# All Questions

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294 views

### Line Integral Motivation

Is there a case to be made that the topic of line integrals should only involve vector fields? My colleagues and our textbook take the position that line integrals should only be taught from a vector ...
265 views

### How can I introduce a speech about the Fibonacci sequence creativiely?

I am a high school senior student. Soon, I am giving a presentation about the Fibonacci sequence and I am searching for a creative way to start my speech. I was wondering whether someone in this ...
99 views

### Does studying elementary number theory improve one's proof skills and ability to understand algebra and analysis? [closed]

I'm taking a number theory course and don't know whether it's worth it. I currently can't understand algebra and real analysis and decided to take # theory to see whether this would help me prove and ...
134 views

### Interesting math lesson on integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs

I have to deliver a lecture for secondary school, about one of these topics: integers, Euclid's Elements, polyhedra, prime numbers, non-Euclidean geometry, arithmetic functions or graphs. It should ...
169 views

### Math Scholarships for the highly advanced

I was wondering if there are any special math scholarships in the United States of America for High School students with high capacity in mathematics. At the age of merely 16, I see great potential ...
83 views

### In which order should I read these topics? [closed]

In which order should these topic be read if one have to understand mathematics topic well? Differential Equations Game Theory Graph Theory Linear Programming Probability Statistics Vector ...
144 views

### How to preserve axioms from the positive numbers in the negative numbers?

It isn't so hard to convince students of grade 8. 9 that $-2$ is greater than $-4$, but it still make some confusion with an axiom says that ( The whole is greater than part ), which is true in the ...
385 views

### I'm in 8th grade and just finished Algebra 2. What math would I do for the next 4 years? [closed]

I'm in 8th grade and just finished Algebra 2. What math would I do for the next 2 years? In what order would math I would do in 9th, 10th, 11th, and 12th grade. Thanks!
74 views

### What are some of the struggles that come with teaching introductory formal logic?

I'm currently an undergraduate student who wants to do research on the pedagogy of formal logic. As a result, I wanted to know what are some challenges that instructors (or even students for that ...
91 views

### What books are good to study Solid Mensuration?

Preferably I want those that contain the following topics: Solid Figures Polyhedrons Prisms Pyramids Prismatoid Truncated Prisms Cylinders Cones Spheres I've been ...
47 views

### Reference Request: Suitability of a text and corresponding video lecture series request for “Matroid Theory”

I am an undergraduate student from the CS background. While reading a portion of the text "Introduction to Algorithms" by Cormen et. al. I came across a section of Matroids. I was unable to ...
232 views

### Workbooks for advanced high school math topics

I'm looking for advanced workbooks and exercises for working in class (math high school/undergraduate level) covering the following topics (or some of them): Logic and sets (propositional calculus, ...
145 views

### Making epsilon-delta proofs not just precalculus

In trying to find lecture-length videos of epsilon-delta proofs, I've found that almost all of them just start with the definition and then work through the algebra to get the answer. In effect, it ...
108 views

### How to use Calculus to give an explanation for a video by Lewin [closed]

In the video by the well-known physicist Water Lewin Link Here, in which he demonstated a series of experiments of rolling objects. Many are quite surprising. At the end of the video, the attended ...
103 views

### How to teach geometric patterns? [closed]

I would like to know how to teach geometric patterns in secondary school. I want to elaborate worksheets, which could include different kinds of strategies related to this topic. Are there resources ...
184 views

### How can I make “complex” graphs that combine multiple functions with a software?

Til today I've been using geogebra to sketch functions for my students quizzes or homework. Sometimes I use the ones that I found searching in google, but this takes a lot of time specially because I ...
210 views

### Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (not ...
182 views

### Can $y^{(n)}$ be used as a way of representing higher order derivatives?

I have never seen this notation, but I think that it follows in a similar vein for function notation. So if $y=f(x)$, then $y''=f''(x)$. Then by that, can we say that $$f^{(n)}(x)=y^{(n)}$$
113 views

### How to build addition with sets?

I was taught under the New Math, so I should know this, but I am afraid I was tricked. Using the cardinal, it is easy to define a multiplication, as the cardinal of the cartesian product is the ...
239 views

### The sequence of chapters

I'm using a textbook but in my course the chapters are numbered differently. For example, the book has the following chapters: Real Numbers Square Roots Polynomial in a single variable (they don't ...
3k views

### Project Based Learning (PBL) ideas for secondary math topics

I have searched the web but not found too much that fits what I want. So, I thought I would try asking here. I am looking for projects to use as PBL for grade 10 math. Specifically for the topics of: ...
165 views

### Vector Algebra Text [closed]

Recent developments in Geometric Algebra have extended vector algebra to include the outer product (wedge product) and bivectors. Is there a Vector Algebra text (preferably at the advanced high ...
74 views

