Questions tagged [history]

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

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30 votes
8 answers
8k views

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 ...
24 votes
5 answers
6k views

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 ...
12 votes
3 answers
706 views

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 ...
13 votes
0 answers
506 views

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 ...
0 votes
0 answers
89 views

What books were used to teach the old Scholarship level exams in the UK?

The scholarship level looks like it could have some interesting questions: https://en.wikipedia.org/wiki/Scholarship_level Any ideas on what books or resources were used to teach this level?
16 votes
5 answers
1k views

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 ...
5 votes
1 answer
342 views

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 ...
21 votes
3 answers
1k views

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 ...
17 votes
5 answers
798 views

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 ...
20 votes
8 answers
797 views

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 ...
4 votes
1 answer
322 views

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 ...
2 votes
2 answers
142 views

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&...
2 votes
1 answer
189 views

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 $2x+3=6−x$, ...
19 votes
8 answers
3k views

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 ...
7 votes
1 answer
234 views

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 ...
102 votes
35 answers
20k views

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 ...
5 votes
2 answers
302 views

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), ...
20 votes
3 answers
3k views

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 $...
12 votes
1 answer
524 views

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 ...
27 votes
6 answers
772 views

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 ...
4 votes
2 answers
363 views

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 ...
9 votes
5 answers
900 views

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 ...
-1 votes
1 answer
217 views

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 ...
8 votes
1 answer
462 views

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 ...
10 votes
3 answers
424 views

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 ...
6 votes
0 answers
189 views

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 ...
5 votes
0 answers
218 views

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 ...
23 votes
13 answers
1k views

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, ...
15 votes
4 answers
528 views

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 ...
12 votes
1 answer
431 views

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 ...
8 votes
3 answers
949 views

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 ...
25 votes
5 answers
4k views

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 ...
11 votes
2 answers
2k views

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 ...
17 votes
4 answers
778 views

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 ...
4 votes
0 answers
80 views

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 ...
6 votes
1 answer
433 views

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 ...
5 votes
1 answer
572 views

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 ...
4 votes
1 answer
233 views

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 ...
3 votes
2 answers
875 views

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. ...