's user avatar
  • 9,639
5 votes
1 answer

How does the average level of expected mathematical sophistication at high school level increase?

I remember reading an old calculus book (years 1920-1930) and in the preface it was portrayed as revolutionary because it was for high school students. Nowadays, that is not revolutionary, because ...
Babu's user avatar
  • 595
2 votes
2 answers

Arithmetical Progression

I recently came across a very old Algebra textbook from the 1860s, and on the chapter discussing "arithmetical progression", it says there are "20 cases for arithmetical progression&...
Wasp's user avatar
  • 187
2 votes
1 answer

When and where were textbooks that use set notation for basic algebra solutions?

A past question described a school where many teachers insisted that answers to algebra problems had to be phrased in set-theoretic language or notation. For example, when asked to solve $2x+3=6−x$, ...
Malady's user avatar
  • 133
4 votes
1 answer

Successor to School Mathematics Study Group (SMSG)

From reviews on Amazon of the various high school math texts by Mary Dolciani et al of the SMSG, I assume that there might be a successor to the approach (referred to as “the new math”) taken by the ...
nowradioguy's user avatar
7 votes
1 answer

Solving open problems through a misunderstanding

We all know the (apparently verified1) anecdote recounting George Dantzig arriving late to a lecture (by Jerzy Neyman), and later solving two open problems written on the board, mistaking them for ...
Joseph O'Rourke's user avatar
5 votes
2 answers

Undergraduate Vector Calculus Notation Mess

Question 1: What are your arguments in favor of the big array of different notations used in the context of undergraduate vector calculus: line integrals, surface integrals (of scalars and fields), ...
Behnam Esmayli's user avatar
4 votes
2 answers

How much math would a non-STEM major have studied in 1950?

I've spoken to several people who attended US universities in the decades before I was born, and I was somewhat surprised to find that it seemed to be common (based on the anecdotes I received) for ...
Robert Columbia's user avatar
9 votes
5 answers

Does anyone use the cubic formula these days?

I am writing a story for young people about the history of the development of the cubic formula and complex numbers, partly because it has so much drama and partly because it's amusing that complex ...
Sue VanHattum's user avatar
  • 21k
17 votes
5 answers

Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?

Have there been any major content (not pedagogical) changes in the basic US high school mathematics curriculum since the mid-1990's? More specifically, if I wanted to become a tutor of high school ...
Robert Columbia's user avatar
8 votes
1 answer

When (and why) did geometric means of more than two numbers exit the secondary curriculum?

In contemporary US secondary mathematics textbooks, geometric means occasionally make a brief appearance. For example: In Geometry, students learn that when an altitude is dropped to the hypotenuse ...
mweiss's user avatar
  • 17.4k
-1 votes
1 answer

Duodecimal by Stealth

It is widely recognised that the Duodecimal number system is superior to the decimal system. However, it is plainly obvious that trying to introduce such a system would be difficult, especially in a ...
pdmclean's user avatar
  • 967
10 votes
3 answers

The royal road to calculus

In the early 1900s Felix Klein lay out his vision for secondary mathematics curriculum. He wanted schools to teach calculus, so that universities would not be burdened by it. And at the core of the ...
Manya's user avatar
  • 201
6 votes
0 answers

Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
katana_0's user avatar
  • 349
15 votes
4 answers

Why is polynomial factorization over the integers part of secondary school curricula?

By "polynomial factorization over the integers", I mean problems and solutions like the following: Problem: Find a factorization into irreducible polynomials for $24x^2 +x - 10$ and ...
K B Dave's user avatar
  • 323
12 votes
1 answer

Where can I find primary sources from the New Math movement in the 60s?

I'm interested in learning about the New Math movement from a historical perspective. I've located some secondary sources about the topic, mainly parodies, highly critical restrospective articles, or ...
Alexander Gruber's user avatar
20 votes
3 answers

Why are $m$ and $b$ used in the slope-intercept equation of a line?

The slope-intercept form of the equation of a line is often presented in textbooks (in the US) as $$y = mx + b\,,$$ where $m$ is the slope of the line and $b$ is the $y$-intercept. How did $m$ and $...
Mike Pierce's user avatar
  • 4,845
8 votes
3 answers

What did math educators think about the transition to widespread classroom use of calculators?

When we have discussions about which technology to include in our classrooms today, we are often somewhat conflicted with many standard arguments and worries being presented on both sides. To help ...
Chris Cunningham's user avatar
5 votes
0 answers

SMSG Calculus Usage?

Did anyone out there have experience with SMSG's Calculus text? Our school system (Amherst, MA) used SMSG texts from my 6th grade class onward. But for HS Calculus (1969) we didn't use the two-part ...
Richard Larson's user avatar
11 votes
2 answers

What on earth was Old Math?

