Questions tagged [teaching]

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2
votes
3answers
473 views

Rhombuses, kites etc

As a high school teacher, I sometimes wonder about the usefulness of certain topics. Some topics seem to be in the textbook because they have always been there, not because they lead anywhere ...
2
votes
3answers
275 views

Enlighten younger students about the concept of “procedural justice” in mathematics?

I am tutoring a 16-year-old student from my home country (in Asia) in, roughly speaking, precalculus. I would like to give him a feeling of procedural justice, so to speak, in modern mathematics, ...
3
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7answers
302 views

Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

A friend of mine that teaches math has made many times the following experiment : drawing two circles on the blackboard representing two sets A and B such that A and B are disjoint writing on the ...
6
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3answers
214 views

How to overcome the frustration in teaching and doing research at the same time

I understand that this website is designated particularly for teaching-related topics. However as many of us do agree that being a lecturer, we are supposed to run both teaching and research duties at ...
4
votes
6answers
3k views

How to convince students of the implication truth values? [duplicate]

How can I convince students that "P implies Q" is true when P is false, independent of what truth value Q takes? Is there any real life or a convincing argument for this? I have given the analogy ...
0
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0answers
123 views

What makes education in Finland so good?

This is a question more about education in general than math education but there is no general education Stack Exchange website so I decided to write this question here. If this question is more ...
8
votes
3answers
207 views

How to motivate students to do proofs?

I am finding it difficult to motivate students on why they should how to prove mathematical results. They learn them just to pass examinations but show no real interest or enthusiasm for this. How can ...
2
votes
1answer
127 views

Revision Lecture, what are the aims?

I will give a 2-hour long revision lecture on a Mathematics area. The aim of this lecture is to help the students prepare for the exam test. The course was rather long, covering 5 chapters and a ...
19
votes
6answers
2k views

Teaching indefinite integrals that require special-casing

I encountered the following concern when teaching indefinite integrals. I believe that many of us may overlook this. May I be wrong? Let's consider the following example. Find the indefinite ...
4
votes
2answers
204 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 ...
5
votes
3answers
173 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 ...
5
votes
1answer
146 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? ...
4
votes
2answers
839 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 ...
3
votes
1answer
91 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 ...
6
votes
4answers
429 views

Students understand during course but can't solve exam

I am teaching a math class where the students, most of them, tell me that they can understand the materials given by me during the course. I test them during the course too and they seem to get it. ...
3
votes
3answers
337 views

Teaching math by serving it as games with rules first, not intuition?

Just now I'm thinking a crazy reversed idea: Is it good to teach math to elementary students without starting from its real world motivation or making it intuitive first, but rather by realizing that ...
1
vote
1answer
110 views

Pythagorean triples

What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is ...
5
votes
3answers
162 views

CoTeaching Elementary Linear Algebra

I and my colleague will teach an elementary linear algebra next few weeks, but the way our course is planned mostly is by turn teaching. By that I mean, my partner will teach the first 8 weeks of the ...
9
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3answers
346 views

Integral calculus from the modern viewpoint

This is a soft question. What is the purpose of teaching techniques of integration at the college level? More specifically, in the sense of putting integration into practice, what value does ...
4
votes
1answer
78 views

One course/subject, one class, two lecturers

This is my first question here, so please correct me if I'm wrong in my way of asking. My question is suggested directly by the title. In my college institution, for each subject, half of the ...
5
votes
1answer
188 views

Should students teach other students?

I am interested in creating a curriculum that helps cultivate students abilities to teach one another. Specifically good one-on-one instruction includes elements like: Examples, Pictures, Humor, ...
2
votes
1answer
172 views

“Basic ideas” as a concept in teaching maths?

In Germany there exists a concept whose name might be translated as "basic ideas." The core of the concept is to offer the students an idea of what they are learning, e.g. in the context of ...
4
votes
3answers
215 views

Limit of questions that a student should ask in class without upsetting professor?

Days ago a professor told me to ask in class when I don't understand something and that he could keep explaining until it's clear for me. Being honest I'm a little slow to understand mathematics in ...
2
votes
2answers
126 views

Ideas for high-school proof class?

