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6
votes
3answers
83 views

Looking for a collaborative drawing solution

Preparing for a class I teach this summer and stumbled upon a technology problem. I want to show my students a graph, ask students to annotate it privately (eg mark mean on a histogram) and then ...
4
votes
2answers
79 views

Study multiple subjects at the same time or deep dive into one?

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense ...
-4
votes
0answers
22 views

Modulo operator operations [closed]

Ok so I have this equation ((M % a) % b)=((M % b) % a) where M is some positive integer. Now I need a equation something like <...
11
votes
7answers
8k views

Why should or shouldn't we teach functions to 15 year olds?

Background The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for ...
11
votes
13answers
891 views

Symmetry - practical uses

My girlfriend is studying to become a math teacher, and asked me what I have ever used symmetries for. I'm a web developer, and do some designing from time to time, so I answered that symmetry have ...
0
votes
2answers
119 views

manual solutions to graduate textbooks [closed]

Where can I find manual solution for textbooks like Advanced Linear Algebra by Rotman or Introduction to Smooth manifolds by Lee? any help would be appreciated
2
votes
2answers
204 views

Looking for rigorous books to review geometry, trig, and precalculus

I've taken Calculus 1 and it's time to relearn because I've forgotten some of it. But it's been a couple months since I've done any solid mathematics. I was hoping for a book that would include ...
10
votes
10answers
2k views

Should mathematical logic be included in a discrete mathematics course for computer science?

I am going to teach 2nd-year undergraduate students in applied math or computer science a course called "Discrete Mathematics for Computer Science". Most students who take this course plan ...
6
votes
6answers
424 views

Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
5
votes
2answers
474 views

Calculus limits taught in the US vs Spain?

So, I realize this can be a broad question, so I'll narrow it down. I have lived in Spain and own several Math textbooks from that country (the equivalent of 8th grade and high school Math). Has ...
23
votes
15answers
3k views

What books are like Knuth's Surreal Numbers?

I'm looking to find more examples of books which bridge the gap between "story" and "mathematics" using narrative and all those other wonderful features we might find in Harry Potter or some other ...
21
votes
8answers
6k views

How do I learn advanced mathematics without forgetting?

I am pursuing mathematics through distance education and I find that it takes me a long time to understand the concepts (e.g. sigma fields, measure theory, connected topological spaces, etc.). After I ...
2
votes
0answers
75 views

Locus of the maximal turning point and the point of inflection

Suppose you have a carton that has the form of a square with sides of length a. If we want to produce a box out of it whose height is x we might deduce the following formula: $$V_a(x)= x(a-2x)^2=a^2 x ...
34
votes
15answers
8k views

Justifications for: Why learn mathematics?

I wonder how you teachers walk the line between justifying mathematics because of its many—and sometimes surprising—applications, and justifying it as the study of one of the great ...
19
votes
4answers
190 views

How do you handle a wide ability range when delivering a 50 min tutorial with lots of material to get through?

So far I've tried building my presentation from elements, each of which is differently paced. A lot of tutorials are given just by rapidly writing fully worked solutions on the board, thereby leaving ...
3
votes
0answers
60 views

“Rough subitising / estimation” for better intuition and ability to apply arithmetic

tl;dr: Why do so many students have poor intuition of numbers, and what can be done about it? $$$$ I've always been good with numbers. As a maths tutor, one of the things I notice is how poor the ...
26
votes
5answers
649 views

Alternatives to University Lectures: Non-lecture Mathematics Classes

I am looking for resources for designing undergraduate mathematics classes that are not lecture-based. (Bonus points if the design is for an introduction to proof course). For example, Robert ...
5
votes
4answers
205 views

Showing applications of calculus to intro students

So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-...
5
votes
0answers
70 views

Converting an Online Course Back to In-Person

As I wrap up my Spring semester online courses, I'm starting to think about next Fall when (hopefully) our university will return to full in-person classes. Because of COVID, over the last year I have ...
18
votes
8answers
5k views

Children's counting problems: Is this question phrased correctly?

Look at the following example: Which picture has four apples? A B C D B is the expected answer but should not the correct answer be BCD? Technically if a set has exactly $m$ elements, then it ...
6
votes
4answers
503 views

Courses equivalent to College Algebra in other countries?

In USA, there is a course called College Algebra and a course description may look like the following: This course provides students an opportunity to gain algebraic knowledge needed in ...
82
votes
15answers
14k views

Should I design my exams to have time-pressure or not?

Is it better to design an exam with fewer questions and relaxed timing or with more questions and a resulting time-pressure? One the one hand, it seems that students who really know the stuff will ...
3
votes
0answers
144 views

Self study curriculum for a working professional who is enthusiastic about mathematics

I had some mathematics education during my high school and Electrical Engineering studies, but I never used any of them during my career as a software professional. Now I am again coming across Linear ...
4
votes
2answers
195 views

Geometric and Graphical perspective on completing the square

I just read an interesting article that helps to understand completing the square, and prove the quadratic equation from a geomterical perspective. My question is how do I understand the graphical ...
1
vote
1answer
214 views

Are there real life examples of normed vector spaces?