I'd like to able to follow discussions/arguments about maths education, but many of them revolve around the transition to new math. I was taught in the UK in the early 90s, and none of the examples ...
Khorne's user avatar
  • 121
13 votes
0 answers

Was math education following a western trend?

After some research on the recent history of math education in the U.S., from the new math movement to the beginning of the 21st century, I understood that the historic flow of the math education ...
Henrique Augusto Souza's user avatar
4 votes
0 answers

What are the best expository pieces related to the Van Hiele models?

The Van Hiele model (wikipage) "is a theory that describes how students learn geometry." I would appreciate further insights into the original model, later models that expanded or re-worked it, and ...
Mika Ike's user avatar
  • 401
16 votes
5 answers

SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?

I was introduced to the SMSG math curriculum at Topeka High School between 1965 and 1966. my recollection (somewhat defective for medical reasons) was that the Topeka (KS) school system rolled the ...
user5565's user avatar
  • 161
25 votes
5 answers

When did US mathematics programs start failing to prepare incoming students for books like "Baby" Rudin?

I've seen in a lot of questions about "which textbook to use for intro analysis", and inevitably Rudin's Principles of Mathematical Analysis comes up, with the (almost cliche) rejoinder that "today's ...
user avatar
19 votes
8 answers

Teaching the History of Mathematics in High School

Is any time being spent on the history of mathematics in high school classes today? Few observations as a student - I had to discover Cantor many years after I was introduced to set theory. I had ...
Karthik Thiagarajan's user avatar
6 votes
1 answer

Who is E. Kim Nebeuts?

I just learned the name E. Kim Nebeuts from the quote at the beginning of Joseph O'Rourke's answer to this question. Curious, I google searched. All I saw on the first 2 pages of results was things ...
benblumsmith's user avatar
  • 1,936
12 votes
3 answers

Fighting math phobia with history

After years of experience in some area of expertise, you can easily forget how difficult it can be for the uninitiated to grasp some fundamental concepts, and, indeed, people often edit out of their ...
Tom Copeland's user avatar
20 votes
8 answers

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
Conifold's user avatar
  • 424
5 votes
1 answer

History Of Infinite Series

What is a good source for the history of infinite series? Moreover, why do we learn them? Are they really useful on their own, or are just tools / stepping stone for studying series of functions ...
Vagabond's user avatar
  • 339
12 votes
1 answer

The origins of $\operatorname{cis}(\theta)$

There is a abbreviation used in high school mathematics that is almost never seen outside of it: $\operatorname{cis}(\theta) = \cos(\theta) + i \sin(\theta)$, where cis stands for cosine + i sine. As ...
Simon's user avatar
  • 223
23 votes
13 answers

Historical tidbits to liven up calculus classes

What are some examples of math history that can be mentioned in calculus classes, either to liven things up or to provide additional perspective / insight on the material being learned? For example, ...
littleO's user avatar
  • 1,007
4 votes
1 answer

On using different notations for the same objects

Historically, in set theory we use two different notations to refer set theoretically same objects $\aleph_{\alpha}$ and $\omega_{\alpha}$. The folklore justification of this dual notation is that we ...
user avatar
3 votes
2 answers

Examples of cultural limitations on math education

Based on Maggie Koerth-Baker's article, "What do Christian fundamentalists have against set theory?", it seems there are some parts of culture which put some restrictions on math education. ...
user avatar
17 votes
4 answers

Historically Motivating Concepts

I have been reading this site for a while, and was glad to find an entire tag devoted to "concept motivation," which is currently my area of interest. However, my particular focus has not been ...
user1598's user avatar
  • 273
103 votes
35 answers

What female mathematician can I introduce to my High School students?

I enjoy talking about Pythagoras when I teach the Pythagorean theorem. I sometimes mention Descartes when introducing Cartesian coordinates. And Leibniz and Newton are mentioned in many calculus ...
David Ebert's user avatar
  • 3,905
27 votes
6 answers

Would taking 5 minutes to explain the history behind a mathematical idea help stimulate learning the idea?

I read a paper in my "Research Issues in Mathematical Education" class that I have applied to the Undergraduate Calculus I and Calculus II class that I teach. I take five minutes to explain the ...
Todd Thomas's user avatar
  • 1,218
31 votes
8 answers

What was the problem with New Math? Why did it end?

During the 60s, people in the US (and also in Europe), school curricula introduces New Math where students began with set theory in the first grade before learning to perform addition or ...
Markus Klein's user avatar
  • 9,448
21 votes
3 answers

When did the American school system's progression of math classes take its current form?

In the United States, secondary education students generally progress through pre-algebra courses, then algebra, Euclidean geometry, more algebra/trigonometry, then calculus or statistics. I am ...
Brian Rushton's user avatar