I have a math degree and have been hired to teach a proof class at a summer program. Our goal is to help the students learn the material they need for school (they take an algebra class separately) ...
5
votes
2answers
171 views

How to explain NP-hardness and NP-completeness to students

Computer science is becoming more and more important for mathematicians nowadays. Terms like big data, algorithm, artificial intelligence and others are frequently on the news. Many mathematical ...
4
votes
2answers
185 views

What is the ideal teaching style for Calculus exercises only?

A Calculus class for 1st year students may have two subclasses (with two different lecturers) : The main class (which covers the theories and concept), and the 'response' class (which provides and ...
10
votes
4answers
198 views

What are the best places online where math educators can discuss their experience?

As a math teacher I often experiment new things (for instance non obvious ways to use technology in the classroom, or new ways to teach something), and I think it would be useful if I could share my ...
9
votes
5answers
495 views

teach that $\frac10$ not defined properly

there're some students, who belive that $$\frac10 = \infty $$ I need to teach them that this is not true and $\frac10 $ is undefined, mathematically and give a good picture (for there minds) what ...
27
votes
10answers
8k views

How should a student's inefficient calculation be pointed out?

One time I watched a student solve the equation $0 = (x-2)^2-9$ for $x$ like this. $$\begin{align*} 0 &= (x-2)^2-9 \\0 &= (x^2-4x+4)-9 \\0 &= x^2-4x-5 \\0 &= (x+1)(x-...
5
votes
3answers
323 views

L'Hopital's Rule: Why do we need it?

I'm preparing a design/teaching experiment for my Curriculum Design Course right now. I've decided to cover L'Hopital's rule with a student I've been working with for a year, so skill wise he's ready ...
7
votes
2answers
166 views

Should basic exercises be solved before formulas are introduced?

I was watching (as a fellow teacher) a lecture on arithmetic progression. It so happened that a formula was rapidly introduced and used. The formula was $a_i = a_1 + (i-1)r$ (I trust the terms ...
4
votes
2answers
283 views

How to explain Chinese remainder theorem?

I want to explain Chinese remainder theorem to master level computer science students. There are two versions of CRT one is number theoretic and second requires the definition of ideals, groups etc. ...
12
votes
3answers
1k views

How to teach abstract algebra for the first time?

I am a Ph.D student in computer science. I am TAing one course this semester, which requires the basics of abstract algebra like rings, fields, ideals, and basic theorems about them. I have done two ...
7
votes
2answers
115 views

How can I get a better result making math videos with a tablet?

First question in this stack. Here it goes: So, I had this 2 or 3 year old intuos tablet and I said why not? And started doing my own videos. I've been making my own videos for my students last ...
4
votes
0answers
75 views

Research on how to teach math to children - what proven approaches are there to teaching math effectively? [closed]

I posted a related question on the Math.SE, but was directed here where I'm asking an similar but different question. I've been tasked with helping to redesign a math curriculum for an enrichment ...
4
votes
4answers
229 views

How to become a good teacher in the classroom when first starting to teach?

This semester is my first time to teach Calculus II in a classroom which contains around 25 students. (In fact, this is a discussion class.) I didn't have much experience about teaching. For instance, ...
1
vote
0answers
131 views

Is there an IGCSE maths question bank?

I've all the past paper , but I would like to know if there is any question bank. It may be helpful for the student in their preparation for the tests (if there is any)
7
votes
0answers
125 views

How can I deal with the time pressure of teaching a short course?

I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
14
votes
1answer
287 views

Addressing fundamental math errors

I am looking for ways I can correct fundamental math mistakes. I am currently tutoring someone taking a course which is a cross between first year calculus and grade 12 functions. In high school he ...
16
votes
6answers
554 views

Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\...
11
votes
4answers
590 views

What is most motivating way to introduce Fermat's Little Theorem

What is the best way to introduce Fermat’s Little Theorem (F$l$T) to students? What can I use as an opening paragraph which will motivate and have an impact on why students should learn this theorem ...
15
votes
5answers
574 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
1k 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
273 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
223 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
132 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^\...
10
votes
1answer
544 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
209 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
300 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
234 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 ...