# All Questions

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### Math tools for restructured lectures

We are in the process of restructuring our math lectures to a more modern style. For that we want to use some math tools to show students how math is done in a more current state. Our math is more ...
168 views

### Book recommendations for Math for Biochemistry Course

I am a mathematics teacher currently teaching at highschool level. I have taught at college level and I do have some preparation about topics such as differential equations and multiple integrals. ...
62 views

### Math textbook for secondary school using Logo like language

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
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302 views

### Generating function example

I'm about to introduce the Generating Function concept to a couple of kids. The plan is just to roughly follow Herbert Wilf's Generatingfunctionology's first 12 pages, until Fibonacci numbers and Ch 1....
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1 vote
103 views

### Math textbook for secondary school using Logo like syntax

What math textbooks for kids do you know that use Logo or similar languages with visual robots like Turtle (in "The Turtle Geometry") that demonstrate space motions, transformations of all ...
• 83
254 views

### The value of homogeneous divisibility rules and of a numeration

Everyone knows about several divisibility rules. But any teacher knows how difficult students are even with the criterion of three in base ten. For example, many teachers have encountered the classic ...
195 views

### Having students assess what problems they're ready for

Does anyone have experience with giving students a collection of problems where they have to assess which ones they have the knowledge to solve? I was exploring the connection between video games and ...
• 4,425
1 vote
2k views

### How can graduates learn and apply university-level math, but fail to solve competition problems?

It's pretty common for people to learn and apply university-level math yet not be able to solve competition problems. Isn't this sentence a contradiction? Please unpack this sentence? Is https://redd....
157 views

### What are the differences between the $n$ permutations of the Edwards & Penney Differential Equations books?

Edwards and Penney are the authors of a popular differential equations textbook. Bizarrely, there seem to be $2^4$ permutations of the title: Some versions have "Elementary" and some don't ...
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81 views

### Engaging in a puzzle without a guidance of a leader while simultaneously being a component of that puzzle

I have done couple of activities and experienced how interestingly students are engaging. At the end I explained the Mathematical concepts related to the activities. Here I'm suggesting two of those, ...
• 1,154
447 views

### how to parametrize these bands related with spinors? [closed]

In a recently viewed educational video focused on the concept of spinors (available at this link:https://youtu.be/b7OIbMCIfs4?si=5ZZLxdGotxAj6YwP ), an intriguing visual representation caught my ...
3k views

### What's the most practical and efficient way to sort exams on paper?

There are a lot of sorting algorithms to sort a list on a computer, and a lot of theory about them. However, my problem is not how to sort a list under the quite well defined conditions of a computer, ...
• 1,097
454 views

### Overcoming Dyslexia and Building Intuition

I am 25 and have been studying mathematics on my own for several years, but I am still between the middle and high school levels. My main weakness is my dyslexia. I sometimes forget words or confuse ...
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3k views

### The effectiveness of "honors" classes

In many universities there are honors math classes. For example, instead of having five "mixed" Calculus I sections they arrange one "honors" class and four "ordinary" ...
• 1,410
269 views

### How to prove, without the LOTUS formula, to student that $V[aX+b]= a^2 V[X]$?

The mainstream way to show $V[aX+b]= a^2 V[X]$ is by using LOTUS. However, LOTUS seems to me too powerful and out-of-reach for a last-year high-school student. Therefore I was wondering if we could ...
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2k views

### Trade-off between writing neatly vs scribbling (scribbling aims to maximise working memory)

Maths is already quite an abstract subject, so to spend time discussing the quality of a student's or even a research-level mathematician's handwriting seems rather tedious. I proceed nonetheless. ...
136 views

### When teaching an upper-level proof based course, what criteria do you use to determine which and how many problems to assign?

When teaching an upper-level proof based course, what criteria do you use to determine which and how many problems to assign? And, as a corollary question: How do you determine the level of success ...
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1k views

### why or when do we use the general form of conic sections?

why write a conic in this form? for any real A, B, C, D, E, and F, a conic may be expressed as $$Ax^2 + Bxy +Cy^2+Dx+Ey+F=0$$ why wouldn't it be more natural to write the conic in standard form with ...
• 1,068
369 views

### How to assess students in real analysis?

Terence Tao says the following in the preface to his book Analysis I: With regard to examinations for a course based on this text, I would recommend either an open-book, open-notes examination with ...
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82 views

### International Baccalaureate - where to find the detail of the math programs?

Does anyone know what is the exact program of the International Baccalaureate in math? I've been looking for the MYP and DP programs in the website of the International Baccalaureate Institute but ...
• 225
271 views

### Why do some (pre-) calculus text allow $r<0$ in polar coordinates?

Form this question, I was surprised to learn that it is common for calculus textbooks in the US to allow $r<0$ when discussing polar coordinates. This answer by Dan Fox summarizes some mathematical ...
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117 views

### Real-World Problems for Teaching Extrema and Derivative Tests in STEM Education

For educational purposes, I am seeking example problems in the realm of natural sciences, engineering, and business that satisfy the following criteria: Consider a one-dimensional real function $f$ (...
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439 views

### Why is $a+b = b+a$?

In primary school, it's extremely easy to show that $a \times b = b \times a$, as follows: The surface of a rectangle can be calculated using the formula $\text{Basis} \times \text{Height}$, as in ...
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1k views

### Dominance of connectives: Why do we teach this?

These were two actual exercises given to students I have been tutoring for a college algebra class: I have been working very hard to convince my students of the importance and utility of learning ...
• 404
4k views

