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Questions tagged [curriculum]

For questions about contents, order, background, alternatives in curricula.

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11
votes
3answers
225 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 ...
13
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4answers
532 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 ...
14
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4answers
3k views

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? ...
5
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3answers
212 views

Modeling vs. Application vs. Context

Our undergraduate mathematics program has recently seen a large drop-off in majors (suspected reason: our growing (but separate) undergraduate statistics program is seen as being a more employable ...
10
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8answers
561 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 ...
6
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4answers
1k views

Integrate Coding into the Geometry Curriculum

My supervisors want to see coding integrated into the ninth grade Geometry class. This class is mostly concerned with proofs--not too much algebra. These students know a decent amount of the visually ...
13
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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 ...
6
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2answers
142 views

Mathematics that can be worked into 8th grade engineering course

I have a section of 8th grade engineering/mathematics. The class is meant to be a support/enrichment environment rather than instructional, they have a separate math teacher for pre-algebra/algebra. ...
9
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3answers
715 views

What are the mathematical prerequisites to quantum mechanics?

Which topics - what skillset in mathematics need the students to possess to be able to proceed with learning quantum mechanics without hitches like need for explaining notation or understanding the ...
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 ...
14
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1answer
322 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, ...
4
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1answer
256 views

Definition of "curriculum"

In standard usage does the word "curriculum" mean That which ought to be taught and learned, as prescribed by authorities (i.e. teachers and textbook authors and the like); or That which actually is ...
3
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0answers
150 views

Why is combinatorics not a part of the Tripos?

I do not officially study mathematics, so I always rely on what's on the internet. Specifically, I follow the schedules of the Tripos – the math program at Cambridge, supposedly one of the most ...
8
votes
2answers
297 views

Is multiplication by zero clear for and understood by K-3 students?

For K-3 students, perhaps it is not acceptable to introduce multiplication by zero as a property or definition. Instead, the child may think about multiplication as, e.g., repeated addition. Examples ...
12
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3answers
364 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
478 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 ...
15
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4answers
549 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 ...
9
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1answer
2k views

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 ...
35
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17answers
11k views

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 ...
4
votes
1answer
148 views

Is there communication between junior high math and science departments?

Recently, my junior high school (aka middle school) reorganized their curriculum. Instead of teaching middle school physics, chemistry, and biology in that order, they reversed it. The logic was that ...
15
votes
1answer
272 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 ...
6
votes
2answers
372 views

Summer program for 'international' undergraduate students of mathematics

I see that most of the american universities have mathematical summer programs with lectures and mini-courses (note: I'm not talking about undergraduate research programs in this question) for ...
14
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4answers
729 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 ...
8
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3answers
292 views

Lie Theory: significance and relevance to undergraduate education

I have been strongly recommended to read the book Naive Lie Theory. In the introduction one can read: "This naive approach to Lie theory is originally due to von Neumann, and it is now possible to ...
10
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8answers
2k views

How early and how much can you teach kids and teenagers about vectors?

I have met kids and teenagers who I believe are capable of understanding the concept of a vector. However, I have only heard of a select number of schools who teach it to young people. Here's my main ...
9
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4answers
2k views

Secondary Geometry Curriculum Sequencing?

I am currently student teaching, and the main class that I am focusing on is a secondary geometry class. I am currently following my classroom mentors curriculum sequence which looks something like: ...
11
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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?
-5
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4answers
709 views

Why we mistaken coin toss to be an example of classical probability?

It is now well known that a random coin toss has 1/6000 probability of landing on its edge. So the out-dated model that a coin toss always land on either heads or tails with probability 1/2 is wrong. ...
7
votes
1answer
153 views

Modern primary-school math curricula (e.g. Everyday Math, Bridges) for accelerated learners

How do modern primary-school math curricula like Everyday Math, Bridges, TERC, etc. approach the "problem" of providing enough challenge to young students who are very comfortable with math and who ...
12
votes
1answer
466 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 ...
9
votes
2answers
655 views

What caused the (relatively) recent popularity of set theory?

When I was growing up during the 1960s, "set builder notation" constituted a large part of what was then the "new math." Question: When and why did "set theory" become popular in math education? ...
5
votes
2answers
5k views

Naming of calculus courses

Many people on this site refer to undergraduate courses called "Calculus I" or "Calculus II". In my country (Australia) there is no standard naming convention for university maths courses, and ...
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 ...
6
votes
0answers
200 views

How is cooperative learning being used in vector calculus, and what are the origins of this work?

I'm doing some research about cooperative learning in vector calculus. It seems like what cooperative learning in calculus is referred to varies over time. In 1987, there was an MAA book, Calculus ...
3
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0answers
224 views

Most important nonstandard math courses [closed]

Most students with aspirations of a pursuing a PhD in pure mathematics at a top grad school takes the "standard" curriculum as an undergrad which includes 2x algebra, 2x analysis, 1x complex analysis, ...
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 MathOverflow. Here at LSE, everything we teach in mathematics should have some application to the social side of life. ...
11
votes
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, ...
14
votes
2answers
1k 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 ...
15
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6answers
13k views

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 ...
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 ...
12
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13answers
948 views

Symmetry - practical uses

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 ...
18
votes
4answers
892 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 ...
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
votes
3answers
9k 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 (...
46
votes
12answers
31k views

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) ...
11
votes
3answers
721 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 ...
36
votes
7answers
5k 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 ...
22
votes
3answers
922 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 ...
7
votes
1answer
524 views

What universities in the United States have Spanish-language mathematics classes?

This is a simple question, which I haven't found the answer to online. Due to the increasing number of Spanish-speaking students in American universities, I've been interested in teaching Spanish-...
12
votes
3answers
879 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 ...