# All Questions

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### Importance of standardization of definitions of mathematical terms

Don't we need to use internationally recognized standards in defining mathematical terms since differences in definitions play very much important role in finding a unique solution for a given problem ...
250 views

### Definition for Mathematical Formula

Imagine that you were writing an elementary book, for example for high school learners, and at the beginning you had a glossary where you wanted to write the definitions for common mathematical words (...
• 43
1 vote
129 views

### Tangent line to a curve

How would you define tangent line to a curve at a given point on the curve? I think in secondary education it is not sufficient to say a tangent line is a straight line touching a curve at a given ...
61 views

### Symmetry of mathematical expressions in problem solving

**How would you use symmetry of mathematical expressions in problem solving in order to save time by minimizing simplifications? This is not related to geometrical symmetry which is very much ...
66 views

### Why when someone is reading it is so hard to keep attention up? [closed]

Why when someone is reading it is so hard to keep attention up? I would like to add tags like: neuroscience voice sound strategy attention speech but those are not in the list of tags
1k views

### Explaining difference between improper integrals that converge and diverge

How would you explain the difference in the results given by integration of the two functions $y = \frac{1}{1+x}$ and $y = \frac{1}{1+x^2}$ ? The graphs of these two function look so similar on ...
1 vote
171 views

### What is the MOST efficient paper/mental multiplication algorithm for integers?

What is the most efficient (fastest) multiplication strategy that can be done mentally or with a pencil/paper? We can include strategies that use interesting tools like Napiers Bones or Soroban math. ...
• 175
209 views

### For students who don't have instant recall with basic arithmetic, should I be stubborn about training them to have instant recall before moving on?

I'm a maths tutor, and my students/tutees are aged $11 - 18.$ Obviously I have limited time with students, usually one hour per week. Moreover, if parents don't see improvement over a year or two they ...
285 views

### How do I teach the difference between Linear Equations and Equation of a Line

I am more of an Intuitive Learner and Teacher so while looking at Linear Equations chapter I see that they are teaching Equations of Line there, which in my opinion is wrong. See How I understand it ...
109 views

### What are your experiences with Buck’s Advanced Calculus?

I stumbled across the book when searching for rigorous alternatives to Rudin with some solutions. It’s an “old school” (1965) calculus text but, I think, covers similar material to Rudin in a more ...
• 141
384 views

### Motivating Students Through "Random Teaching"

I am recently into a sort of teaching which I shall term "Random Teaching". It involves: Asking student for a random word (not related to math remotely, say "cake") Preforming a ...
189 views

### Multivariable Calculus Project Ideas

Next semester, I am going to teach a small section of advanced high school students a class of Multivariable Calculus (it's about 3-4 students that have completed AP Calculus BC). Multivariable ...
• 1,982
160 views

### Are there pre-printed wall images that might engender understanding in a very young child?

I just read Moebius Noodles. (Thanks for the recommendation Sue). Part of the book talks about keeping images about math around the house. My child's 18 months. But I figure, why not now. It's passive;...
• 579
1 vote
81 views

### References to learn modern functions applied to integration and numerical series problems and how to teach them to Calculus students

I think most of us have met integration problems concerning the trigonometric, polynomial, exponential, hyperbolic and power functions in the calculus courses. But many of the problems in this website ...
• 11
68 views

### What software can I use for remote math tutoring?

I am preparing to do some remote tutoring and I am looking for software to help me out. Requirements: Drawing area shared by the tutor and the student, both can draw on the page Multiple drawing ...
• 129
790 views

### Walter Warwick Sawyer: How has reading his works changed your learning or teaching? [closed]

I recently worked my way through Walter Warwick Sawyer's book, Mathematician's Delight, which has opened my eyes to Maths. I used to fear maths, feeling I was incapable. Sawyer (among other authors) ...
229 views

### Is there a widely respected early childhood math curriculum?

If it's a good idea to work on reading and language from early childhood, I'd bet that it's a good idea to work on math and quantities too. I have an 18 month old. I've pretty much been winging it ...
• 579
428 views

### Can a science educator teach math?

I don't mean to sound rude and denigrating to math educators but I always imagined that a science teacher (physics/chemistry), who has to know math, would be eligible to teach math? Ignoring the ...
• 797
91 views

### How does the average level of expected mathematical sophistication at Highschool level increase?

I remember reading some old Calculus book (1920-1930 time) and in the pre-face it was written it was being revolutionary in being one which could be used to teach in highschool out of. Nowadays, that ...
918 views

### Is "Annular Ring" redundant?

I've come across the term annular ring in parentheses following washer in my calculus textbook: "has the shape of a washer (an annular ring)". The definition of the word "annular" ...
• 153
86 views

### How to let students answer a Moodle Quiz by typing (or pasting) LaTeX code?

Good morning, I use Moodle for Mathematics High Schools Students. They have to reply to questions by writing some short formulas. I've not yet figured out a way of doing this without installing ...
219 views

### Simple way to explain Sine theorem applications

what is the simplest way to explain how to determine whether the resolution of a triangle (finding all its sides and angles, given 3 of them) using the sine theorem gives one or two solutions and ...
• 39
149 views

### How to study for a mathematics undergraduate entrance examination?

TL;DR: Tell me which topics should i study the most, based on this three tests: Mathematics (A): 2020 2019 2018 This question may sound a bit weird, since the natural answer would be "study ...
• 39
1k views

### Is the Wronskian still assumed for graduate education?

About thirty years ago, in a practice GRE (Graduate Record Exam) math test in the US, a question assumed the student knew the definition of the Wronskian. I had never heard of this determinant before. ...
947 views