I'm trying to explain some basic concept to my kid (he just started learning basic algebra following Discovering Algebra: An Investigative Approach by Jerald Murdock ). For example homeomorphism means ...
2
votes
4answers
331 views

Is it necessary to teach the definition of a limit for engineering majors? [closed]

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...
7
votes
4answers
414 views

Statistics Class Held in a Computer Lab

I'm looking into holding my basic statistics class in a computer lab in the future to avoid a lot of the by-hand computing that happens in statistics classes. For example, very few students get ...
4
votes
0answers
71 views

Objectives for group work in undergraduate pure maths

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
3
votes
2answers
185 views

How to make an introductory course on Statistics interesting

I am going to teach this probability and statistics course in a couple of weeks. The probability part can be made very interesting, in my opinion, easily. But I am a little worried that I might make ...
1
vote
0answers
159 views

Resource request: 3-4 page review of exponentials and logs

I'm teaching a physics class that has a year of calculus as a prerequisite, but as so often happens, many of my students have forgotten a lot of the much more basic math from earlier classes. In ...
2
votes
1answer
131 views

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
18
votes
4answers
2k views

Computational topology for engineers

Increasingly, I see computational topology being applied to problems involving sensor networks, robotics, data analysis, signal processing and various other areas. The topics I mention are interesting ...
6
votes
2answers
263 views

When working with 12-16 year olds, how should I graph functions when the domain technically isn't $\mathbb{R}$?

Let us assume that I want to graph any of the functions below. A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy. Comment: One cannot ...
25
votes
5answers
7k views

How does a teacher come up with plausible wrong answers for multiple choice tests?

When taking a MOOC in calculus the exercises contain 5 options to select from. I then solve the question and select the option that matches my answer. Obviously only one of the options is correct. But ...
14
votes
3answers
2k views

How many of “The Seven Laws of Teaching” are still relevant for teaching maths today?

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...
-1
votes
2answers
160 views

What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
20
votes
5answers
3k views

Grating mathematical phrases---How to correct?

As mathematics educators, we all have come across students using mathematical notation incorrectly (looking at you, $\frac{d}{dx}$ vs $\frac{dy}{dx}$ or $\frac{\infty^2}{\infty}$). My question focuses ...
13
votes
4answers
273 views

Analyzing an answer to the following problem: Give meaning to $\frac{4}{5} + \frac{2}{3}$

Case: Exam Problem given to student at university: Give a problem/context illustrating the operation $\frac{4}{5} + \frac{2}{3}$ Answer by student: Anna and Beatrice buy flowers for grandpa for his ...
6
votes
7answers
3k views

How do you handle the frustration of having to GRADE student exams / homework?

A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs. Or - a student may just write an arbitrary step without ...
9
votes
3answers
480 views

Why is distribution prioritized over combining?

In every algebra (or basic analysis) book that I've seen, three properties of real numbers are taken as axiomatic: commutativity, association, and distribution of multiplication over addition [$a(b + ...
29
votes
11answers
3k views

What are the arguments for and against learning the multiplication table by heart?

I think, a lot of students are bothered by learning multiplication tables by heart, in particular when it comes to numbers greater than 10. Why should one learn (or not learn) these things by heart?
17
votes
4answers
3k views

How does the workload of a high-school mathematics teacher compare to a university-level instructor?

This question could be very broad, and so I'd like to make it more specific. In the United States, mathematics educators generally work in secondary education or college education (elementary school ...
7
votes
7answers
3k views

What is the preferred way to denote the Pythagorean theorem equation?

I am teaching 12-16 year olds. How should I write down the Pythagorean theorem equation? Some alternatives: $a^2 + b^2 = c^2$ $\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$ $\text{leg}_1^2 + \...
0
votes
1answer
205 views

in what sense is the subject of finite group theory 'algebraic'?

[cross posted from mse] the class of all finite groups is not closed under produtcs - example: the product over all finite cyclic groups - thus it is not a variety of algebras, ie, it's not ...
24
votes
5answers
2k views

Should we “program” calculus students, like the physicists seem to want us to?

If it is true that we first learn formalism...how to do things that we don't understand, should we regard teaching students mathematics as programming dumb machines with formal rules (to the greatest ...
6
votes
3answers
286 views

What is the purpose of “instant” tutoring?

I want to start by sharing my teaching philosophy: I believe in teaching in a way that is primarily student-centered. That is, I prefer to do less talking to give the student(s) more time to practice ...
7
votes
4answers
390 views

Source material to study number theory?

I don't know if this is the correct site to ask this question, but I felt it was off-topic on the Mathematics forum. I really like Number Theory and would like study some on my own. Which books should ...
28
votes
1answer
5k views

Which product of single digits do children usually get wrong?

(I was inspired by the comments in this answer to ask this question.) I have some multiplication table cards from Kumon that have a list of commonly mistaken multiplications: $7\times 8, 4\times 8, 11\...
7
votes
2answers
285 views

Phase shift vs. horizontal shift, and frequency vs. angular frequency in sinusoidal functions

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...
12
votes
5answers
632 views

About the effectiveness of self-studying maths (compared with other subjects)

An important feature of mathematics is that it is relatively easy (compare to many other subjects) to know whether or not one's understanding is correct. There are plenty of ways to check: one can ...

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