All Questions
3,687
questions
15
votes
5
answers
2k
views
How to deal with answers containing completely off-topic/random/very wrong arguments?
It often happens that students answer (partly) a questions in an exam (lets assume this part is okay), but then add something completely off-topic or something very wrong in their answer (see examples ...
- 9,388
21
votes
5
answers
8k
views
What is a method you use to handle the students who thinks they "know it all"?
This is a typical problem in my undergraduate Calculus I class. Many of these freshmen come in having made an A in their High-School Calculus class, and believe they know everything they need to ...
- 1,208
14
votes
4
answers
2k
views
What is a wise reaction to a silly question?
I like students' nice questions too much (sometimes much more than their nice answers). It shows that they are thinking on what I am teaching and I am successful to make them curious about the subject....
user230
17
votes
8
answers
3k
views
What to do when your students are all getting A's
Now, the title of the question definitely needs some background!
In some courses, everyone can get an A and it's no problem (especially later grad courses).
However, many times it is good to have a ...
- 11.7k
10
votes
2
answers
165
views
How does an advisor effectively motivate progress on an independent project?
When an excellent student is working on an honors or independent study project, the advisor's job is to not only serve as the content expert, but also to motivate the student to complete the project.
...
- 21.1k
10
votes
4
answers
286
views
Problems sets for instruction
What resources are available for any grade level K- 12 that are aligned with the Common Core Mathematics Standards and Mathematical Practices that have sets of problems or problem banks that can be ...
- 161
12
votes
1
answer
330
views
Probability textbooks repository
(This question was posted more than two years ago on math.stackexchange.com and, although there were some worthwhile answers, none actually answered the question as phrased.)
Has anyone compiled a ...
- 1,690
19
votes
5
answers
999
views
How to nurture a good student?
When you encounter a very bright student in a first-year (college/university) class (and who is therefore bored), what do you do?
Leaving them to their own devices can be problematic. It can lead to ...
- 1,530
86
votes
15
answers
16k
views
Should I design my exams to have time-pressure or not?
Is it better to design an exam with fewer questions and relaxed timing or with more questions and a resulting time-pressure?
One the one hand, it seems that students who really know the stuff will ...
- 4,086
19
votes
3
answers
1k
views
What is Discovery-Learning, and why is it so controversial?
In my home province Discovery Learning is getting a substantial amount of pushback.
I've been trying to follow the discussions, but have been struggling because I can't seem to get a clear answer as ...
- 291
10
votes
4
answers
1k
views
Examples of Good Mathematical Games for a Mathematical Olympic
As a crazy idea in a coffee break after a boring lecture I suggested my students and colleges that we can have some fun in our department by participating in a "Mathematical Olympic Games". They ...
user230
8
votes
4
answers
510
views
Examples of Research Level Math Discoveries Done by Undergraduate Students
A good way for motivating young students in undergraduate level is telling them that you can do great works!
Question. What are good examples of research level mathematical discoveries done by ...
user230
14
votes
5
answers
778
views
Community College Remedial Mathematics difficulties for students
I've been teaching remedial mathematics for the better part of a decade, and I've noticed a big trend in my classes lately. Many of my students are able to grasp the more complex ideas but still ...
- 3,646
6
votes
3
answers
604
views
Which one is more natural, empty set or set of all sets? [closed]
In a "foundations of math" undergraduate course when I was talking about the axioms of set theory I said: "Well! The most trivial example of a set is a set which has no elements we call it the empty ...
user230
19
votes
12
answers
2k
views
Mathematical problems for preschoolers
What are some mathematical problems that are feasible for preschool children to stimulate their intellectual development?
There are multiple natural laws that are not apparent to them, for example:
...
- 8,907
5
votes
2
answers
113
views
How are secondary-education mathematics jobs advertised in the United States?
A large portion of 4-year university mathematics jobs are advertised on mathjobs.org.
Is there a similar, centralized location for secondary education mathematics jobs? If not, what are the standard ...
- 11.7k
24
votes
5
answers
557
views
Any support for mathematical "learning types?"
Back when I was an undergrad calculus TA, I participated in a general TA training class. We were taught to be mindful of different "learning types," such as visual learners, audio learners, and ...
