Questions tagged [teaching]

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How do you teach the order of a series of events?

I’m looking for research-backed methods for teaching which order a series of events are in. Notably, ordinality in my case is far more important than cardinality. Even better if the technique allows ...
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0 votes
2 answers
167 views

student doesn't bring a homework in a 1-to-1 class [closed]

What should a tutor do? I have students who even ask for homeworks, because they have desire for new knowledge in math. However, in my experience, most pupils hate mathematics. Should I ask their ...
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17 votes
6 answers
4k views

Do I really need to cover solids of revolution in my Calculus I class?

I will be teaching Calculus 1 soon, using Stewart's Calculus: Early Transcendentals as a reference. I can't help but recall my time in high school AP Calculus and my first semester undergraduate ...
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13 votes
16 answers
6k views

How does one tutor an A-level student past the derivative paradox?

Background: I am new to this site, but have 1500 reputation on the main Maths Stack. I am (age-wise) a secondary student of maths, but for a very long time have been informally learning at home and ...
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  • 241
2 votes
1 answer
160 views

How can maths assistants at a college be extra helpful for professors?

I am a maths graduate student. A little background: In the coming semester, I will be assisting a prof whom I admire and whom I also want to thank a lot, and I actually will have a lot of free time. ...
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6 votes
0 answers
86 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 ...
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5 votes
2 answers
324 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 ...
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4 votes
2 answers
105 views

Resources for teaching mathematical modeling to high school teachers

I am looking for resources for teaching math modeling to high school teachers with rusty math background. It will be a 6-week course. Some tips/directions on simple projects would be helpful. I would ...
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10 votes
2 answers
3k views

Why are all educational textbooks copyrighted? ©

I had an idea to improve education in my country with the help of textbooks by popular authors. I thought to publish videos on YouTube with comments and practical explanations about what the author ...
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5 votes
2 answers
237 views

What is the name of this teaching style?

I'm planning to teach a series of lessons on expanding and factoring binomials using a certain visual method for my edTPA assessment. Each lesson is pretty much going to be structured the same way in ...
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5 votes
1 answer
219 views

Sensible amount of repetition 7 year old

We are now in lock-down, so while homeschooling my son I get to se exactly what he does for math. He has been getting a huge amount of repetitive practicing of really simple math, despite being quite ...
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  • 53
1 vote
2 answers
231 views

Is playing and teaching chess appropriate in private lessons?

I am giving tutoring to a high school student since more than one year and half. He is about 17 years old. He has excellent results in mathematics, being best student in his class for the last year ...
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  • 113
3 votes
1 answer
490 views

How to explain the LCM algorithm to an 11 year old?

Tl;dr: I am trying to teach my sister how the LCM algorithm works but I just can't figure out how to explain it intuitively. The best explanation I can give is that you're trying to construct a number ...
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4 votes
4 answers
515 views

Teaching calculus in AP without the formal definition of the derivative

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 ...
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1 vote
2 answers
262 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\...
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1 vote
5 answers
273 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 ...
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  • 129
5 votes
0 answers
55 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 ...
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  • 151
3 votes
1 answer
390 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 ...
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6 votes
4 answers
288 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 ...
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  • 161
10 votes
2 answers
479 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 ...
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  • 483
9 votes
4 answers
4k 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 ...
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  • 219
2 votes
3 answers
210 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 ...
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  • 123
36 votes
18 answers
9k 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 ...
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  • 833
3 votes
1 answer
165 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 ...
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  • 59
4 votes
2 answers
189 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 ...
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  • 16.9k
3 votes
2 answers
351 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,...
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9 votes
1 answer
741 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 ...
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  • 273
1 vote
1 answer
106 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 ...
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2 votes
2 answers
191 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 ...
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  • 325
4 votes
2 answers
145 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 ...
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8 votes
4 answers
308 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 ...
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  • 559
7 votes
3 answers
681 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 ...
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4 votes
4 answers
1k 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 ...
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  • 496
11 votes
1 answer
3k 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 ...
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  • 113
3 votes
2 answers
402 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, ...
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  • 147
5 votes
7 answers
380 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 ...
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6 votes
3 answers
256 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 ...
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  • 377
4 votes
6 answers
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 ...
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  • 1,225
9 votes
3 answers
308 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 ...
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  • 1,225
3 votes
1 answer
691 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 ...
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  • 39
20 votes
6 answers
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 ...
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  • 377
4 votes
2 answers
3k 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 ...
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6 votes
3 answers
466 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 ...
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5 votes
1 answer
176 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? ...
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  • 151
4 votes
2 answers
873 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 ...
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3 votes
2 answers
171 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 ...
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7 votes
4 answers
2k 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. ...
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  • 307
4 votes
3 answers
418 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 ...
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  • 307
1 vote
1 answer
123 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 ...
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  • 1,225
5 votes
3 answers
189 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 ...
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  • 307