All Questions

1
vote
0answers
8 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 ...
1
vote
0answers
18 views

Topics in Mathematics for a 15 minute demonstration

I need to appear for an interview for the post of Assistant Professor in Mathematics in an undergraduate college. My Backgorund : I have studied topics like Algebra comprising of Group Theory,Ring ...
-1
votes
0answers
21 views

Where can I get a sample assessment brief for BTEC HN Engineering Unite 39 further mathematics (H/615/1507)

http://www.sbcs.edu.tt/wp-content/uploads/2017/07/Unit-39-Further-Mathematics.pdf I just want some questions to workout so I will be prepared for tests that cover these learning objectives.
7
votes
3answers
840 views

Is is a bad idea to use an old textbook such as Differential and integral calculus, with examples and applications for calculus course?

I am wondering if it is a bad idea to use an old textbook, such as Differential and integral calculus, with examples and applications by George A. Osborne. This book was published in 1906 and there ...
0
votes
0answers
39 views

Find unit price of each item given the total spent [on hold]

I am trying to help my daughter in her math and there is this question I can't quite get my head around, The sum is: Three friends go into a book shop. Salma buys a cook book and a novel, she pays \$...
2
votes
2answers
77 views

How to introduce Group Theory to a general audience in 15 minutes?

How to introduce Group Theory to a general audience in 15 minutes? I know that it will be quite tough to introduce Groups to a general audience in such a short time. So what will be a good way to ...
1
vote
3answers
206 views

Word for the dimension of the vector space in which a vector lives?

The following issue comes up whenever I teach linear algebra: I want to have a quick way to say that a vector $(x,y,z)$ is in $\mathbb{R}^3$. I am tempted to say that it has "length $3$". But then ...
6
votes
1answer
132 views

Structure of math textbooks

Math textbooks for undergraduate and graduate students are almost always structured in the same way. Each chapter/section/etc. has it's definitions, theorems, propositions, etc. with proofs following ...
11
votes
4answers
219 views

How to deal with “Why can't I just do …” in real analysis?

I'm teaching introductory real analysis at a large public university in the US. A common question from students is of the form "Why can't I just do it like this?". i.e. Often a student has come up ...
-2
votes
0answers
31 views

A 13-lot lottery game [closed]

A sports lottery game consists of 13 games. For each game, there are three alternatives: team A wins, team B wins or both teams tie. Who wins the 13 results. In addition, in each one of the 13 games, ...
8
votes
3answers
234 views

Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ — why?

I'm currently teaching a couple of courses that have a calculus prerequisite, and within the last week I've had two students make notational mistakes that amount to writing $y\frac{d}{dx}$ rather than ...
3
votes
5answers
175 views

How to make a student not look easy over mistakes such as the wrong sign

I am teaching entry calculus to a bunch of students outside class (more like complementary to their math classes, without making much connections) and I can teach on a much more individual level than ...
5
votes
2answers
156 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
0answers
173 views

Teaching methods to make a weak student good at math? (particularly student from social science background)

I am currently teaching a high-school student, 1st grade Social Science. He is weak in mathematics. My initial strategy was to explain basic concept but with high repetitions, so that he can have a ...
10
votes
3answers
211 views

Formats for Calculus instruction at different colleges and universities

In the comments under another question, a couple of people expressed interest in how Calculus is taught at the University of Michigan. I'm not convinced a question that narrow is appropriate for this ...
3
votes
0answers
90 views

A proof based Multivariable Calculus and Linear Algebra

May I know how can I teach a proof-based Multivariable Calculus and linear algebra as a single course? While there are quite a few known books in the field such as: 1) Vector Calculus, Linear Algebra ...
0
votes
2answers
87 views

Returning Student for STEM - Brush-Up Resources? [on hold]

All, I am hoping to wade into an Electrical Engineering or Mechanical Engineering degree, but I have been out of college for almost 10 years. My last major exposure to math was good grades in ...
5
votes
7answers
252 views