- 2,165
21
votes
9
answers
2k
views
Why do students have problems with showing that something is well-defined? How can this be improved?
I see a lot of students struggling when they have to show that something is well-defined. I have the feeling that this is often not understood.
Two examples:
When defining a sequence $x_n= g(x_{n-1}...
- 9,388
4
votes
1
answer
130
views
Would chapter mini-projects be more beneficial than weekly homework for large classes n>100
I am trying something new this semester in my Calculus classes. I currently have over 400 students, and there is no way I can find the time to grade and give constructive criticism on all the ...
- 1,208
2
votes
2
answers
66
views
Psychological and Sociological Researches on Teaching [closed]
Teaching is a social activity and very sensitive to any change in social parameters. Even the simplest acts of a teacher could cause some positive/negative reactions of students and conversely. Each ...
user230
12
votes
2
answers
432
views
How to test knowledge on the real numbers in a written exam?
In German universities, the first-year students typically start their analysis courses with introducing the real numbers. Most commonly, the incompleteness of $\mathbb{Q}$ is discussed using the ...
- 4,781
10
votes
2
answers
232
views
When to encourage students to read mathematical literature written in English (in non-English speaking countries)?
There is a lot of mathematical literature in some non-English languages (French, German, Spanish, etc.) that students from these countries don't need to read English literature (at least) for their ...
- 9,388
4
votes
2
answers
75
views
Historical Development vs Official Development
In some cases the historical development of a mathematical subject/tool is not straightforward. Mathematicians define a particular notion and work in an accepted direction. After a while they come ...
user230
17
votes
4
answers
2k
views
Surprising examples of Cavalieri's principle
I showed my calculus students two circular cones with the same base and height, but one of them "right" and the other slanted, and asked which had a greater volume. They all answered correctly that ...
- 6,520
20
votes
5
answers
612
views
Making standards for "showing work" explicitly clear to students
I do not mean for this thread to be a discussion of whether or not students should show work on an exam, whether they should be docked points for just "seeing" an answer and writing it down, whether ...
- 10.7k
61
votes
4
answers
6k
views
Is it worth grading calculus homework?
I am a young math educator. I've TAed four semesters of calculus for various instructors. Some instructors have required me to grade selected problems in homework sets. Another required me simply to ...
- 852
15
votes
1
answer
4k
views
What experimental studies have been done on the Kumon method of teaching and learning mathematics?
My dissertation involved, among other things, the East Asian way of teaching and learning mathematics. (See, for example, Leung (2001).) I was particularly interested in the Kumon method. Although I ...
- 10.8k
35
votes
3
answers
4k
views
What happened to the Moore method?
I always read about the Moore method with great enthusiasm. Somehow I always felt that it should be how we do it in an ideal world, but it is impossible to use because of time and other constrains.
...
- 4,229
18
votes
3
answers
271
views
How can creativity be incorporated into elementary school mathematics?
Creativity is the core of research mathematics. However, most introductory math consists of learning fixed rules to perform basic, essential mathematics.
Thus, for many elementary school students, ...
- 11.7k
10
votes
2
answers
343
views
Quotations of Great Mathematicians as a Source of Inspiration for Young Students
I like using quotations of great mathematicians as a source of inspiration for young students. I think even a short sentence could have a great influence on forming their research interests and point ...
user230
21
votes
13
answers
1k
views
How can I familiarize elementary school students with infinities larger than $\aleph_0$?
Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as ...
user230
19
votes
15
answers
1k
views
What is fairly new theorem one can teach (and prove) to an undergraduate student?
Many students complain about how old the things in mathematics are. When students finish their undergraduate studies, there are usually not able to state results and prove them which were found after ...
- 9,388
5
votes
2
answers
160
views
How can one deal with classes split up (in terms of previous knowledge)?
Imagine a class which is split completey regarding previous knowledge which is in some way needed for the class.
How can you deal with such a class? How can you - without giving too much workload to ...
- 9,388
14
votes
4
answers
1k
views
What should I do with kissing problem?