### Is it a good idea to give partial points in grading

When grading problems on quizzes and exams, I often break them down into sub-problems, each worth a portion of the total points. I use rubrics to award partial credit for each sub-problem. However, ...
106 views

### Is there national grade distribution data for introductory service courses?

I am looking for US average national or state grade distribution data for courses that are typically considered as math service courses: precalculus, calculus 1,2,3, linear algebra, differential ...
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78 views

I've been utilizing edstem.org for facilitating math and logistics discussions in my course. Its support for LaTeX and hand-drawn illustrations has been convenient. Typically, students post questions, ...
285 views

### How would you prepare students for "Alice and Bob" Putnam problems?

Every year the Putnam Competition features at least one question that describes Alice and Bob playing game, and asks for one player's winning strategy or something similar. Since these questions are ...
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297 views

### Understanding common multiples

Imagine a class of students who don't know what smallest common multiples (LCMs) are, or indeed what multiples are. (Notice I said "smallest" rather than "least" so as to avoid ...
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138 views

### When can students understand the intersection of two circles?

I'm interested in learning two transitions: (1) When can students reason (intuitively, but accurately) to conclude that two circles in the plane could intersect in $0$, $1$, or $2$ points, or are ...
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230 views

### Recreational mathematics to create sense of mathematics

Recreational mathematics serves as a valuable educational tool by enhancing interest, fostering engagement, and refining mathematical thinking. While it often falls outside traditional curricula, ...
• 1,154
174 views

### Comparison of two ways to introduce translation to 12-14 year olds

I consider pupils 12-14 years old, who are new to translation. On the other hand, they have been accustomed to placing points in a coordinate system, especially when studying relative numbers. In ...
276 views

### What are pros and cons of requiring students to create their own math questions, and what are some tips to make it work well?

I will teach a special class of 10 high school students who are aiming to study math at top universities. The purpose of the class is to increase students' interest and ability in math. There is ...
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147 views

### Advice and Remedial Algebra Resources for Students Committed to Calculus

I've got a student in my introductory calculus course. They're failing because they lack algebra skills. They understand the concepts just fine, and can articulate their understanding fine, but get ...
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4k views

### What theorems from single-variable calculus break down in the multi-variable context?"

In teaching multi-variable calculus, it's insightful to discuss with students not only how certain concepts from single-variable calculus extend to multiple variables but also where these extensions ...
4k views

### Effectiveness of Requiring Students to Repeat Proofs Presented in Class

In teaching mathematics, I've avoided asking students to replicate proofs I've demonstrated in class, believing this approach primarily tests memorization rather than understanding or critical ...
478 views

### Why use the vague notion of "vector" when you have $\mathbb R^2,\mathbb R^3,\mathbb R^4,\ldots$?

I'm reading an introductory course on groups. In this course, the author illustrates concepts using the vectors of the plane. For example, "the set of vectors in the plane(or in space) is a group ...
3k views

### Applications of High School Geometry

Sometimes I struggle to give my students a sufficient number of reasons why they should study Geometry in high school, other than that it helps them think and increases their understanding of the ...
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237 views

### Does some textbook on probability use a particular way (described here) of accomplishing the segue into continuous distributions?

Imagine an introductory probability course that assumes the students have had first-year calculus and understand mathematical reasoning. At some point in such a course has explicated several families ...
• 1,915
160 views

### Looking for interesting tasks and activities for 6th grade students for a course on problem solving

I am a teacher at a gifted center up to middle school grades, and I am looking for interesting tasks and activities for gifted 6th grade students for a course on problem solving and using varied ...
383 views

### Any known platform to post self made math questions

Background I am a class 10 student who is fond of maths. I like making math questions. Question I do not know of any platform where I can post these questions for others to practice and learn. I ...
227 views

### About a difficult exercise for 12 years pupils

You have to go from a point $A$ (start) to a point $B$ (arrival) by crossing a river $(d)$ and traveling as little distance as possible. Pupils first do a search by trying several paths $1,2,3,4$ and ...
1 vote
146 views

### When Interpreting "If A, then B" as "A coupled with B" is rational?

It is known that the meaning of a conditional statement in fuzzy logic can vary depending on the interpretation and context. As we know, some ones interpret "if A, then B" as "A coupled ...
2k views

### Confusing variables with units in simple equations

I have noticed that beginning algebra (or pre-algebra) students can easily make the following type of error, confusing variables with units when being introduced to equations for proportional ...
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467 views

### Resources for designing math degree programs

I'd like to know where I can find resources which are helpful when one has to design or improve grad and undergrad degree programs in pure and applied mathematics. In particular, I'm searching for up-...
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452 views

### Regarding finding eigenvalues and minimal polynomial of an operator with limited tools while following Sheldon Axler

I am using the textbook Linear Algebra done right by Sheldon Axler (fourth edition) to teach an undergraduate linear algebra course. Please find here a link to the book here. Now Axler does not ...
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552 views

### Motivating a definition of "gap" in a line just barely more advanced than the one used in the typical first-year calculus course

Imagine a course barely getting into some topics more theoretical than what is done in the typical very staid first-year calculus course, and the kind of students for whom such a course is appropriate....
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109 views

### What books does a Chinese institution use in the undergraduate maths courses?

Can anyone share the books that a Chinese maths undergraduate follows during their course? Also what are some of the problem books and exam papers that the Chinese students use to become better in ...
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1 vote
595 views

### Is integrated math class the same as mathematics class?

The first high school I went to I did Integrated Math 1 my Freshman year, Integrated 2 my Sophomore year, and Integrated 3 my junior year. My junior year I transferred to a continuation school where I ...
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