How to explain fractions to 7 year old kid

I am finding it difficult to convince my kid that 2/4 and 1/2 are same. As per the kid, 2/4 is more than 1/2 since in first case the boy gets 2 candies out of 4 and in second case he gets 1 candy out ...
9
votes
1answer
250 views

Is it the college teacher's responsibility to help the struggling students? [on hold]

I understand that at high school level or below, teachers usually spend extra effort helping those students who are struggling. However, how about at college/university level? Here are two ...
5
votes
2answers
113 views

Better ways to explain mutually exclusiveness and dependency of events

I am teaching probability on mutually exclusiveness and dependency of events. Let me take a simple example as follows. A box contains 2 red balls and 3 purple balls. They are identical except for ...
5
votes
1answer
114 views

For what subjects and grade levels is the take-home exam suitable?

I'm starting my job as a mathematics teacher in an intermediate school. I want to follow some new way of assessment and I'm really curious about take-home exams; are they suitable for any subjects? ...
2
votes
1answer
131 views

How can I explain horizontal shifts to a 12-year-old by analogizing with $\text{your money} = \text{my money} + 1?$

My 12-year-old cousin thinks this explanation is the most comprehensible, but she still can't relate the analogy with wealth inequality If I say ...
7
votes
4answers
131 views

Making physical 3D models

I was thinking to make classroom illustrations of some 3D mathematical objects, such as graphs of 2 variable functions, minimal surfaces, etc. My question is, what would be a good way to go about it? ...
7
votes
1answer
128 views

Flipped introductory real analysis resources?

I am going to teach a flipped real analysis class next term, using Abbott's book. Does anyone know of resources for such a class? I have found the article: "Flipping the Analysis Classroom" by ...
4
votes
2answers
239 views

Should young math students be taught an abstract concept of form?

Should a more general concept of the "form" of an equation or expression, be taught to math students as young as elementary school? I'm a fairly new tutor--do more experienced teachers think this ...
17
votes
2answers
2k views

Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found

Over the years I have occasionally encountered a number of Algebra 2 textbooks that make an incorrect (or at very least extremely misleading) claim along the lines that "all solutions of a polynomial ...
6
votes
1answer
126 views

Fun classroom exercise for mental rotation

I'm training to be a teacher and I am doing a maths lesson later next week. The topic is geometry, the students are 12-year-olds. More concretely, I've been given a selection of exercises that I may ...
1
vote
0answers
73 views

What are mathematical definitions? How are they decided upon? [closed]

What are mathematical definitions? When(at what stage) and how do mathematicians come up with the basic definitions of the new mathematical concepts they have found? I BELIEVE in math I BELIEVE it's ...
2
votes
1answer
94 views

Accessible written proof of the Nash Indifference Theorem (game theory)?

In game theory, the Nash Indifference Theorem states that if a mixed strategy $A$ is a best response to a mixed strategy $B$, then every pure strategy in the support of $A$ is also a best response to $...
25
votes
3answers
4k views

Difference between high school and college calculus courses

I am curious why students who take calculus in high school often do so poorly in college calculus. I am an instructor at an engineering college and I've noticed a decent number of students who have ...
4
votes
1answer
81 views

Making modular arithmetic interesting for school kids

This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later: $$\color{red}{\...
5
votes
2answers
149 views

Presenting ways to find a resultant force

To begin with I am working in a high school classroom where the students are working on the applications of vectors. The beginning of the lesson is about calculating direction and magnitude of vectors ...
4
votes
2answers
140 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
votes
1answer
114 views

Open Rings-First Abstract Algebra Text

Building off my own experience and the responses to "Rings before groups in abstract algebra?" I've decided to teach Abstract Algebra using a rings-first approach. However the various texts mentioned ...
6
votes
0answers
98 views

Is there any example of a “forwards/backwards” induction?

