Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [curriculum]

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

3
votes
2answers
157 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 ...
0
votes
1answer
84 views

Roadmap to studying PDEs for analyzing Quantum Physics better

I am studying the basics of Quantum Physics (involving the characteristics of Schrodinger's Wave equation without actually analyzing it rigorously mathematically) this semester. I was wondering, ...
6
votes
4answers
245 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. ...
0
votes
0answers
115 views

What makes education in Finland so good?

This is a question more about education in general than math education but there is no general education Stack Exchange website so I decided to write this question here. If this question is more ...
0
votes
1answer
129 views

Integrated math curriculum in different countries

One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European ...
4
votes
0answers
126 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 ...
5
votes
4answers
318 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
votes
2answers
167 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 ...
10
votes
3answers
296 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 ...
6
votes
2answers
231 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 ...
5
votes
2answers
152 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 ...
3
votes
0answers
88 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 ...
1
vote
0answers
121 views

I’m considering buying Art of Problem Solving. For those who read it, what’s your review of it? [closed]

As you know, Art of Problem Solving includes 11 books that comes with their solutions and they are PreAlgebra, Introduction to Algebra, Introduction to Counting and Probability, Introduction to ...
5
votes
1answer
186 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
votes
1answer
112 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 ...
-2
votes
1answer
168 views

Proving basic Theorems and properties in high school [closed]

Why high school teachers do not emphasize knowing the proofs of properties and theorems in math. In my 40 years of teaching prospective high school teachers, I rarely found students who can derive ...
-3
votes
1answer
89 views

When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
2
votes
1answer
218 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 ...
6
votes
3answers
584 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 ...
14
votes
4answers
302 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 ...
6
votes
1answer
150 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? ...
7
votes
2answers
362 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 ...
6
votes
0answers
88 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
votes
2answers
185 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 ...
0
votes
2answers
191 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 ...
6
votes
4answers
1k 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 ...
3
votes
1answer
102 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 ...
10
votes
4answers
664 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 ...
10
votes
4answers
383 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 $\...
7
votes
0answers
61 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 ...
0
votes
1answer
94 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. ...
8
votes
5answers
504 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 ...
5
votes
5answers
273 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
votes
1answer
360 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
votes
3answers
210 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
votes
4answers
357 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
votes
4answers
1k 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
votes
3answers
156 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 ...
11
votes
8answers
519 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
votes
4answers
761 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 ...
11
votes
2answers
794 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
votes
2answers
123 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
votes
3answers
529 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 ...
20
votes
8answers
1k 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
votes
1answer
262 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, ...
5
votes
1answer
231 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
votes
0answers
132 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
247 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. ...
12
votes
3answers
304 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
366 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 ...