# All Questions

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### Is there a canonical name for a polynomial-like expression allowing for negative powers?

When introducing the techniques of differentiation, polynomials come up all the time as great examples to familiarize students with the "power rule" and the linearity of differentiation. A ...
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1k views

### How to teach using brackets in sums?

How one should teach using brackets in summation? For example, why is it correct to write $\sum_i a_ib_i$ but $\sum_i a_i+b_i$ should be written as $\sum_i (a_i+b_i)$ But $\sum_i\frac{a_i+b_i}{2}$ is, ...
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2k views

### Are there examples of central symmetry, without axial symmetry, in nature?

Examples of axial symmetry abound, but I could not find an example of pure central symmetry (that is, without axial symmetry)! Do you know of any? A butterfly shows axial symmetry, what shows point/...
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### Research into how students read algebraic expressions

In answering another question What is the justification to teach the (redundant) use of parentheses in multiplications? I was left wondering what we actually know about students' progression in terms ...
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### What is the justification to teach the (redundant) use of parentheses in multiplications?

Example: 5 x 18 = (5 x 10) + (5 x 8) instead of 5 x 10 + 5 x 8?
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2k views

### Should math for elementary teachers content be taught under the direction of the math department?

I recently was appointed math department chair at a small university. We have a 3 credit math for elementary teachers content course. Administration told us they will change this course into an ...
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28 views

### How do I calculate the odds of something not being selected in a sample? [closed]

I have a population that a sample was taken from, and one "group" was not selected in the sample. I am wanting to find the probability of one group not being selected. I will use red/blue ...
7k views

### ‘Lies to children’ in mathematics and statistics education

In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children: A lie-to-children is a statement that is false, but which nevertheless ...
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360 views

### When teaching online, how does the teacher teach visual concepts?

What would one suggest for online math teaching to draw diagrams? Is Tikz or Matplotlib too slow for helping to visualize problems during the lesson?
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170 views

### Common mistakes in probability

$\DeclareMathOperator\Var{Var}\DeclareMathOperator\Bern{Bern}\DeclareMathOperator\Pois{Pois}$Question: What not-trivial mistakes do students often make when solving problems in probability theory, ...
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251 views

### Introduction of group action as morphism of groups

The usual definition of a group action is as follows. Let $G$ be a group and $A$ be a set. An action of $G$ on $A$ is defined to be a map $\rho:G\times A\rightarrow A$ satisfying certain conditions. I ...
1 vote
61 views

### Best Free Direction Field Plotter?

Can you recommend one for a first or second year calculus course? Ideally the website that can plot direction fields: is free is 100% WYSIWYG (does not require any coding or markup or anything of the ...
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136 views

### Relearning math after long COVID using AoPS or developmental math textbooks?

This is a little bit of a niche topic. I've dealt with a pretty bad dose of long COVID that has caused some serious gaps in my mathematics (basically causing terrible arithmetic skills and a really ...
• 369
157 views

### Example of a phenomenon from real life where there is a limit going to infinity

I haven't been able to find examples in real life where we have a function or sequence such that the limit goes to infinity when the independent variable goes to infinity. The only one so far is ...
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1k views

### Is it meaningful to add a number to itself a fractional number of times?

(Migrated from the math stack exchange, where I received an apt-seeming suggestion to pose the question here, at the math-educators stack exchange) I introduce my young kids to basic math concepts in ...
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155 views

### How does learning math differ from learning second foreign languages (L2)?

Peer-reviewed publications analogize learning math to learning a L2. But what are the DisAnalogies and CounterArguments? How can you distinguish learning math from learning L2? Luciana Oliveira, ...
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1 vote
179 views

### A high school level proof that $a/b > 0$ [closed]

Is there a high school level proof of the following? If $a,b > 0$ then $a/b > 0.$
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1k views

I'm trying to learn arithmetic from scratch again. Even though I can use it, I'm not sure if I can teach it to someone and I believe if you can't teach something properly, there might be loopholes in ...
174 views

