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Questions tagged [curriculum]

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

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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 ...
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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 ...
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1answer
174 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, ...
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1answer
110 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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1answer
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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 ...
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1answer
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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 ...
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1answer
201 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 ...
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3answers
551 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 ...
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4answers
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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 ...
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1answer
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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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3answers
253 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 ...
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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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2answers
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“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
182 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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4answers
392 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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1answer
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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 ...
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4answers
580 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 ...
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4answers
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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 $\...
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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
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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. ...
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5answers
432 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 ...
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5answers
247 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 ...
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1answer
295 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 ...
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3answers
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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 ...
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4answers
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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 ...
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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? ...
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3answers
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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
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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 ...
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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 ...
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2answers
725 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 ...
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2answers
116 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. ...
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3answers
502 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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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 ...
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1answer
247 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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1answer
116 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 ...
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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 ...
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2answers
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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. ...
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3answers
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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 ...
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2answers
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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 ...
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4answers
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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 ...
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1answer
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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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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 ...
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1answer
120 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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1answer
218 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 ...
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2answers
215 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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4answers
475 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
221 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 ...
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6answers
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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 ...
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880 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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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?