I like to make the "dominoes" analogy when I teach my students induction. I recently came across the following video: https://www.youtube.com/watch?v=-BTWiZ7CYoI In this video, a sequence of ...
7
votes
6answers
351 views

How to make students understand/remember that $x^2 = a$ has two solutions?

I teach math in university, in France. This semester I have first-year bachelor students. I am becoming increasingly annoyed that they cannot remember the simple fact that $x^2 = a$ has two solutions ...
11
votes
9answers
4k views

Why do inequalities flip signs? [closed]

Is there a mathematical reason (like a proof) of why this happens? You can do it with examples and it is 'intuitive.' But the proof of why this happens is never shown in pedagogy, we just warn ...
3
votes
0answers
120 views

How to explain angle hunting to students

$I$ is a point of the circle of diameter $JK$. The perpendicular bisector of $JK$ cut the semi-circle not containing $I$ at $M$. Let $N$ and $P$ be the orthogonal projections of $M$ on $IJ$ and $IP$. ...
2
votes
2answers
126 views

Line Integral Motivation

Is there a case to be made that the topic of line integrals should only involve vector fields? My colleagues and our textbook take the position that line integrals should only be taught from a vector ...
2
votes
0answers
103 views

Complex logarithm and $\mathbb{C}/2i\pi \mathbb{Z}$

Is it possible and is it a good idea to introduce the additive group and metric space $\mathbb{C}/2i\pi \mathbb{Z}$ very soon, at the same time as the complex logarithm $\log(r e^{i \theta}) = \ln(r)+...
4
votes
3answers
313 views

Advice on Full Time Community College Math Instructor Position

I have to do a teaching demo on the following: Please treat the committee as students in your Calculus II class. Please take 12-15 minutes to introduce your lesson on the Taylor Series and its ...
1
vote
1answer
142 views

About the word “limit” used in calculus

In the introduction of the limits chapter of a scholar book I can read (translated and abstract) the following examples: "the price of a product has a limit value that, from this price, the number of ...
11
votes
2answers
210 views

“Always/Sometimes/Never” vs. “True/False” questions for mathematical reasoning

Has anyone performed a study on the differences between student interpretations of these words? Background: When I taught high school geometry and later undergraduate precalculus, I noticed that ...
2
votes
0answers
94 views

I want to learn how things functions and work continue my life work

I am 37 years old and I have a mild learning difficulty. I never went to a special school, but yes, I got some help and I never got held back. I left my grades on borderline. I always loved to learn ...
2
votes
2answers
85 views

What are tutoring strategies for students struggling in math?

I am a tutor for a student and I work with him 7 days a week, for about 2-3 hours a day. The student severely struggles with math, although I am a tutor for every subject (he is in high school). His ...
7
votes
4answers
365 views

Is the constant term a coefficient?

I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term. That's not what's taught today. Current text books are vague on ...
1
vote
3answers
242 views

Is there a difference in the content taught at each university?

Say you have college A, B and C that are each ranked in the top 100 in the US News or other similar rankings. Admissions (SAT scores, GPA, et cetera) standards, quantitatively, rank A>B>C as the ...
3
votes
1answer
82 views

More intermediate steps or check well-understanding

I work as a math tutor mostly for talented high-school students that are passionate about mathematics and want to learn more of it beyond school programs. They are very smart kids, but I noticed that ...
2
votes
3answers
174 views

Math Anxiety get in the way of my Graduate School, I want to continue PhD

Probably it's just another advice-seeking CS student about math.. Well. I have math anxiety. Im a CS student, back then in undergrad I deal with code everyday, as long as my program work smoothly, i'm ...
4
votes
0answers
54 views

Formal linear combinations: motivating examples

I want to introduce formal linear combinations in an upper-level undergraduate combinatorics class. By this I mean expressions like $7 \operatorname{cat} + 5 \operatorname{dog} - \sqrt{2} \...

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