Questions tagged [curriculum]

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

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6
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0answers
127 views

Compare depth and scope of math syllabus between Malaysia's STPM, Gao Kao and A level

Are the math syllabi of these three exams comparable? Which syllabus' scope is wider and deeper? Which helps students to be better prepared for math in undergraduate level? I believe that A level is ...
7
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2answers
312 views

“Personalized System of Instruction” (PSI) vs. “Individually Prescribed Instruction” (IPI)

This question may be a bit overly-broad for MESE, but I am hoping to find some responses that can help to fill in my understanding of two similar forms of instruction that had their heyday in the ...
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2answers
391 views

Is it possible to have taken intro to proofs, calculus 3 and differential equations and still lack the ability to do proofs?

Ideal Undergraduate Sequence Main question: I looked above and what I'm interpreting out of it is that one should be able to do proofs after studying some intro to proofs class, calculus ...
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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 ...
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4answers
431 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 $\...
3
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1answer
104 views

Are Proficiency Strands Hierarchical?

In Australian math curriculum, four strands of mathematical proficiency are defined: : Understanding Fluency Problem Solving Reasoning Are these items hierarchical - I mean, for example, is ...
9
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2answers
640 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? ...
13
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4answers
516 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 ...
12
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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 ...
13
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3answers
471 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 ...
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 ...
7
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0answers
65 views

Where can I find a comparison of mathematical subjects taught for primary and secondary school around the world?

I have been searching this for a long time, but most of what I find spends more time on cultural aspects and what is expected from the teacher, etc. Perhaps this is really trivial to find, but I am ...
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1answer
137 views

Using Substitution in place of the balance model

How does substitution work as an alternative to the balance model in introducing solving equations? My biggest worry is that, lacking a concrete representation, is too abstract for middle schoolers. ...
12
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3answers
830 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 ...
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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 ...
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 ...
5
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5answers
304 views

Should the construction of triangles be taught?

Constructing triangles (or other shapes) seems to be quite an obsolete topic, and yet, they feature in almost every high school math competition, to disappear completely in college. In recent years in ...
3
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1answer
662 views

Why is the convergence of infinite series covered in Calculus II?

I'm teaching AP Calculus BC for the first time this year. The AP curriculum is an attempt to cover most of the material in a two-semester university freshman calculus series, and so I am reminded of ...
11
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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 ...
5
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3answers
197 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 ...
15
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4answers
543 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 ...
6
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2answers
135 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
676 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 ...
14
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1answer
318 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, ...
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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 ...
4
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1answer
252 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 ...
4
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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 ...
14
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4answers
673 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 ...
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 ...
13
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2answers
359 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 ...
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2answers
294 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 ...
22
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3answers
892 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 ...
12
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3answers
323 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
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2answers
471 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 ...
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, ...
10
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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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4answers
839 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 ...
15
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1answer
268 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
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2answers
345 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 ...
8
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3answers
280 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 ...
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: ...
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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 ...
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?
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2answers
901 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 ...
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4answers
680 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. ...
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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 ...
7
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1answer
145 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
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1answer
430 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 ...
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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 ...