# All Questions

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-3 votes
0 answers
59 views

### Research Paper on Integration [closed]

I am really interested in studying some of the research paper basically based on integration , Is there any source which provides some of the recently published research paper ? Thanks A lot :))
2 votes
3 answers
374 views

### Logarithms properties, continuity and circular reasoning

I have a doubt relating to logarithms. Anticipating some answers, I know that a "mathy" way of doing things is defining the function by its properties ($f(xy)=f(x)+f(y)$) and then just build ...
-2 votes
0 answers
78 views

### Did Ramanujan prove any of his problems?

Ramanujan has given some wonderful theorems in number theory as claimed by the highest calibre mathematicians . As in the movie , the man who knew infinity we saw that Ramanujan gave very abstract and ...
• 197
3 votes
1 answer
113 views

### The easy and the hard problems involving independent events

In probability, two events are independent if the incidence of one event does not affect the probability of the other event. Math textbook often has problem checking if two events are independent or ...
• 131
0 votes
0 answers
64 views

### Resources to introduce Modular arithmetic

We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
• 1,153
37 votes
5 answers
13k views

### Which cognitive psychology findings are solid, that I can use to help my students?

I read recently on this site that the growth mindset seems not to be real. I did not know that (I admit that I don't follow research into learning as closely as I would like). Can I turn that ...
• 933
4 votes
2 answers
286 views

### Correct notation of a Sample space

From the very beginning I have used the notation $S = \{ H , T \}$ as the Sample space for tossing a coin once and $S = \{ HH , HT , TH , TT \}$ in the case of tossing a coin twice.I have several ...
• 1,153
8 votes
6 answers
4k views

### Would you correct grading mistakes downwards if there is a mistake in grading?

In a recent exam, I give student a true or false question asking them to decide if a statement is true. After the grades have been published, a student pointed out that I misread the statement and ...
• 380
0 votes
2 answers
110 views

### Math Progress for Year 2 Student?

Have a year 2 student that is years above his peers. Each topic I introduce he has already learnt and understood. I've extended the topics we work on for him but the topics I introduce are rudimentary ...
0 votes
3 answers
433 views

### What is this symbol called?

I know how to pronounce the first symbol as "theta", but the other symbol that looks like a circle with a vertical slash, I don't know what to call it. I would appreciate any help. Thank you
• 17
0 votes
7 answers
420 views

### How Can I Encourage Students to Use AI Like ChatGPT Across Math Courses?

I've been using ChatGPT (GPT-4) to help with creating quiz questions, solving math problems, and answering students' queries in my classes. Although it sometimes gets things wrong, with the right ...
• 380
4 votes
1 answer
192 views

### Producing defective matrix examples

It's easy to come up with examples of interesting diagonalizable matrices $A\in M_n(\mathbb{C})$ with a prescribed set of eigenvalues $\lambda_1,\dots,\lambda_n$ because you can start with your ...
14 votes
7 answers
8k views

### What Basic Math Skills Should Be Expected of Students in a University-Level Linear Algebra Course?

I am currently teaching a university-level linear algebra course and recently encountered an issue that made me question the assumed foundational math skills for students in this course. The issue ...
• 380
-2 votes
0 answers
171 views

### How do I get the logic behind calculations in optometry? [closed]

I am an optometry student who is struggling with the calculations in ophthalmic lenses, optics, and visual optics. These are core subjects in my course. I have not found the logic behind most of these ...
6 votes
3 answers
1k views

### What are the essential topics in undergraduate financial mathematics?

When I was an undergraduate 15 years ago I did not take any financial mathematics courses. Recently I was approached by an undergraduate, whose ultimate goal is to go into the financial sector, and he ...
• 161
5 votes
3 answers
623 views

### What is a corequisite course?

My department has eliminated its remedial mathematics courses and implemented a corequisite system. I did not participate in the original design, so I found myself unable to understand the new system. ...
• 153
23 votes
6 answers
8k views

### What skills do algebra teachers wish their students had mastered before taking algebra?

I am designing 10 hour weekly summer math learning opportunities for students taking algebra next school year. I would like to know from algebra teachers what skills they wish their students had ...
1 vote
1 answer
156 views

### Theory of semiotic mediation in teaching math at high school [closed]

I am working on the theory of semiotic mediation in teaching math at high school. According to the theory I need an artefact that is appropriate for high school (secondary school). In many papers ...
• 131
21 votes
10 answers
5k views

