All Questions
3,428
questions
-2
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0
answers
42
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Mathematician or not [closed]
I'm from India here education system is quite different. Students are not interested to ask why? I took maths for B.Sc, at that time I realized I need to understand maths alot. It drained my time. ...
2
votes
0
answers
64
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when dealing with sequences, should we teach students to start at 0 or 1?
the reason I prefer starting at 0 is due to a computer science background and also, I think it helps to start at 0 because there are certain reasons that demand it (in particular the combinatorics) ...
- 797
4
votes
4
answers
1k
views
Point Deductions - Exams and Quizzes
With regard to an undergraduate statistics course, I am developing a standardized list of point deductions with the TAs (doctoral students) so that graders are consistent in what they are taking off ...
- 143
5
votes
0
answers
97
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Online math quiz: students make short video explaining solution
I am teaching high school math. My students are generally hardworking and competent. Class sizes are about 35.
We were recently forced online due to the pandemic, and I have been searching for a way ...
- 209
1
vote
0
answers
61
views
What is the text for "the other second-term course in analysis at MIT?"
My question comes from first few paragraphs of preface of "Analysis on Manifolds" by James R. Munkres, as excerpted below:
A year-long course in real analysis is an essential part of the
...
- 11
3
votes
6
answers
913
views
Is this motivation for the concept of a limit a good one?
tldr: There is a simple intuitive definition of a limit for monotone sequences, and I suggest that it can be used to motivate the (more complicated) standard definition. I am asking for feedback on my ...
- 419
5
votes
0
answers
58
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Potential topics for a university level mathematical thinking module
Social science training typically involves statistics as equivalent to "quantitative methods", particularly statistical modelling but also some material about data quality and exploratory ...
- 151
10
votes
1
answer
118
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How to explain the concept "Without loss of generality" (through examples)?
This is not a precise question. I am curious to know how do you present to your students the (imprecise) concept of "without loss of generality", and how to use it correctly/incorrectly.
I ...
- 419
8
votes
3
answers
173
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Encouraging students to see value in things that can't be measured
It's very tempting for a student who is overly excited about mathematics to discount intellectual work in other fields, particularly the humanities, where the nature of knowledge and knowledge ...
- 2,657
2
votes
0
answers
115
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Split in pedagogy of propositional logic
In some sources where I read about propositional logic, it is shown that the propositions come with a truth value baked into the sentence. In other books, it is said that the truth value a proposition ...
5
votes
8
answers
8k
views
What do you do in order to drag out lectures?
I posted earlier about how I was surprised that a typical Calculus 1 course that meets 3-4 hours each week for 15 weeks only barely manages to reach the fundamental theorem by the end of the course. ...
- 105
2
votes
1
answer
497
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Help needed to find 7th & 8th grade completed math samples
I am trying to find samples of completed homework, class work and tests for 7th and 8th grade math in the US. I can find a million blank workbooks but not copies that students have completed with ...
- 29
1
vote
2
answers
611
views
Why can't students master math simply by passive reading?
Yearly, at least one student emails me this question, after wholly relying on passive reading then failing the exam. They successfully remember and can regurgitate everything from the textbook and ...
- 165
0
votes
3
answers
222
views
To improve in math, why precisely do students need to solve problems, unlike driving that AI cannot do?
Too many parents ask me why students need to work and struggle on exercises to succeed at math — like end of chapter questions in textbooks, and problem sets. Bewildered, they analogize to some ...
- 165
4
votes
1
answer
155
views
Why is there variation in the meaning of "Standard form" for a quadratic?
I'm teaching this year out of "Precalculus with limits" by Ron Larson [7th ed], and the following expression appears in the unit introducing polynomial functions:
$f(x)=a{(x-h)}^2+k$
He ...
- 379
6
votes
3
answers
925
views
Geometry in the Community College Curriculum
As many Americans know, the “traditional” high school sequence is:
Algebra 1
Geometry
Algebra 2
PreCalculus
Calculus
For those who take developmental education at the community college level, it ...
- 339
3
votes
2
answers
1k
views
What is a good pacing for a Calculus 1 undergraduate course?
I am going to teach a Calculus 1 course next semester, and I have 15 weeks for the course material. The class meets MWF for 50 minutes each. I have taught this class before using the same syllabus, ...