There are two young lovers in one of my crowded calculus classes. Sometimes when I am explaining an idea I see they are kissing each other and some of the other students are watching them and pay no ...
user230
14
votes
2
answers
239
views
How shall we use online math forums such as math.SE in mathematics instruction?
What is the best way to use online mathematics forums, such as mathematics.stackexchange.com or Khan Academy, in mathematics instruction?
I regularly encourage my undergraduate students to ...
- 4,086
17
votes
3
answers
328
views
Teaching a class you never took
How can you design an adequate course for a subject you never formally had classes?
This is similar to teaching somebody else's class.
As an example, suppose you are an algebraic geometer and you ...
- 3,030
9
votes
3
answers
179
views
Motivating student by showing them where we are heading to
Why is it so uncommon to find material that shows students how everything is connected?
A recurrent question from students is why are polynomial so important? If we shown them how these are related ...
- 237
9
votes
2
answers
2k
views
How does a take-home exam differ from a homework assignment?
I've taught several upper-level courses recently, and have considered giving take-home exams to reduce the time pressure in the classroom.
However, their homework already consists of proving various ...
- 11.7k
30
votes
9
answers
5k
views
Teaching by Slides, Yes or No?
Mathematicians use (Powerpoint/Beamer) slides for their lectures. My question is about using slides for teaching math. There are several positive and negative arguments about teaching by slide show. e....
user230
11
votes
4
answers
439
views
How can I encourage my students to team work?
I have a motto, "My class is not an Olympic swimming pool! It is a museum full of the masterwork paintings! Relax and enjoy all of this mathematical beauty which I am drawing on the blackboard!"
By ...
user230
24
votes
6
answers
2k
views
What are some good rules for handling student questions during exams?
For example, I gave an exam earlier today with a problem that ended in the sentence
Use the chain rule to find $(f\circ g)'(3)$.
During the exam, one of the students asked me what the circle ...
- 8,189
16
votes
5
answers
1k
views
Is Peer Instruction suited to mathematics classroom?
Peer Instruction is a method developed by Eric Mazur in Harvard, designed with a student-centered approach in mind. In a nutshell, the core of the method is that when presented with a problem, ...
- 3,030
26
votes
9
answers
2k
views
How can mathematics educators encourage innovation and creativity?
Almost by definition, innovation requires that things be done differently than established custom has it, and comes from the young more often than from the old.
In a field as old and established as ...
- 1,755
11
votes
4
answers
665
views
Example for a theorem where the (more) formal proof is easier than other argumentation (e.g. imagination)
When students ask me for the use of the formal and abstract theory, I often would like to give answers they wouldn't understand. For instance, one application of abstract vector spaces and the banach ...
- 4,781
7
votes
2
answers
1k
views
How do I become a Scarer?
Racism is not an easy subject to talk about so let me to explain my question by a more soft example.
This question originally belongs to Michael Wazowski an undergraduate student of the Monsters ...
user230
38
votes
10
answers
2k
views
Reasons for (not) distinguishing $f$ from $f(x)$
Formally, if $f$ is a function, $f(x)$ is a value. So for instance, $f$ can be continuous, but not $f(x)$.
In teaching at school and university, notation is quite often mixed up, e.g. the function is ...
- 4,781
15
votes
3
answers
1k
views
How should I deal with overenthusastic students?
This is sort of an opposite question to keeping quicker students engaged?.
Sometimes I encounter students who are overenthusiastic about the course; they're constantly moving faster than the rest of ...
user37
14
votes
4
answers
2k
views
What are effective alternatives to a written math exam to evaluate knowledge?
Some students do not do well under pressure or testing situations and cannot demonstrate their knowledge of a math subject with a written exam. On the other hand, I think that students that do not ...
- 1,430
13
votes
2
answers
239
views
How to create and support a mathematics club or group that will last?
Math clubs and groups tend to be small and prone to dying out. Once the organizers or members graduate, the club no longer exists.
At my university, I have seen the creation and death of two ...
- 1,430
10
votes
1
answer
228
views
Can math movies help us in teaching?
There are many cinematic and documentary movies about mathematics and mathematicians in every field of mathematics. Particularly in logic, set theory and philosophy of mathematics, which are my ...
user230