All Questions
3,559
questions
2
votes
2
answers
316
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
1
vote
0
answers
117
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 ...
- 165
11
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
571
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 ...
- 351
8
votes
6
answers
739
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 ...
- 351
4
votes
0
answers
103
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 ...
- 249
6
votes
1
answer
282
views
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
6
votes
3
answers
197
views
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 ...
- 169
0
votes
1
answer
85
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 ...
- 691
4
votes
1
answer
201
views
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 (...
- 425
-2
votes
1
answer
148
views
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 ...
- 691
2
votes
0
answers
94
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 ...
- 3,044
5
votes
1
answer
107
views
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
views
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 ...
- 425
8
votes
2
answers
245
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 ...
- 539
12
votes
6
answers
9k
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
97
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
566
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, ...
- 954
2
votes
1
answer
97
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
11
votes
10
answers
883
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 ...
- 227
0
votes
2
answers
139
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 - ...
- 904
4
votes
1
answer
90
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 ...
- 233
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
283
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 ...
- 10.7k
10
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 ...
- 1,437
7
votes
7
answers
1k
views
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 ...
- 4,119
5
votes
1
answer
178
views
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
733
views
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
148
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
views
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-...
- 916
0
votes
0
answers
180
views
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) ...
- 1,482
6
votes
4
answers
712
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. ...
- 503
27
votes
7
answers
5k
views
What value is there in requiring students to answer word problems in complete sentences?
This is related to my previous question What value is there in requiring students to declare the dimensions of an answer when it is already clear from context? , but with a different focus.
A sizeable ...
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11
votes
4
answers
3k
views
How can I build a protractor without a protractor?
We all know how to use a protractor; it is taught in elementary school. However, I was wondering what type of knowledge is required to build one from scratch.
For instance, was the understanding of $\...
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5
votes
4
answers
2k
views
When is the best time to return a graded assessment?
I teach high school Pre-Calculus. In an effort to make my lessons more efficient time-wise, one area I think I can improve is choosing the right time to return graded assessments to my students (that ...
- 1,243
2
votes
0
answers
112
views
Is there any way of explaining the Cayley/Beltrami–Klein metric to undergrads?
How to explain the Cayley-Klein or sometimes called Beltrami–Klein metric concept to find the distance between two points in a hyperbolic space to an audience with no higher education than maybe a ...
- 21
6
votes
2
answers
129
views
Workflow for class notes/slides and examples?
I am teaching high school math in a room with no whiteboard but a projector. I have a tablet that I write on with a stylus and this is projected at the front of the room.
I have been making PowerPoint ...
- 165
2
votes
1
answer
119
views
Do properties of exponents apply only to positive real numbers? [closed]
A common rule given in textbooks is:
If $a$, $b$, and $x \in \mathbb{R}$, then $(x^a)^b=x^{ab}$.
Suppose I write:
$(-9)^{1/2}=(-9)^{2/4}=((-9)^2)^{1/4}=(81)^{1/4}=3$.
But this contradicts the fact ...
- 165
-3
votes
2
answers
145
views
Best natural language(s) for conveying, conceptualizing, teaching, understanding, and learning Probabilistic & Statistical concepts & theory?
English can be precise but it is rather 'flowery' and easily gets in its' own way. East-Asian natural languages like Mandarin, Cantonese, Korean, and Japanese are notorious for permitting the ...
2
votes
6
answers
567
views
Why is calculus important for pre-service Math basic school teachers?
Why should pre-service math basic school teachers take calculus courses?
Should this course be different from calculus courses offered to engineering?
- 1,482
2
votes
1
answer
135
views
Calculus/analysis as basis for basic school topics
I'm looking for examples of facts/results in basic school that are supported by calculus/analysis. Here is an example:
Consider the infinite decimal expansion (a usual topic in basic school): basic ...
- 1,482
0
votes
3
answers
184
views
The two paradigms of seeing a functions
When we are first taught functions , we are typically taught of them as maps between real numbers and we taught to think of them mainly as a mapping between elements. It seems intuitive to take this ...
5
votes
1
answer
140
views
video tutorials by students for classmates - concerns?
I ask students to create tutorial videos where they explain course material (e.g how to do a math problem about a topic they are learning about, e.g. integration, induction). In this past, the ...
- 503
0
votes
2
answers
188
views
Can 5 - 3a be described as five minus three times a?
The question asks students to describe the expressions in words. This is a student's answer:
"$(x + 4) \times 2$" is "$x$ plus four times two"
"$5 - 3a$" is "five ...
- 311
5
votes
3
answers
2k
views
How can I help/tutor a friend who is taking the same course as me?
I am a STEM major and have a good friend who is a non-STEM major. We are both taking a CS minor, me because it is relevant to my field of study and he because he wants a backup plan in case his ...
- 249
3
votes
1
answer
79
views
Fitch Style Deduction in Non-Logic Classes
Has anyone experimented with using Fitch-style proofs as a teaching aid in courses outside of logic specifically and if so, how was the technique received by students?
- 1,054
-1
votes
1
answer
149
views
Counting principles in combinatorics
How we have to start describing counting principles in combinatorics,what we need to apply first, addition principle or product principle ?
I have seen many starts with product principle rather than ...
- 691
6
votes
4
answers
2k
views
What are some rationales to teach Computer Science students Sequences and Series?
I was asked to teach the following topics to undergraduate Computer Science (CS) students in a discrete math course:
Sequences (definition, convergent sequences, find the limit of a convergent ...
- 539
14
votes
7
answers
3k
views
Applications for logarithms in a business math course
Context: I am an assistant professor at a small liberal arts institution in the US.
The title really says it all: I am looking to provide applications for logarithms in a business math course (most ...
- 1,247
-2
votes
1
answer
201
views
math syllabus US education system 1-12th Grade
Please share links to websites / pdf files containing syllabus in subject mathematics in US education system Grades 1-12.
Thank you.
- 7