Questions tagged [curriculum]

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

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9
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3answers
739 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 ...
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4answers
994 views

Why is set theory not taught at the outset of math education?

A beginner in math, reading Badiou, I found the following quote on set theory in Being and Event: The axiomatization consists in fixing the usage of the relation of belonging, $\in$, to which the ...
9
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4answers
3k views

Can we skip Newton's Method?

I am teaching an introductory calculus course for high school juniors and seniors. It is not formally described as an AP Calculus course, but it is supposed to map roughly onto Calculus AB. The ...
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: ...
9
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2answers
660 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? ...
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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5answers
711 views

Is algebra unnecessarily quadratic intensive?

I don't know about all algebra courses, but the following is the basic outline of my algebra years: Alg. I - Lots of linear graphs and solving systems of equations. Alg. II - Lots of quadratics, some ...
8
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4answers
256 views

Should school syllabus include chapters partially?

In my locality, many schools have this tendency to partially include this and that chapter in the syllabus (for almost every subject). For example, (most of the chapters are subdivided in two or more ...
8
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2answers
302 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 ...
8
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3answers
301 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 ...
8
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1answer
310 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 ...
8
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0answers
69 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 ...
7
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1answer
550 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-...
7
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2answers
339 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 ...
7
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1answer
154 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 ...
6
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4answers
412 views

Why do standard geometry textbooks not start with trigonometry?

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
6
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4answers
6k views

Should we finish algebra before starting geometry?

Comparing an old french mathematics book for grade 9 and a new one, one obvious difference is the ordering of the chapters. In the old book, all the algebra chapters are grouped together then all the ...
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4answers
354 views

Is the education system in Finland particularly good?

Inspired by this question: What makes education in Finland so good? Finland has marketed itself as a top country in education. Indeed, at some time, the Pisa results in Finland were quite good. ...
6
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2answers
215 views

At what point in the curriculum should the tensor product be introduced?

I remember my linear algebra teacher mentioning tensor products as an advanced topic that would be covered in upper level algebra coursework. During undergraduate abstract algebra, tensor products ...
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 ...
6
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3answers
174 views

Forming a Study Model for a Self-Study Beginner

I am very new to this platform so I may have misunderstood the intent of this site, or might seem a bit off, but please bear with me because I know what I want for certain. I always wanted to study ...
6
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2answers
148 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. ...
6
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1answer
152 views

How do I work in creating education standards?

I'm interested in playing a role in determining mathematics curriculum and goals for K-12 students. I'm currently a college student. How do I even begin down this path? Math? Political Science? ...
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2answers
304 views

Mainstreaming math student

I'm working one-on-one with a student who is part of a sponsored refugee family. He's bright and a good learner, but has had a lot of interruptions to his education. No indication of any learning ...
6
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2answers
386 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 ...
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0answers
288 views

What is the controversial 8th grade algebra mentioned on this answer?

An answer on this site mentions that it would be more appropriate to criticize Efforts to force kids to take algebra at lower and lower ages, such as attempts in California to make all kids take ...
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0answers
149 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 ...
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0answers
201 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 ...
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5answers
315 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 ...
5
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3answers
219 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 ...
5
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2answers
6k 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 ...
5
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2answers
177 views

In what grade do kids (New York, US) learn common differences?

I'm teaching an after school workshop for a few 7th graders. I was having them try to predict the next item in a complicated sequence. After some failed attempts, one of the kids started analyzing the ...
5
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1answer
127 views

Associate Degree in Mathematics

A close friend of mine is investigating Associate Degrees in Mathematics with the goal of assessing the plausibility of offering an online A.A.S. at a US institution. I'm curious if anyone here has ...
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2answers
198 views

What are the benefits of an expertly curated learning pathway?

What are the benefits of an expertly curated learning pathway? Like that provided by a major publisher's textbook - CPM, a school district's mandated curriculum - IM's Open Up Resources or a ...
5
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1answer
204 views

Should students teach other students?

I am interested in creating a curriculum that helps cultivate students abilities to teach one another. Specifically good one-on-one instruction includes elements like: Examples, Pictures, Humor, ...
5
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0answers
149 views

Which countries adopt metacognition in their official math curricula?

I know Singapore and Brazil explicitly adopt metacognition as one of their maths curricular pillars. The relevance of metacognition is recognized by OECD that has written a state-of-the-art report ...
4
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1answer
350 views

Are kindergartners supposed to be steered from squares being rectangles?

Question 1: What are the literature, status, debates, references, etc regarding this matter please? Apparently, some (woohoo weasel words!) consider that squares are rectangles too advanced a topic ...
4
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1answer
258 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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2answers
248 views

Why are "homogeneous differential equations" in the standard ODE curriculum?

Here I mean a differential equation of the form $y'=f(x,y)$ where for some $\alpha$, we have $f(tx,ty)=t^\alpha f(x,y)$ for every $t$. I have no idea why this topic seems to appear in every ODE ...
4
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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 ...
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0answers
230 views

Are there any studies evaluating the impact of the Mathematics Vision Project?

I have found very little online that compares & critiques the MVP vs traditional curricula. Any suggestions & pointers would be welcomed. The MVP is an implementation of Common Core Standards ...
3
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2answers
259 views

Looking for a rigorous middle school self-study math course

My son is in 5th grade (US) and since he is doing remote learning, we have been doing a lot of topics in pre-algebra just using worksheets. I'd like to start him on a formal middle school curriculum, ...
3
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1answer
767 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 ...
3
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1answer
306 views

Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?

I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
3
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1answer
105 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 ...
3
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0answers
151 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 ...
3
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0answers
226 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, ...
2
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3answers
477 views

What is the motivation for teaching Factoring by Grouping?

This seems like such a niche trick to teach students when factoring polynomials. Like, the polynomials I've seen textbooks ask students to factor by grouping seem so cherry picked that I can't imagine ...
2
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2answers
2k views

Curriculum in USA vs. Canada

(1) When do students in Canada learn about the four triangle centres (centers), circumcenter, incenter, orthocenter, and centroid? In the USA (more precisely, Indiana), the math curriculums are by ...
2
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1answer
226 views

Teaching Quantifiers Before Logical Connectives

In this short question, I would like to ask whether it is possibly good to teach quantifier before logical connectives in a logic introduction lecture? I know there is a relationship between them but ...