Questions tagged [curriculum]
For questions about contents, order, background, alternatives in curricula.
109
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11
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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
520 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
200 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 ...
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8answers
555 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
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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
137 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
692 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
319 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
253 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
148 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
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2answers
295 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
votes
3answers
324 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
474 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
544 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 ...
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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
147 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
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1answer
269 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
360 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
699 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 ...
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3answers
284 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
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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
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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
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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?
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4answers
693 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
151 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
443 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
649 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
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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
223 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
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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
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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, ...
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
12k 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
votes
13answers
927 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 ...
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4answers
868 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 ...
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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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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 (...
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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
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3answers
716 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 ...
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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
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3answers
896 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
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1answer
492 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-...
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3answers
849 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 ...