### Resources for Unit Rates

I am currently mentoring my little brother in mathematics. There is an issue with the pedagogy of unit rates. For example when given the following concept " 11.00 U.S. Dollars to 20 Planet X ...
40 views

### Setting up a new Ximera course with randomized values in problems

I'm working on converting a course to make it free to the students, and I'm considering using Ximera. What I haven't found online is documentation for/information on tips and best practices for ...
131 views

### Where can I find a good course on tensor calculus not focused on applications and physics?

Where can I find a good course on tensor/ricci calculus not focused on applications and physics? I've been running into lots of tensor-theoretic stuff in differential geometry, so I don't know if ...
413 views

### Should students get another chance at a math question because of English troubles?

The question is John has locked a 4 digit combination lock with each of the numbers 0-9. He knows the numbers 1,4,6, appears exactly once, but he does not remember the position of the numbers and he ...
198 views

### Cautionary tales for Gaussians/the central limit theorem?

In any undergraduate course on probability, one of the fundamental results that is discussed is the central limit theorem. Apart from the interesting mathematics needed to prove the result (most often ...
141 views

### Undergraduate Interview Maths Questions [closed]

I am trying to compile a document of preparation questions to use in mock interviews with students applying to study Maths at top UK Universities. I have many questions already, but it is always ...
102 views

### How to address opportunities for improvement with a teacher

My daughter’s 5th grade teacher gives some pretty impossible questions and I don’t think she understands the material she’s teaching. For example, this question has no context from previous questions ...
113 views

### Calculus book for basic calculus and repetition from videregående (Norwegian high school)

Does there exist a textbook in Norwegian (bokmål and nynorsk should both be fine) that covers the more advanced mathematics (needed for calculus) from videregående (secondary school, includes both ...
540 views

The title is self-explanatory, but what is the appropriate response to "motivate your answer"? Should you prove your answer? Should you just explain it, or give the intuition for it? For example, ...
109 views

### Verifying Simple Expression Equivalence in a Spreadsheet

For simple expressions with easily derived canonical forms (eg polynomials and simple rational expressions), is there a way to leverage existing tools to verify that two expressions are equal when ...
116 views

### A robot to simulate differential equations for undergraduate students. [closed]

I was recently at EPFL drone days and enjoyed a demo of a robot that could follow a black line like in the sketch (I can improve the sketch on demand): Then I remembered my good all times at the ...
115 views

### Pythagorean triples

What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is ...
109 views

### Workshop about ODEs and connected rates of change (A-levels)

I'm preparing a workshop about ODEs and connected rates of change for pre-college students (smart and interested in mathematics). I'd like to include some fun parts as well - even if these are ...
197 views

### Comparing the magnitudes of the slopes of two lines

I am going over rate of change with my 8th graders tomorrow and I foresee a difficulty. I would like to see different ways to explain this for my students who have trouble with it. In terms of ...
97 views

### Moving lines in schematic diagrams

I am self-teaching myself precalculus.My biggest sticking point is to move lines within a diagram, especially, functions in the coordinated plane. For instance, doing horizontal and vertical shifts of ...
139 views

### Create Problems for Polynomial Interpolation

I want to create problems concerning polynomial interpolation for students. However, I need those problems to differ in difficulty for the different students. What I could always do is solve some ...
59 views

### What are different Mathematical concepts which can be introduced to 12-16 year students in an activity based way

Activities are a great way to engage students with Mathematics. And that also helps them to visualise mathematical facts. For example, Pi in its decimal form appears to have no pattern (we used to say)...
166 views

### Resource request: 3-4 page review of exponentials and logs

I'm teaching a physics class that has a year of calculus as a prerequisite, but as so often happens, many of my students have forgotten a lot of the much more basic math from earlier classes. In ...
64 views

### Is there any video lecture series on (UG level) graph theory (might not be specific on any books) but the video/content quality is like that of MIT?

Previously I had asked a question about something similar, but more constrained. But now I ask something more general. I just got hold of the Linear Algebra by Prof Gilbert of MIT and they are just ...
58 views

### History of business calculus/linear algebra curriculum

I will be teaching a combination of business calculus and business linear algebra, two classes that have been around awhile at my school. I’m assuming people are familiar with these types of classes. ...
196 views

### Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
112 views

### Mental visualisation ability test for each age?

What are standard tests for mental visualization (image, representation) for kids? So far I know about mental arithmetics and spatial rotation tests. Is there any other way to check mental vision ...
71 views

### Number theory in an introductory course on discrete dynamical systems

Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
43 views

### Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...
74 views

### How long should we spend on teaching students the basics of subject?

Highschool-courses, at least in my country, are structured in a way that you tackle with a higher level of a given subject after some time constraint. So, after one year, you get to a higher class ...
132 views

### Would the SMSG textbooks provide adequate extracurricular study?

Context: I'm a Grade 11 IBDP student and very fond of math. Assuming that I get the spare time to self-study material alongside the syllabus, I wish to spend it constructively (the only step I've ...