Questions tagged [teaching]

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3
votes
4answers
271 views

Teaching calculus in AP without the limit definition

Years ago as a college freshman I was taking my first calculus course. Another freshman skipped it because he had calculus in Advanced Placement in high school. I mentioned we were learning the limit ...
1
vote
2answers
202 views

How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and $$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...
1
vote
5answers
228 views

Practical case for solving with system of 2 equations

When I teach basic math I want to emphasize on it's power (algebraic part for starters) as a tool for solving certain problems you cannot solve with naked brain, so that one models a problem with ...
4
votes
0answers
45 views

Looking for papers with teaching-oriented style

I am looking for papers that have the similar style to Hervé Lehning's 1989 The American Mathematical Monthly article "From Experimentation to Proof" (PDF link via lehning.eu). It's like ...
3
votes
1answer
146 views

Is there an arithmetic book similar to “Teach Your Child to Read in 100 Easy Lessons” by Siegfried Engelmann?

I have found Engelmann’s book (mentioned in subject) to be extremely effective. Is there an equivalent to this book for teaching Arithmetic? I believe the overall approach or method is called Direct ...
6
votes
4answers
219 views

What are other strategies for a 7 year old for addition and subtraction besides counting fingers?

We recently received feedback from our 7 year old daugther's school teacher. One of the things mentioned was that our daughter still counts her fingers when she does addition and subtraction. The ...
10
votes
2answers
458 views

Is there research to back up the claim that math classes help develop analytical skills?

When I teach math classes, one goal I have in mind is to help students develop the cluster of thinking skills usually called analytical skills or critical thinking skills. And I think that math ...
9
votes
4answers
3k views

The Future of Worksheets - will they still be used or abandoned?

I run a German website for mathematics education. We produce lessons, each of which contains various kinds of media, such as an introduction, videos, wikis, software, worksheets, and online tests. We ...
2
votes
3answers
195 views

How to evaluate students in a “do all you can” exercise?

Imagine a math problem that consists in doing all sum operations you can in 2 minutes. And then imagine these are the correct operations each student has done (each list entry represents a different ...
29
votes
17answers
7k views

How do I show students the Beauty of Mathematics?

I teach many high school students, and all of them complain about being unable to fully understand mathematical concepts. I try to show them the joy of learning and deepen their understanding through ...
3
votes
1answer
154 views

Why teaching undergraduate-level mathematics is so complicated? [closed]

Many of my professors are experts in their field, but they are just not able to teach. I mean: most of the times they are confusing, don't follow a logic sequence in their speech or keep a superior ...
4
votes
2answers
167 views

Resources for Learning Multiplication Facts

A recent question (@Namaste) made me realize that it would be good to pull together the best resources for learning the multiplication facts. When seen as a rote memory task, this can turn students ...
3
votes
2answers
319 views

How to teach linear programming and reductions?

Do you know any textbook with problems+solutions to support teaching of linear programming and reductions, and in particular, cover standard and slack forms, formulation of problems as linear programs,...
9
votes
1answer
711 views

How to (or should one) distinguish between lowercase and uppercase letters orally when lecturing?

I sometimes teach calculus in English whereas it's not my native language. For example, during a course about antiderivatives, how do you (orally) pronounce $f$ vs $F$? Which are the best? "the ...
1
vote
1answer
100 views

How to address opportunities for improvement with a teacher

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...
2
votes
2answers
187 views

Introductory exercise for the addition of large natural numbers

I'm starting a repetition with my students in 5th grade after they learned in elementary school how to sum up larger natural numbers (also 5- to 6-digits) by writing down that calculation. As ...
4
votes
2answers
117 views

Road map to teach undergrads a first course in real analysis that concludes with convergence of fourier series

I am planning to teach (unofficially, I am a Grad student) a course in real analysis. Aim of the course is to understand the convergence of Fourier series. I want to start with the notion of ...
8
votes
4answers
289 views

Examples of informal explanations that cause misconceptions

Every good teacher knows that giving an informal explanation (that is, an explanation not based on strict definitions and maybe making use of metaphors, intuition, or everyday language) of a ...
7
votes
3answers
285 views

Graph theory teaching materials for young students

Does anyone have any good sources to teach upper primary so grade 7 students basics on graph theory? The only ones I can find are for like upper middle school and high school, and having trouble ...
4
votes
4answers
650 views

Best Way to Learn Trigonometry

What are the best resources to learn trigometry? I recently decided to pursue a BS in mathematics at uni. I used to fail all my math classes with D's or F's until I started teaching myself, and so far ...
10
votes
1answer
2k views

Diagram of Methods to Solve Differential Equations

I am currently trying to build a flow chart to visualize all tests there are to tell whether an ordinary differential equation is solvable and how to solve it. This is for tutoring purposes. The ...
4
votes
4answers
556 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 ...
3
votes
2answers
382 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, ...
4
votes
7answers
352 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
votes
3answers
241 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 ...
9
votes
3answers
261 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 ...
3
votes
1answer
376 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 ...
20
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
1k 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
207 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
155 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
850 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
2answers
144 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 ...
7
votes
4answers
724 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. ...
4
votes
3answers
381 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
114 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
175 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
votes
3answers
366 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
83 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
197 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
180 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 ...
5
votes
3answers
317 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 ...
3
votes
2answers
147 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
199 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
219 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 ...
11
votes
4answers
209 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 ...
10
votes
3answers
408 views

How to teach Leibniz and Newton's notation

There has been many posts here and in MSE about different notations of differentiation. See for example this, this and this. However, those questions only deal with the common misunderstanding about ...
9
votes
6answers
584 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 ...
28
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-...