- 105
2
votes
2
answers
280
views
What age student should be able to answer this question?
I was having a conversation about math education in the USA. Would an excellent middle school student, high school student, or college freshman be able to answer this simple question:
Exercise 0 If $...
- 121
2
votes
0
answers
109
views
What do you use to make your course materials?
I'm a second year teacher teaching Precal for the first time.
I have a few textbooks, but the problem is that my school does not (and will never) have class sets of any of them for students to use.
To ...
- 167
9
votes
4
answers
6k
views
How can a teacher help a student who has internalized mistakes?
John is trying to learn some field of mathematics. John's teacher Sarah gives constructive criticism to John after seeing John's attempts on exercises related to the field he studies. Later, John ...
4
votes
2
answers
519
views
What other mathematicians have advocated for freely publicizing detailed solutions, to every exercise?
Besides the 2 mathematicians quoted below and me, who else has touted free dissemination to students of detailed solutions, to EVERY exercise and problem (like in textbooks)? I uphold this ...
- 165
5
votes
4
answers
393
views
Why don't exercises ask readers to discover results themselves, before requiring proof? Why disclose the result in the question?
How can students learn to discover results themselves, if textbooks just spoonfeed them right in the exercise, before asking them to prove it? Why don't these textbook problems educate students on ...
- 165
4
votes
0
answers
87
views
What should I do when I, as a math tutor, use incorrect verbal notation?
I do freelance tutoring; the math-related ones are mostly 1-2 hour one-on-one sessions for high school and college students taking calculus classes. Often I find myself scrambling for words - I don't ...
- 237
6
votes
1
answer
223
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What are some ways that one can progress from stage 2 to stage 3 of the rigor stages that Terry Tao has described?
Terry Tao describes 3 stages of one's mathematics education on his web blog.
1: Pre-rigorous
2: Rigorous
3. Post-rigorous
I know how one can progress from stage 1 to stage 2 (this simply can be done ...
- 181
7
votes
3
answers
171
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How to keep your hands clean while using a blackboard?
(I'm not sure if this counts as on-topic for this StackExchange community. If not, please let me know and I'll delete the question!)
When teaching math in front of a class, I often use a blackboard ...
- 171
0
votes
1
answer
81
views
Standardization of evaluation tests [closed]
What kind of standard we need to maintain when preparing advanced level mathematics term test papers ?
In many cases I have seen test papers prepared using exactly past paper questions and in some ...
- 367
5
votes
1
answer
145
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Elementary examples for non-reversible logical steps
While listening to recordings of Calculus $I$ lectures, I noticed that some students get confused between showing that "some object $x$ is a solution", and showing that "every (...
- 419
-2
votes
1
answer
122
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Finite sum of infinite series
I have two issues related to finite sum of infinite series,
1) How you would to describe 2 when you talk about the infinite geometric series 1+ 1/2 + 1/4 + 1/8 + .....
2) How you would compare using ...
- 367
2
votes
0
answers
52
views
A computer program for learning addition and multiplication table
The setup: A 10 year old kid who knows addition up to 10+10 but is 3 times as slow with it as the rest of the class (with very low percentage of mistakes though: out of 50 problems only 1 or 2 are ...
- 849
6
votes
2
answers
109
views
Online seminars in Mathematics Education [closed]
Is there a website where online seminars in Mathematics Education are announced? What resources are available when seeking to join a mathematics education community?
5
votes
1
answer
96
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Examples of random variables that are measurable with respect to a strict subset of $\mathcal{P}(\Omega)$
When teaching random variables for the first time, most of us say that it is a function $$X : \Omega \to \mathbb{R}$$ without any further restriction. Of course, a more general definition is to say ...
- 223
12
votes
7
answers
3k
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Does induction really avoid proving an infinite number of claims?
I am teaching calculus $1$ this semester, and I saw the following motivation for using induction by another teacher:
Since we can't go over "manually proving" all claims $1,2,\ldots$ and ...
- 419
8
votes
2
answers
212
views
Should we require students to take notes in class?
When I teach undergraduate level math course, I make slides with a lot of white space.
In my classes, I write on my slides with an iPad and project the screen to a big TV.
After a class, I provide ...
- 245
13
votes
6
answers
8k
views
Why is a Calculus III student more likely to solve this problem?
