Questions tagged [teaching]

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15
votes
5answers
593 views

How should I introduce the concept of a function to a precalculus student?

My brother has not taken a math class in $10-15$ years. He is studying for the GRE so I have been teaching him a chapter or two from my precalculus book. So far, he has learned (and excelled at) basic ...
9
votes
6answers
2k views

Greatest common divisor applications

What are some real-life applications of gcd? I am looking for a motivating way of introducing this topic in an elementary number theory course.
5
votes
3answers
276 views

How to teach to draw graphs of quadratic equations without knowing calculus?

In the country I'm living we learn how to draw the graph of quadratic equations such as $y=x^2$ or $y=x^2+5x+3$ before knowing calculus (in fact we don't even learn calculus until we begin the ...
13
votes
3answers
234 views

Repeating basic material in exercise class at university

I am a teaching assistant in mathematics at a university in Continental Europe. The course for which I am an assistant is a third year course, so usually the students are expected to know the basic ...
5
votes
2answers
137 views

At what educational stage are angles greater than 180 introduced?

Prompted by the question, "How to denote angle?," I am interested to learn when students consider and reason with angles $> 180^\circ$. For example, when do they reason with an angle of $270^\...
11
votes
1answer
627 views

How to denote angle?

I'm teaching mathematics on my free time for young pupils. Once I have seen that they denote angles like $\angle ABC$. But sometimes I have difficulties to understand whether they mean an angle or its ...
3
votes
1answer
211 views

How to ask a student a question to get the answer '…integer not continuous…'

Context: a very basic level statistics package computer lab. A scatter plot is produced for one integer variable versus another integer variable. The students are asked why the points form a grid ...
6
votes
3answers
351 views

Is there a more intuitive way to solve combined rates of work problems?

I am helping my brother study for the GRE and we have come across some problems like this in my old precalculus textbook: 1) Karen and Betty have been hired to pain a house. Working together, they ...
8
votes
3answers
246 views

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of: notes written during the lecture ...
33
votes
13answers
15k views

Why do we teach complex numbers?

In algebra II, USA, we teach our students complex numbers. However, after algebra II, they never use complex numbers until pretty much complex analysis. The whole point of teaching them complex ...
5
votes
1answer
639 views

Is the current education system as bad as most critics and famous pure mathematicians try to convey? [closed]

Throughout elementary, middle and high school mathematics is quite merely about memorizing concepts and formulas, understanding the theorems (without their proofs) and applying acquired knowledge in ...
2
votes
0answers
176 views

Core-Plus Mathematics: Similar Resources for grades 7-9

I'm looking for rich educational resources similar to core-plus mathematics, for grades 7, 8, and 9. Is there any such material?
1
vote
3answers
90 views

Determining sets to show sufficiency of a condition?

$p \to q$ that means (among others) $p$ is a sufficient condition for $q$. To show the sufficiency, I teach my study by determining the set for $p$, the set for $q$ first and comparing their ...
4
votes
2answers
4k views

Notation of line segment and its length

I have sometimes seen a notation where $AB$ could mean either the line segment or its length. Why do the same notation can be mean both? Should one teach pupils to use for example notation $d(A,B)$ or ...
2
votes
0answers
83 views

What should I teach 13 to 15 years old pupils to learn competition mathematics? [closed]

I would like to teach some young and talented pupils basics of competition mathematics. What kind of methods, topics and theorems should I teach to those who are good at school mathematics but have no ...
15
votes
6answers
811 views

What is a better way to explain these claims about limit are not true in general?

As a TA who led calculus* 1 and 2 discussion section and holds office hour** in the previous year, I heard the following (wrong) arguments several times. $\displaystyle \lim_{x\to \infty} \sqrt{...
3
votes
2answers
1k views

Teaching Models for Mathematics (like 5 E's in Science)

I want to find and know about teaching models in mathematics. There's such a model for teaching science: the 5 E's model: Any suggestion (books, references, etc.) would be greatly appreciated.
4
votes
2answers
528 views

Why “plug in numbers” when solving inequality?

Let me use this example, Solve $x^3-4x>0$ After factorization, we have $$(x+2)x(x-2)>0$$, in order to have product of several numbers positive, even(0,2,4,...) of them have to be negative ...
13
votes
3answers
956 views

Is it better to provide students with guided notes or to have them write their own notes, or both?

When I taught calculus, I posted my notes after the lecture. Then I had the students fill out a mid-quarter evaluation, and a lot of them wanted me to post my notes before class. What I started ...
11
votes
3answers
649 views

Teaching algebra to visually impaired or blind students

I am currently writing an independent project investigating the teaching and learning of algebra for students with a visual impairment. I am struggling to find literature specifically about teaching ...
7
votes
3answers
192 views

References for graduate education

A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate ...
15
votes
7answers
3k views

Students strictly follow the steps and notations in sample problems without understanding them

It's just an observation, but I'll be highly appreciated if anyone with experience in teaching (or TA-ing) lower-division calculus can explain this phenomenon in detail. I'm one of a TAs who's ...
10
votes
2answers
263 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
8
votes
4answers
400 views

Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
11
votes
1answer
218 views

How can I be more prolific as a maths teacher with my visual handicap?

I have a chronic visual handicap and am in need of adequate level of accessibility support while learning and teaching mathematics from and to the visually challenged as well as the sighted. I'm ...
13
votes
4answers
889 views

As a TA, how to reduce imprecise notations/statements in students' exams

I'm not a course instructor, just a TA of the first quarter calculus course who lead discussion sections and grade exams. When grading the midterm, I found large number of students showed some ...
3
votes
0answers
47 views

clasification of teaching licensures and certifications particularly for teacher-students

There is a lot of certification and licensure tests for teaching (math and etc) particularly for teachers and teacher-students (PACT, Praxis & PPAT, edTPA, RESA, ... in US and TAT in India and etc)...
8
votes
1answer
590 views

Should $\varphi$ be monotone in the integration by substitution?

I'm trying to calculate $$\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\sin t \cos^3 t\,dt$$ using integration by substitution $$\int_{\varphi([a;b])} f(x)dx=\int_{[a;b]} f\left(\varphi(t)\right)|\varphi'(t)|...
6
votes
4answers
2k views

Why convert to sums of two squares?

Why bother writing a given integer as the sum of two squares? Does this have any practical application? Is there an introduction on a first year number theory course which would motivate students to ...