### How can I improve my Retake Policy?

I teach Pre-Calculus at a public high school in the United States. This school year, I allowed my students to retake any assessment regardless of how they performed on their first attempt. However, ...
• 1,019
105 views

### How to create a platform for students asking questions quickly and privately?

When studying math in class, many students have a few moments falling behind, and they are reluctant to ask a quick question. Do we have a way (like an online web page or tool) for students to quicky ...
1 vote
180 views

### Importance of exploring skills in mathematics

How can you improve exploring skills in high school mathematics education in order to guide students to get better opportunities to become mathematicians ? Here are my suggestions, Let students to ...
111 views

### Generating exercises about extrema of $f(x,y)$

(I have asked this question on math.stackexchange.com and according to a suggestion from comments I am re-asking it here.) I can generate many examples of functions $f(x,y)$ for which finding local ...
336 views

### Is there anything one can do for students who have given up?

In each class, there are often a few students who seem to have given up early on. In my recent discrete math class, when I asked a student a question, he said he was working on his graduation project. ...
3k views

### Examples of relations that are not functions

When teaching functions, one key aspect of the definition of a function is the fact that each input is assigned exactly one output. I always felt that the "exactly one" part is confusing to ...
• 2,182
5k views

### Explaining why volume of cone is a third of cylinder

I came across this video explaining to kids why the volume of a cone is a third of the cylinder of same cross-sectional radius and height. Essentially the explainer presents pre-created cylindrical ...
• 273
608 views

### Equation of a straight line on two dimensional Cartesian plane

What is the most appropriate way to write equation of a straight line through a given point $(\alpha,\beta)$? If you write it using the standard form $y- \beta = m (x - \alpha )$ Where m is the ...
289 views

### Is it considered a mistake to use different correct notation for writing intervals?

Standard definition of writing interval states that it should be written (a,b) where a<b Due to this being arbitrary and just a convention that we all use, would it be considered a mistake to write ...
238 views

### How well can students learn abstract concepts through concrete examples?

In my own personal experience in teaching linear algebra, where many students encounter abstract ideas for the first time, I find that most students have trouble consolidating observations from ...
• 191
3k views

### What are some examples of great functions that are not too elementary (easy)?

I am teaching precalculus/basic calculus to my class (high schoolers of around 18 years of age), and I'm always searching for nice functions to plot and study (finding the domain, the function's sign, ...
• 643
198 views

### A good way to learn differential equations rigorously

What would be a good books of learning differential equations for a student who likes to learn things rigorously and has a good background on analysis and topology?
• 11
507 views

### What are best practices for building a dedicated space for mathematics majors?

The math department at my institution (a private, four-year college with a total enrollment of about 4000) is in the process of brainstorming about a dedicated study/community space for our math ...
• 1,049
152 views

### Where can I find a collection of bad/misleading data visualizations?

Are there any collections or blogs of bad data visualizations? I know I've seen such misleading graphics in the news or in print, made misleading either maliciously or thoughtlessly, but I usually see ...
• 4,412
390 views

### How can you elicit the $\log x = {\log} \cdot x$ error?

You know the error, when you're watching a student work through an algebraic calculation to solve for a variable trapped in the argument of a function, usually $\log$ or a trig function, and you watch ...
• 4,412
2k views

### What term describes the relationship between tenth, hundredth, thousandth and the number ten?

What term describes the relationship between tenth, hundredth, thousandth, et cetera (1/10, 1/100, 1/1000, ...) and the number ten? (Despite what some may say, I don't accept that "decimal" ...
602 views

### Real-world applications of taxicab metric

The taxicab metric can be used to measure distances in idealized gridded cities. However, usually this serves only as a fun exercise for students. I'm looking for engaging (as non-technical as ...
• 251
378 views

### Student forgets to remove dx after integrating

I am tutoring another US college student in a Calculus 1 class. Initially, she was having trouble with basic concepts, but after much prodding most of the conceptual difficulties seem to have been ...
• 137
821 views

### Finding an analogy to explain the function of a binary adder

I want to find an intuitive analogy to explain how binary addition (more precise: an adder circuit in a computer) works. The point here is to explain the abstract process of adding something by ...
• 25
202 views

### How to understand the book and the material to the deepest possible level?

I'm a first year mathematics major and I have a problem with my learning process. In my university, I only have books and questions that the university published, so I have to learn the most of the ...
1k views

### Do we need to practice equation derivation while learning math if equations will be chunked and automatized?

When I was learning the Pythagorean theorem(at time A), I was just told to memorize it. I used it often before trying to derive the equation(at time B), and I think actually I have forgotten the ...
• 139
166 views

### References for mathematical notation for foreign students in the U.S

I teach quite a few foreign students at a U.S. university. Frequently students are placed in our most remedial math class due to not having placement scores and failing to test out of the course. I ...
• 301
120 views

### Resources for Teaching Parameterization of Curves/Surfaces

In classes like Calc 3 or Computer Graphics, I want my students to be comfortable describing common curves and surfaces parametrically (such as lines, triangles, circles, or surfaces of revolution). ...
• 1,939
284 views

### Is it normal for a child to strongly prefer addition to subtraction?

My six-year-old daughter enjoys addition but not subtraction. When we walk together, I like to give her some "mental mathematics" questions, such as "What is 13 plus 33" and she ...
• 4,015
4k views

### What should be memorized in math and what should be reference table?

I can never figure out what should be a memorization concept and what should be in a reference table. For example, in calculus, you are expected to memorize all the derivatives and integrals but in ...
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