Questions tagged [curriculum]
For questions about contents, order, background, alternatives in curricula.
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What should be included in a freshman 'Mathematics for computer programmers' course?
Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) ...
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14answers
16k views
Why is learning mathematics compulsory?
In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and ...
36
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7answers
4k views
A Lexicon of Math Mistakes
Neil Postman wrote an interesting (and freely available) article called "The Educationist as Painkiller." I highly recommend you read the article for your own enjoyment and as a background to this ...
35
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17answers
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Why are triangles so prevalent in high school geometry?
A colleague and I recently discussed what we call the "Triangle Trap." High school geometry covers a very large unit reflecting the common core:
Classifying Triangles
Triangle Angle Properties
...
29
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7answers
2k views
Mathematical education by country
Depending on the university, there are always slight differences in the syllabus and the structure of the standard material undergraduate students learn.
But I also noticed that undergraduate ...
27
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10answers
7k views
Should LaTeX be taught in high school?
This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
26
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4answers
2k views
How should LaTeX be taught to university students?
There are several groups of people that would benefit from learning LaTeX in college. Future teachers can use it to write exams, scientists and mathematicians can write papers, and everyone can write ...
25
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4answers
3k views
Common Core, threat or menace? Or maybe ok after all?
I have a background in math but no contact with secondary education or kids. I hear all sorts of stories ... horror stories mostly ... about the Common Core math curriculum in the USA. Then I hear ...
23
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5answers
683 views
Do all high school students need the same 3-year sequence of math courses?
I continue to be troubled by the amount of symbolic manipulation in a typical Algebra 2 course. Once a student has completed Algebra 1 and Geometry, shouldn't there be another option for them if a ...
23
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3answers
8k views
Why aren't logarithms introduced earlier?
I've always been puzzled by the unequal treatments of square roots and logarithms in school mathematics. In the United States, most students know what a square root is before they enter high school (...
22
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8answers
2k views
Should we teach trigonometric substitution?
This is the question that was not asked here. Also related is this question, but both presuppose that it will be taught and ask about how best to do it. My question here is, suppose we are designing ...
21
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3answers
833 views
What can be said about Lie groups in a first abstract algebra course?
Lie groups are among the most important examples of groups in mathematics and physics, but they are rarely discussed in introductory undergraduate abstract algebra courses, which tend to focus on ...
20
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3answers
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How to advise students who want to do a “Bourbaki”-style study?
There are some good students who understand a lot and are very critical. Such students tend to think that they will only understand abstract algebra if they have followed a course about logic; or they ...
20
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2answers
837 views
Should geometric algebra be presented early on in undergraduate education?
The Cambridge University GA Research Group’s website along with the “Geometric Calculus R & D Home Page” should serve as a good introductions to geometric algebra, along with the Wikipedia ...
18
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4answers
681 views
Emphasizing Statistics instead of Calculus
In a 3 minute talk on ted.com, mathematician Arthur Benjamin made the argument that it makes sense to give emphasis on statistics instead of on calculus in school, after students have been given a ...
17
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7answers
3k views
Was there an SMSG (New Math) “Algebra 2” text?
This question has been kicking around in the back of my head for a couple of years, but the impetus to post it now came from reading the related question at When did the American school system's ...
16
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6answers
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Ideal Undergraduate Sequence
What is the perfectly (maybe unrealistically) ideal undergraduate sequence for a undergraduate majoring in pure mathematics who takes 2-3 mathematics courses per semester assuming a strong AP Calculus ...
15
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4answers
2k views
Why is rounding half away from zero the only method taught?
Rounding to the nearest even digit is very practical in a lot of areas (e.g. statistics, accounting), but is never taught anywhere from elementary school to college. Even in R, the go-to statistics ...
15
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4answers
521 views
Thought experiment: Utopian college-level math curriculum without external constraints
An old favourite topic of mine to daydream about on pleasant afternoons is this:
If you could completely redesign the university-level mathematics curriculum from the ground up to be as good as it ...
15
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5answers
1k views
Cost and benefits of compartmentalization in k-12 curriculum
This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic.
K-12 mathematics textbooks (understandably) divide ...
15
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1answer
264 views
Order of Topics in Introductory Proofs Class
Beginning next semester I am teaching a course in proofs and mathematical problem solving at my local university. For some background, the university is primarily a commuter university and the ...
14
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8answers
2k views
How should I introduce the Chain Rule
I'm halfway through my first year of teaching AP Calculus to high school seniors. It's been going generally well, but I'm feeling like I really could have done better getting them into the Chain Rule....
14
votes
5answers
530 views
When is it a good idea to avoid talking about why something works?
I am teaching, among other things, a college algebra course this semester. In this course we do a lot of conceptual things but we also do some techniques to prepare students for calculus. One of the ...
14
votes
4answers
374 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
...
14
votes
2answers
995 views
Introducing the Lebesgue integral before Riemann's
Has anyone attempted to introduce, or has data on such endeavor, Lebesgue integration before Riemann? I've seen many discussions about how the Riemann integral is obsolete and that it is presented ...
