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2
votes
0answers
59 views

Looking for an educational game from long ago, possibly called Mother Goose

OK so this is really old school. Back in the 1980s, as a latchkey kid, I played on the computers in the library in elementary and middle school. There was this one bizarre educational game that I'd ...
4
votes
2answers
576 views

How to test student's skills in programming or using software?

I am going to teach an undergraduate statistics course next year. My plan is to spend less time on theory and a more time on teaching students to doing some statistics on computer. However, this ...
-2
votes
0answers
34 views

Does the row space contains everything orthogonal to the nullspace in linear algebra? [closed]

Does the row space contains everything orthogonal to the nullspace in linear algebra? In chapter3 of Gilbert Strang's linear algebra and its applications (4th edition) ,about orthogonal vectors and ...
7
votes
3answers
205 views

Example of why proof by exhaustion is inelegant

There's a nice example of why people dislike proof by exhaustion on the Wikipedia page. The problem statement is "prove that all years in which the Modern Olympics are held are divisible by 4&...
6
votes
3answers
292 views

What's a good notation to show elements of relation composition?

Teaching discrete mathematics, we pose (from the textbook) questions on finding compositions of relations, notably, relations on very small finite sets with only 3 or 4 elements (as an introductory ...
-4
votes
0answers
29 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 <...
4
votes
2answers
116 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 ...
7
votes
3answers
146 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 ...
0
votes
2answers
125 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
5
votes
2answers
486 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 ...
2
votes
0answers
76 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 ...
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 ...
3
votes
0answers
63 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 ...
6
votes
6answers
463 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
0answers
71 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 ...
1
vote
1answer
223 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 ...
5
votes
4answers
209 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-...
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 ...
4
votes
0answers
72 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 ...
2
votes
4answers
333 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 ...
4
votes
2answers
197 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 ...
2
votes
2answers
213 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 ...
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 ...
3
votes
2answers
187 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 ...
6
votes
2answers
267 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 ...
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 ...
13
votes
4answers
278 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 ...
15
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; ...
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,...
-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 ...
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 ...
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 ...
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 + \...
3
votes
1answer
65 views

simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...
6
votes
3answers
288 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 ...
1
vote
2answers
183 views

Should I do all the proof practice problems in How to Prove It, an intro to proofs book?

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
4
votes
7answers
271 views

Should I avoid writing: $ 11:40 - 15 \text{ min} = 11:25$, and what are alternatives to this way of writing?

I want to stress to my students that we should be careful with how we treat the equals sign and that we should always make sure that the units match. However, sometimes I write $ 11:40 - 15 \text{ min}...
3
votes
0answers
143 views

Parkour and Mathematical Practice?

Learning mathematics and learning parkour seem to have a lot in common. Both can be done on varying levels, but to progress in either one needs to overlearn and build basic skills so that these skills ...
5
votes
1answer
111 views

Students reliant on answers provided, but not their own reasoning?

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students ...
7
votes
2answers
286 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 ...
6
votes
1answer
421 views

“Flipped classroom exercises” resources

I was reading this book: "Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq In the preface, the author explains of his "flipped classroom ...
0
votes
1answer
153 views

Matriculation exams like in Europe

I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own ...
5
votes
7answers
636 views

What is a good second book in high school geometry?

I have been looking at questions on Math Stack Exchange and I am frequently coming across topics that sound as if they could have been optional chapters in a high school geometry class, but I have ...
1
vote
1answer
180 views

Did Americans, before new math came in to schools, really say, 'three from two is nine carry the one", instead of borrowing ten from the tens column?

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one'. I never heard of this ...
7
votes
1answer
884 views

How to be a good math teacher at a liberal art college?

I am thinking of taking up a position at a liberal art college. I have taught mathematics at large public universities but I have no idea what is it like to work at a liberal art colleges. So what are ...
5
votes
2answers
201 views

Why are most college level math textbooks black and white only?

Why are higher level math textbooks almost completely black and white? I can't think of any math textbooks on a subject more advanced than calculus that uses colors. Edited to add that the comments by ...
15
votes
2answers
193 views

Tension between the most intuitive definition vs. the most common definition of a concept

Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated. For example, the definition of a relation ...
22
votes
7answers
3k views

How do you coach students who often make small errors?

Some students are prone to making small calculation errors. Not errors in understanding, but errors like adding or multiplying integers incorrectly, or dropping a negative sign. Unsystematic errors in ...
8
votes
1answer
323 views

Grade on proving |$a_1 +a_2+…+a_n| \le |a_1|+|a_2|+… +|a_n|$

In an Advanced Calculus course, students were asked to prove $$|a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$$ for $n$ real numbers $a_1,a_2,...a_n$ I am teaching assistant for this course, and one of ...
1
vote
0answers
57 views

Understanding Modular Arithmetic [closed]

Mathematics Educators. I'm having a difficult time understanding modular arithmetic (particularly its applications for proof writing). I understand very well the basics. I know that $a\equiv b \pmod n$...

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