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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 ...
AcademicCoder's user avatar
7 votes
2 answers
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. ...
NotAMathematician's user avatar
2 votes
0 answers
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 ...
paus's user avatar
  • 83
5 votes
4 answers
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....
athos's user avatar
  • 777
1 vote
1 answer
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 ...
paus's user avatar
  • 83
-6 votes
3 answers
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 ...
Stéphane Jaouen's user avatar
15 votes
1 answer
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 ...
TomKern's user avatar
  • 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....
user avatar
6 votes
0 answers
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 ...
SRobertJames's user avatar
0 votes
0 answers
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, ...
Janaka Rodrigo's user avatar
-1 votes
3 answers
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 ...
Humberto José Bortolossi's user avatar
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, ...
Pere's user avatar
  • 1,097
5 votes
2 answers
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 ...
antho's user avatar
  • 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" ...
Maesumi's user avatar
  • 1,410
2 votes
3 answers
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 ...
niobium's user avatar
  • 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. ...
Adam Rubinson's user avatar
4 votes
1 answer
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 ...
SRobertJames's user avatar
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 ...
Lenny's user avatar
  • 1,068
6 votes
1 answer
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 ...
Pedro's user avatar
  • 1,800
3 votes
1 answer
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 ...
niobium's user avatar
  • 225
7 votes
5 answers
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 ...
Kostya_I's user avatar
  • 1,411
2 votes
2 answers
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 $f$ (...
Julia's user avatar
  • 1,275
6 votes
6 answers
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 ...
Dominique's user avatar
  • 2,175
8 votes
3 answers
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 ...
Joel Croteau's user avatar
11 votes
7 answers
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, ...
user avatar
2 votes
0 answers
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 ...
Maesumi's user avatar
  • 1,410
4 votes
0 answers
78 views

Seeking Advice on Incorporating Online Discussions into Course Grading

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, ...
user avatar
5 votes
2 answers
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 ...
Mike Pierce's user avatar
  • 4,845
0 votes
1 answer
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 ...
Michael Hardy's user avatar
4 votes
0 answers
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 ...
Joseph O'Rourke's user avatar
3 votes
1 answer
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, ...
Janaka Rodrigo's user avatar
2 votes
2 answers
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 ...
Stéphane Jaouen's user avatar
3 votes
3 answers
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 ...
Dan's user avatar
  • 1,245
7 votes
2 answers
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 ...
Mike Pierce's user avatar
  • 4,845
22 votes
6 answers
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 ...
Humberto José Bortolossi's user avatar
11 votes
9 answers
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 ...
user avatar
3 votes
4 answers
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 ...
Stéphane Jaouen's user avatar
9 votes
11 answers
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 ...
Nate's user avatar
  • 91
-2 votes
1 answer
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 ...
Michael Hardy's user avatar
4 votes
2 answers
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 ...
Eran Alush's user avatar
5 votes
1 answer
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 ...
GameTime With Aryan's user avatar
2 votes
1 answer
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 ...
Stéphane Jaouen's user avatar
1 vote
0 answers
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 ...
hasanghaforian's user avatar
5 votes
8 answers
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 ...
3rdMoment's user avatar
  • 151
6 votes
1 answer
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-...
Uagi's user avatar
  • 63
4 votes
3 answers
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 ...
user534666's user avatar
-1 votes
4 answers
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....
Michael Hardy's user avatar
0 votes
0 answers
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 ...
Sillyasker's user avatar
1 vote
1 answer
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 ...
Natalie's user avatar
  • 11
14 votes
6 answers
2k views

A good book about mathematical thinking

I am a qualified mathematics teacher but I have left teaching because I could not tolerate the behaviour of students. Now I am a mathematics tutor and I love that I get to teach students who are eager ...
Kristina Dedndreaj's user avatar

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