14
votes
4answers
607 views
Key theorems in undergraduate linear algebra
I've been asked by an high school student what are the $5$ major theorems in Lang's Linear Algebra (and therefore, by extension, in an undergraduate linear algebra course). Firstly, I bluntly said ...
14
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1answer
305 views
Spiral learning in real analysis
Has there been any attempts at developing a curriculum for teaching analysis (here let us be narrow and say real analysis in the sense of rigorous integral and differential calculus) in a multipass, ...
13
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7answers
2k views
Content for a 40-minute lecture on graph theory for high schoolers
I'm due to deliver a session on graph theory for 16–17-year old students (UK sixth formers) as a taster of what studying mathematics at university is like. What would you recommend as content, and a '...
13
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4answers
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Why do we teach calculus in high school rather than a different math course?
In most high schools (in America), I think it is safe to say that the highest math subject offered is calculus.
But why is it calculus rather than number theory or some other branch of mathematics?
...
13
votes
4answers
482 views
Beyond Calculus, an Invitation to Dream Higher for High School
From what I see in the curriculum we use for my children if we stay on track with the current trajectory they'll finish by grade 8 what is usually called Precalculus (USA terminology, includes ...
13
votes
2answers
1k views
How early to start “abstract” math education, or, How to prevent smart kids from never getting exposed to math?
Everybody who is in graduate mathematics had a moment where they realized that mathematics was "their thing", and they decided to dedicate their academic career to it. I don't know of many people who ...
13
votes
3answers
450 views
Teaching Infinitesmals and Non-Standard Analysis
This question is asked from a self-teacher standpoint(I am currently trying to learn more about non-standard analysis on my own), but I'd think it could be applicable to educators also.
What are good ...
13
votes
2answers
330 views
What prerequisites would college students need for a course based primarily on Euclid's elements?
I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary ...
12
votes
4answers
836 views
Is Calculus Necessary?
That title is a quote from Fred Roberts:
Fred Roberts. "Is Calculus Necessary?"
Proceedings of the Fourth International Congress on Mathematical Education.
1980. p.52ff.
"Calculus is not ...
12
votes
1answer
366 views
Teaching K-8 math in the style of “A Mathematician’s Lament”
Here's a link to the full paper, colloquially known as Lockhart's Lament:
Link: https://www.maa.org/external_archive/devlin/LockhartsLament.pdf
In the context of K-8 learning materials that take ...
12
votes
3answers
320 views
Resources on interdisciplinary curricula
As I try to incorporate more history, science, language, computing, and art into my math class I keep finding the lessons to be very successful and my students always seem to enjoy them. While I know ...
12
votes
2answers
415 views
Why don't we teach codomains of functions in high school?
When I was a university student, I learnt that a function is the data of three informations:
the rule that tells how to associate an object $x$ to its image $f(x)$,
A domain $E$ where live the ...
12
votes
3answers
762 views
Is there a program like ALEKS for mathematical logic?
ALEKS (http://www.aleks.com/) is a good way of learning procedural math, because it is very systematic and forces you to master the dependencies of a kind of problem before working on that kind of ...
11
votes
8answers
780 views
Symmetry - practical usages
My girlfriend is studying to become a math teacher, and asked me what I have ever used symmetries for.
I'm a web developer, and do some designing from time to time, so I answered that symmetry have ...
11
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3answers
660 views
What topics could be covered in a course on fractals?
I'd like to propose a class on fractals to my department in the next few years.
One issue is that there seems to be no consensus on what a fractal is (see the wikipedia talk page on fractals, for ...
11
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2answers
2k views
Advanced Calculus vs. Analysis for a first proof-based course
Question: Why was advanced calculus removed as the first proof-based course in favor of real analysis in most curriculums?
I regularly see in advanced calculus books either that:
its purpose is, ...
11
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3answers
223 views
Pedagogical Purpose in Making Students Do Problems in A Less Efficient Way First
Let's assume that a group of students need to learn to solve a certain type of mathematical problem for which there is two general methods of solving it, $X$ and $Y$. We also assume that $Y$ is more ...
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4answers
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Co-curricular lessons between geometry and chemistry?
My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...
10
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8answers
545 views
What topics should be included in a course matching these specifications?
I posted this question on m.s.e., where I upvoted the two answers, both of which said rather little by comparison to what the question asks. Hence this present posting.
Say you have a calculus ...
10
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7answers
2k views
Galois Theory: necessary?
I noticed the discussion of whether the teaching of Galois Theory is necessary on MathOverlflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life....
10
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4answers
417 views
Surrounding a subject and strangling it to death versus concentrating on the main point
Standard calculus textbooks begin by introducing limits, including
limits of a fraction as the numerator and denominator approach $0,$
limits of a fraction as the numerator and denominator approach $\...
10
votes
4answers
1k views
Topics that should be in an undergraduate math programme
According to your experience as students and professors, what are (and why) the courses that should be part of a math undergraduate degree, but that are missing in most institutions?
10
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3answers
345 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 ...
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1answer
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Which math classes should be included in an undergraduate computer science program?
As part of my job search, I've come into contact with universities that are beginning to offer new majors at their university such as applied mathematics or computer science. A frequent interview ...
9
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3answers
701 views
In what curricula are “rectangles” defined so as to exclude squares?
Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is, are ...
