For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

learn more… | top users | synonyms (3)

3
votes
8answers
521 views

Ceiling and floor functions

What are some real life application of ceiling and floor functions? Googling this shows some trivial applications.
2
votes
3answers
203 views

Learning times tables?

I have some weird gaps in my learning, I can do lambda calculus and some basic category theory, but I do not know how to do some of the most basic of arithmetic. (I am in my mid 20s) Seeing this gap ...
6
votes
2answers
166 views

Is it a problem being unable to understand a mathematical definition without examples?

I was reading a book on coding theory, there was a definition fot the Hamming's Distance and also one example. Understanding purely from the definition was hard but the example helped to give meaning ...
9
votes
4answers
637 views

Middle school number theory

Find at least three numbers that satisfy all three conditions: (1) there is a remainder of $1$ when the number is divided by $2$; (2) there is a remainder of $2$ when the number is divided by $3$; ...
2
votes
2answers
14k views

Why are prime numbers important in real life? [duplicate]

What practical use are prime numbers? Why do we emphasise the teaching of prime numbers?
4
votes
6answers
2k views

New & interesting uses of Differential equations for undergraduates?

I'm teaching an elementary DE's module to some engineering students. Now, every book out there, and every set of online notes, trots out two things: DE's are super-important, vital, can't live ...
4
votes
5answers
747 views

How to know a irrationals never repeat?

How would you respond to a middle school student that says: “How do they know that irrational numbers NEVER repeat? I mean, there are only 10 possible digits, so they must eventually start repeating. ...
1
vote
0answers
55 views

Metalanguage on mathematics

I've heard that in the first class of my degree are teaching concepts like metalanguage. What does it mean. Could you give some examples? I've searched on google that metalanguage means representing ...
12
votes
1answer
233 views

Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that ...
8
votes
1answer
158 views

Is it a bad idea to study modern algebraic geometry without having any background in smooth manifolds?

I have a chance to take a course in algebraic geometry developed in the scheme theoretic setting and am considering my options. I have taken graduate courses in general and commutative algebra and ...
1
vote
1answer
190 views

Online homework/testing systems?

I have been using Pearson's MyMathLab Global with my Engineering students. I appreciate its convenience, but the students find its inflexibility annoying (if an answer is expected to be 1.5, then the ...
2
votes
1answer
227 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
1
vote
0answers
40 views

personal enrichment in science and, particularly, in math

What is the best way to expand one's area of thought in science and especially in math? Read scientific journals or view some conferences? What else?
7
votes
4answers
801 views

How to convince a high school student that differentials don't work like fractions in general?

It all started when I tried to convince a 10th grader that if $f$ is a function defined on $\mathbb{R}^n$ the differential is defined by: $\large \displaystyle df = ...
1
vote
1answer
116 views

A way to teach Archimedean property

A student asked me how to understand the Archimedean property, I tried to re-read with him what he has already done in class (well, actually copy from the blackboard in class). However I think I'm not ...
3
votes
1answer
70 views

Is a sandwich appropriate here?

On an exam we were asked: what is the domain of the following function? $$\large f(x)=\frac{\frac{x}{x-2}}{\frac{2x+7}{x-1}}$$ My solution: This is the same as $$\large ...
12
votes
5answers
1k views

How can I convince my math teacher?

Ok, so I got an answer wrong on my exam because my teacher says that the function $f(x)=\frac{(x+2)x}{x+2}=x$ but I insist that it isn't defined for x=-2. If it was then $\frac{x}{x}=1$ for all reals ...
9
votes
5answers
232 views

The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
23
votes
6answers
8k views

Teaching a 4 year old maths

Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from ...
2
votes
3answers
774 views

Modelling with exact differential equations?

I'm teaching some very elementary differential equations to engineering students, and their constant question to me is "What's the use of this?" or alternatively "Where would we use this?" Now, I'm ...
3
votes
3answers
375 views

Alternative model of Euclidean geometry

I'm planning to teach high-school geometry. As usual, this will be by building from axioms. (The axioms used are AFAICT particular to the book I've been assigned, but they're some combination of ...
1
vote
2answers
3k views

What is a standard precalculus syllabus?

I'm about to start teaching a calculus I class next week and I was wondering what I can expect from my students. I'm a Brit teaching in the US so I am unfamiliar with the system. I am hoping that ...
2
votes
2answers
2k views

MOOCs for college-level discrete math?

Specifically I am looking for short lectures (and quizzes) on specific topics. (like Khan Academy offers) Topics I am learning about include; Intro logic-theory + set-theory Notation, negation, ...
4
votes
5answers
203 views

Collecting different answers to a simple problem

I am collecting different answers to the problem below for possible publication in a pedagogical note I am writing. Please post freely (avoiding repetitions), and let your imagination go wild with ...
5
votes
1answer
374 views

Online classes/books in multivariable calculus?

So does anyone know of any good online courses in multivariable calculus? (Or in a possible alternative leap of curriculum, if said path has proven to be better/moar interesting.) I'm coming straight ...
10
votes
4answers
864 views

Recommended survey of mathematics [closed]

What do you see as the most explanatory and beautiful survey of mathematics book...For short is there a book like Feynman lectures but for math?I've looked at Elementary Mathematics from an Advanced ...
2
votes
3answers
113 views

A simple clock problem

A man on his way to dinner shortly after $6.00$ pm observes that the hands of his watch form an angle of $110°$. Returning before $7.00$ pm he notices that again the hands of his watch form an angle ...
-3
votes
1answer
106 views

Elementary Algebra question

Ok guys so I've been out of school for eight years, never used algebra again, also I was forcibly removed from school in 9th grade. I need to ask a few questions on Elementary Algebra, what are the () ...
1
vote
2answers
78 views

How to prove that every uniformly continuous set is a closed set.