### Inner voice when reading mathematics

I am writing some notes for my students, and am curious about how others read mathematics: do you have an inner voice when reading mathematics? What about when you come across a symbol which you don't ...
• 311
-1 votes
2 answers
171 views

### What are your most recommended resources to teach fractions?

Please share your resources for learning and teaching fractions...sites, videos, worksheets etc. I am looking for online resource similar to this: https://worksheetgenius.com/math/fractions-add/ with ...
4 votes
1 answer
136 views

### Usage of cubic equation Vieta's formula

I explained to my kid Vieta's formula of quadratic equation and showed that it can be used to solve quadratic equation (from $x_1+x_2$ and $x_1x_2$ to get $x_1-x_2$) and cubic equation (Cardano's ...
• 777
1 vote
4 answers
220 views

### How to round numbers?

I have often thought that $3=3.0$ so one can round $3.4\approx 3.0$. But some math teachers says this is wrong. Which one is the correct answer? Why this might be wrong?
• 23
6 votes
11 answers
6k views

### Earliest real-world uses of Calculus and Linear Algebra

I want to illustrate in class that real-world applications of mathematics might take time to come to fruit. In this context, I want to find what the earliest real-world applications of Calculus and ...
• 316
1 vote
0 answers
113 views

### Book or curriculum for teaching base-16 numeral system to elementary, middle, or high school children?

In 1862, John W. Nystrom promoted the base-16 (hexadecimal) number system, which he called the "tonal system": Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to ...
• 171
12 votes
5 answers
3k views

### A visualization for the quotient rule

Context: first year didactics of mathematics course for middle school teacher students (in Norway). I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
• 7,202
15 votes
22 answers
8k views

### What are some simple problems that calculators get wrong?

A frequent issue with students is their uncritical over-reliance on computation devices. While these can of course be quite helpful, they also need to be handled with care, because they make ...
• 199
0 votes
1 answer
112 views

### Markov chains - how to translate mathematically the fact that the state at $n+1$ only depends on the state at $n$? [closed]

In a Markov chain of, say, three states $1,2,3$, when proving that the probabilistic state at $n+1$ ($\pi_n$) is equal to the probabilistic state at $n$ times the transition matrix, one has to use the ...
• 225
10 votes
8 answers
2k views

### "Pure Imaginary" or "Purely Imaginary"?

Quick Question: A complex number $z$ with real part $Re(z) = 0$, i.e. something like $-17i$ -- would you call it "pure imaginary", or "purely imaginary"? I'm not a native English ...
2 votes
1 answer
191 views

### How to grade a flipped class to improve participation and attendance

A flipped service course for me is an arrangement where videos are online and on-campus class time is used for problem solving by students. I usually have a homework due date the day after the ...
• 1,410
7 votes
3 answers
366 views

### Why is it written $\tan^{-1}$?

I was showing my neighbour's daughter how to do simple sine, cosine and tangent questions and their inverses. She could do the questions fine but she asked me why the calculator button for inverse tan ...
• 181
1 vote
4 answers
2k views

### An algebra student wants to learn to type commutative diagrams in LaTeX

A maths student takes his first course on homological algebra, and wants to write his answer in LaTeX. What is the simplest way for him to write commutative diagrams in LaTeX?
• 21
1 vote
1 answer
126 views

### Is there a mathematics core assessment rubric?

Many universities in USA ask their faculty to perform a "core assessment" where they evaluate (typically) freshman students, near the end of semester, on their understanding of the courses ...
• 1,410
2 votes
3 answers
376 views

### 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 ...
7 votes
2 answers
155 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. ...
2 votes
0 answers
57 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 ...
• 83
5 votes
4 answers
293 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....
• 777
1 vote
1 answer
96 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
-6 votes
3 answers
248 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 ...
15 votes
1 answer
191 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
5 answers
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....
6 votes
0 answers
152 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 ...
• 119
0 votes
0 answers
76 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, ...
• 1,153
-1 votes
3 answers
442 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 ...
17 votes
11 answers
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, ...
• 1,087
5 votes
2 answers
444 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 ...
• 151
10 votes
3 answers
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
2 votes
3 answers
253 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 ...
• 225
5 votes
5 answers
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. ...
4 votes
1 answer
126 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 ...
• 119
6 votes
6 answers
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

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