Consider this elementary problem:
Define an operation $*$ between integers as follows: $a*b=ab-a+b$. Solve the equation $4*x=36$.
If we give this problem to Pre-Calculus and Calculus III students (...
2
votes
0
answers
95
views
Is there a easy-to-use program that can make a GIF / Video in which an equation is transformed?
Is there a easy-to-use program that can make a GIF / Video in which an equation is transformed?
Like this, which was make (via PPT > Transition > Morph), but ...
- 137
2
votes
3
answers
543
views
Online homework systems for ordinary differential equations
What are the online homework systems for ordinary differential equations?
If you have worked with two or more systems I would like to know how you compare them for ODEs. I have heard of WebAssign, ...
- 584
2
votes
1
answer
93
views
Algorithm vs guidelines for choosing axes divisions when graphing data
A central skill in maths is graphing a set of data on a pair of axes with premarked divisions. Whether the axes are prelabeled with appropriate numbers or not changes the difficulty of this task a lot....
- 885
7
votes
8
answers
598
views
Can it be defended that $\sqrt 4$ is both 2 and -2 (and likewise for general square roots)?
Over the past one or two years, at least two different teachers have told my children that $\sqrt 4$ is $2$ or $-2.$ I don't think this is useful, but if you want to define $\sqrt x$ as the set of ...
- 179
1
vote
2
answers
133
views
As a tutor, should I make students who did badly on timed, closed book past paper tests, do the exact same test again?
As a maths tutor, when I set tests (past papers in particular), if a student does poorly (~50/60% or below), obviously some topics need to be retaught. But should I make them do the exact same test - ...
- 815
4
votes
1
answer
75
views
Ideas and resources helpful in evaluating students with diverse backgrounds
Context
In the case of recently arrived refugee classes (e.g. Ukrainian classes during current times), a first challenge is to establish the individual level of the students in order to tune the ...
- 181
12
votes
8
answers
6k
views
Why does math need to be practiced and exercised, when L1 Linguistic Competence is subconscious?
If 'linguistic knowledge is largely subconscious'3, why isn't math?
Most math instructors sermonize solving exercises and problems. But a student challenged why students need practice — because most ...
user20427
6
votes
1
answer
272
views
What are the leading journals in mathematics education?
Are there any studies that list the leading (English-language) mathematics education journals? Here, "leading" could mean something based on data (for example, citations) or something based ...
- 10.4k
11
votes
5
answers
1k
views
Lowercase vs. uppercase letters for matrix entries
For a matrix $A$ in, say for instance, $\mathbb{R}^{m \times n}$, there are at least two different conventions to denote its entry at position $(j,k)$:
Denote the entry as $a_{jk}$.
Denote the entry ...
- 1,123
8
votes
7
answers
1k
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Write $y=\sqrt{3+x}$ as the composite of two functions
For the question "Write $y=\sqrt{3+x}$ as the composite of two functions", what if a student gives the answer $f(x)=\sqrt{3+x}$ and $g(x)=x$? This answer would be technically correct but it ...
- 4,111
5
votes
1
answer
118
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Which books on geometry and topology are best for teaching an intro graduate course?
I'm teaching a graduate (Master's) introduction to geometry and topology (e.g. some basics on manifolds, vector bundles, algebraic topology). What textbooks have you found are best for teaching a ...
- 151
3
votes
3
answers
728
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New Math Teacher Seeking Advice [closed]
I am new to teaching math, especially middle school math. My own math education was limited to high school and college calculus. These were painful experiences. How to do I go about learning to teach ...
-4
votes
2
answers
123
views
Mathematics and love [closed]
This might seem a bit misplaced, but, is very relevant to mathematics education.
The question is, how can I love someone, and teach students to love, or attempt and complete actions of love, through ...
15
votes
11
answers
4k
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What are some research-level opportunities in mathematics that do not focus on proofs?
The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-...
- 870
0
votes
0
answers
174
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Manipulative materials to teach functions
I am looking for manipulative materials to teach functions (the concepts including domain, image, etc.) and kind of function (affine, quadratic, exponential logarithmic, polynomial, trigonometric) ...
- 1,072
6
votes
4
answers
680
views
what could be some replacement language for the term "spoon feeding"
In some cultures, there is an expression of "spoon feeding" type of instruction, where the teacher shows how to do steps to a problem, and then students are assigned minor variants thereof. ...
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