Questions tagged [curriculum]

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

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9
votes
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 ...
3
votes
2answers
137 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 ...
3
votes
1answer
144 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 ...
2
votes
2answers
845 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 ...
13
votes
7answers
2k views

Content for a 40-minute lecture on graph theory for high schoolers

I'm due to deliver a session on graph theory for 16–17-year old students (UK sixth formers) as a taster of what studying mathematics at university is like. What would you recommend as content, and a '...
27
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10answers
7k views

Should LaTeX be taught in high school?

This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
2
votes
1answer
168 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 ...
6
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0answers
249 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 ...
40
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14answers
16k views

Why is learning mathematics compulsory?

In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and ...
1
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1answer
146 views

Math undergrad courses [closed]

Awhile back I was very weak with my trigonometry so I came to this site asking for help, and it turned out the few answers I got made a huge difference. I excelled at the trigonometry section in my ...
14
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8answers
2k views

How should I introduce the Chain Rule

I'm halfway through my first year of teaching AP Calculus to high school seniors. It's been going generally well, but I'm feeling like I really could have done better getting them into the Chain Rule....
10
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4answers
1k views

Co-curricular lessons between geometry and chemistry?

My school is hyped about the promise of co-curricular education and they are giving the math and science teachers paid days off to develop lesson plans that synergize our learning goals. I'm on ...
8
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1answer
226 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
votes
4answers
226 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 ...
0
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6answers
539 views

Is there a more telling name for “Calculus 2”?

I see a lot of places where "Calculus 1" is referred to as "Introduction to Calculus", or "Single-variable Calculus." "Calculus 3" is referred to as "Multiple-variable calculus." Is there an ...
5
votes
2answers
140 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 ...
5
votes
2answers
194 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 ...
1
vote
1answer
109 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
328 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. ...
-1
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1answer
239 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 ...
5
votes
0answers
138 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 ...
6
votes
4answers
380 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
187 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
344 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
292 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
170 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 ...
4
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0answers
198 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 ...
5
votes
1answer
197 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
118 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
243 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 ...
-2
votes
1answer
96 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 ...
4
votes
1answer
308 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 ...
8
votes
3answers
695 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
369 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
151 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
567 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
104 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
262 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
288 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
4k 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
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 ...
12
votes
4answers
828 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
416 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
64 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
119 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
562 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
289 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
524 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
222 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
477 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 ...