### Which are the most used Greek letters in math textbooks?

I am looking for a list of the most frequent Greek letters used in high school and college textbooks or some other corpora. I've realized my students don't know Greek letters and I would like to teach ...
226 views

### Should one include the unit in the variable? E.g. should one write $x^\circ = 30^\circ$ or $x = 30^\circ$?

I sometimes come across equations like $x^\circ = 180^\circ - \frac{360^\circ}{n}$ where I would write $x = 180^\circ - \frac{360^\circ}{n}$, or like $3 \text{ cm} + x \text{ cm} = 5 \text{ cm}$ where ...
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4k views

### Is patching up a student's poor solution better than providing a good solution?

A student benefits from their attempt at a solution or proof being checked by the teacher. My own view is that, if the student's work is poor, it is best just to provide a model solution or proof in ...
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268 views

### Proof by Contradiction vs. Proof of Negation

In constructive mathematics we make a distinction between "proof of negation" and "proof by contradiction". You can read a great account of the difference in this blog post of ...
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161 views

### How to introduce the use of Greek letters in high school?

I am looking for any hints or experience reports or materials/potential difficulties about how to introduce the use of Greek letters in high school Math/Physics.
266 views

### What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number?

The following is an elementary-level Math Kangaroo multiple choice question: What is the maximum value of the sum of the digits of the sum of the digits of a three-digit number? A. 9 B. 10 C. 11 D....
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4k views

### Students confusing "object types" in introductory proofs class

In my intro to proofs (and discrete mathematics) class, I see a common mistake where students make nonsensical statements because, for lack of a better term, they confuse the types of the mathematical ...
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1k views

### Introductory Books easier than Dover

I'm looking to books introducing different topics of math with fun for my son, to give him a taste of different areas. My son roughly understands A-level topics until single variable calculus (of ...
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76 views

### Where can I find a summary of typical material (e.g., mathematics) taught in US elementaries and high schools?

The reasons for my question are complicated but basically I need information about different subjects, mostly languages (Eng, Spa, Fre), math, and sciences, as taught in different grades in elementary/...
1 vote
95 views

### Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook

Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
2k views

### Calculus problems arising from real research problems

I am visiting my in-laws for the holidays. My sister in law is a statistician. She asked me to take a stab at a calculus problem which was coming up in her research. The Lambert $W_0$ function is ...
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### About instructor's manual in math textbooks: principles, design, uses and impact

It is common that school math textbooks are supplemented with instructor's materials (answers, hints and guidelines). Are there scientific studies on how instructor's materials impact math teaching? ...
2k views

### Problem set recommendations for a student who has taken classes through Calc III, but has very weak fundamentals

I know an undergraduate who just finished calc III, and really struggled with it. However, it seems like a lot of the issues are coming from skills which should have been established during algebra, ...
112 views

### On doing scientific research [closed]

What I want to ask is: can I use the results of others when doing scientific research, whether it is math, physics or other science, without trying to prove them myself or try to verify them? For ...
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160 views

### Learning, exams, math degree

I have only passed the one fourth of my courses so far, which means like one year of the maths undergraduate studies. I live in a different place from where the university i study at is and try to ...
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644 views

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### Why do we use polysemy?

From Polysemy - Wikipedia: Polysemy (/pəˈlɪsɪmi/ or /ˈpɒlɪˌsiːmi/; from Ancient Greek πολύ- (polý-) 'many', and σῆμα (sêma) 'sign') is the capacity for a sign (e.g. a symbol, a morpheme, a word, or a ...
1 vote
107 views

### Quality of a solution in mathematics

How can you determine a quality of a solution for a mathematics problem in general ? If you try to explain too much then solution becomes bit longer and it takes time to go through causing less ...
184 views

### 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, combinatorics) and I ...
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### 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 ...
147 views

### 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 ...
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1 vote
124 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 ...
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