According to the classroom notes "Uniformly Continuous Linear Set" in American Mathematical Monthly, Vol. 62. No. 8(Oct., 1955) pp. 579-580, Author: Norman Levine link. I'm usually confused about the ...
2
votes
2answers
226 views

Probabilities associated with negatively marked questions

First of all: not a native english speaker, and not a mathematician. Please explain as you would to your 10 years old son. I have 120 questions to answer True or False For each right answer, i ...
0
votes
3answers
107 views

Equation that produces negative one if x is less than zero and vice versa

I have tried coming up with something but i couldn't in the end... basically i want something to produce -1 or 1. given value of x will not be equal to zero at any point. But if you want to add that, ...
3
votes
1answer
195 views

Conglomerate in mathematical literature.

I rememeber I downloaded a pdf in category theory and after talking about classes it defined something called conglomerates, but I can't remember what that is and wikipedia has no article on it. ...
1
vote
1answer
65 views

Summer school software courses for middle and high school students?

I'm willing to teach some software for high school students next summer, I have chosen Mathematica. What other scientific software could I teach to high school students? (Matlab and Maple don't offer ...
9
votes
4answers
1k views

Learning math: still paper and pen

Is it, from an educational perspective, still sound advice to recommend people to use paper/a notebook (of the traditional sort, not the device) and pen/pencil? I wonder if computers are a ...
2
votes
1answer
172 views

Ideas for mathematics club

I am planing to suggest founding Mathematics Club in next fall. Here is my attempt for first prototype: -Sources: films(such as Dimensions), interactive stimulation for some mathematical ideas(like ...
13
votes
5answers
1k views

Areas of math that can be “gamified”?

My old high school math teacher has started up a math club recently. It's become quite popular (to my pleasant surprise), and I've been looking for ways to contribute. To that end I've been looking to ...
1
vote
0answers
38 views

Calculating Certainty Based Score in certainty based marking test

According to Tony Gardner-Medwin, the certainty based score (CBS) is expressed by the equation, CBS = ( (T-E)/(3N-E) )^p × 100%, where p = 0.4*(1+E/N) , E=expected no. correct by chance, T=Total of ...
4
votes
4answers
157 views

Resources to help an 8yo struggling with math

Friends of mine asked me for suggestion for one of their children (age 8) who had bad scores at the local Star test (the family is based in California). Both parents work, so they have also limited ...
4
votes
2answers
244 views

Why do Mean, Median, Mode, and Range present in school lessons?

I studied in East Europe and post Soviet mathematical education program have no Median, Mode, and Range terms. Mean (or average) on other hand was studied (with root mean square and sometimes with ...
19
votes
9answers
1k views

Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs?

It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little ...
5
votes
4answers
2k views

Self-teaching myself math from pre-calc and beyond.

Going to be starting grade 12 (pre-calculus) shortly and looking to get ahead. I would like to try some more rigorous stuff on my own and have a couple questions. Ideally I would like to be prepared ...
6
votes
1answer
140 views

The Value of a series

What is the value of the following series $\sum_{n=1}^\infty\sum_{m=1}^\infty\sum_{k=1}^\infty \frac{1}{mnk(m+n+k+1)}$
3
votes
2answers
140 views

How to construct a cube

My friend has asked me this question. I have no idea how to answer, but I think the question is interesting enough to be noted here: Consider 3 pieces of wire (not necessary of equal length). Is it ...
5
votes
7answers
345 views

Is there a name for this type of logical fallacy?

Consider a statement of the form: $A$ implies $B$, where $A$ and $B$ are true, but $B$ is not implied by $A$. Example: As $3$ is odd, $3$ is prime. In this case, it is true that $3$ is odd, and ...
2
votes
1answer
324 views

What textbook should I get to self-learn Calculus? [duplicate]

I did not have the option to take calculus during high school. I would like to pick up this subject during my free time. I am a software engineer. I would like to improve my understanding of maths. ...
5
votes
4answers
12k views

“Tricks” for solving the determinant of a matrix

I've got an exam coming up, and I'm worried that (as I usually tend to do) I will mess up with some minor algebraic calculation in a large problem like finding the determinant of a 4x4 or larger ...
8
votes
3answers
2k views

Reviews/comparison of Python vs Matlab for teaching Linear Algebra

I am wondering about advantages of using Python for teaching introductory linear algebra. I have been using Matlab and I became interested in Python mainly because of several resources, e.g., ...
0
votes
1answer
64 views

Why not number some definitions in Rudin's book?

I'm reading Rudin's Principle of Math Analysis Why some definitions about functions in Chapter 8, there are no the number marks, and the boldfaced words ...
1
vote
1answer
32 views

Is there any rules for choosing letters about $a,b, c$ and $t$, or $2t$

we know:ellipse is the locus of dynamic point whose distances from two fixed points’ sum is fixed value. so I write: $z$ is complex number, and $a,b,c,t$ are reals. $$\begin{align*}\left| ...
0
votes
1answer
128 views

Homogeneity Versus Heterogeneity in Student Groups

There is an overwhelming amount of research regarding homogeneous and heterogeneous grouping in education. The former refers to the practice of grouping "like" students together (regarding age, ...