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Any examples of calculus sequence that deemphasizes calculation tricks?

I'm considering creating a series of classes that explore deeper ideas in calculus without overemphasizing the various computational tricks used in integration and differentiation. My vision is ...
Bilbo's user avatar
  • 251
2 votes
0 answers
110 views

Which Books Comprised The Houghton Mifflin Modern Mathematics Series

Around the 1960s a collection of math books by authors such as Mary P. Dolciani, William Wooton, Edwin F. Beckenbach, Ray C. Jurgensen etc. started to appear which were part of a series of books ...
fire-bee's user avatar
  • 173
1 vote
0 answers
78 views

"Tools" (literarily) for solving linear or quadratic equations

Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
Hauke Reddmann's user avatar
5 votes
5 answers
202 views

Loaning students calculators during exams

Context: I am an associate professor at a small liberal arts institution in the US. I find in my introductory business math course that students sometimes fail to buy a calculator for the course, ...
AegisCruiser's user avatar
  • 1,399
7 votes
1 answer
596 views

Bridging the gap between students' intuitive problem-solving abilities and expressing ideas through formal writing

Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to ...
user1258481's user avatar
2 votes
1 answer
179 views

What age group is this puzzle appropriate for?

I have created the following simple tiling puzzle for children. The puzzle consists of 9 tiles shown below (4 pieces of type A, 4 pieces of type B and 1 piece of type C): The goal of the puzzle is to ...
Will Octagon Gibson's user avatar
2 votes
2 answers
2k views

Where can I find new types of problems regarding graduate level mathematics?

Though not an undergraduate student , I just wanted to know where can I find hard new types of problems regarding the problems in graduate level mathematics. As per my information , standard books ...
Soumyadip Das's user avatar
9 votes
5 answers
2k views

Requesting a Polynomial System of Equations

I am teaching a course in commutative algebra, and it includes a project where the students research on a particular topic, solve a small problem and present it to the class. I usually give my ...
Aravind Gundakaram's user avatar
2 votes
1 answer
159 views

Help finding a YouTube channel for Linear Algebra

I remember watching a youtube playlist on a video about equation of a plane and about vectors in 3D. The video was fully animated in 3D and had good sound effects too. I feel like it had a clock ...
Broy Tennison's user avatar
2 votes
2 answers
245 views

How to motivate ‘unless’ = ‘if not’, with etymology?

My undergrads still reckon Nelson Lande’s 2 motivations for ‘unless’ = ‘if not’ (below) too abstract, formalistic! They crave simpler intuition! Thus I want to proffer a 3rd motivation, this time with ...
user726n98e09t's user avatar
-1 votes
1 answer
37 views

Ratio in Fractional Form [closed]

I have 3 puppies and 2 piglets. Can you that ratio be written in this fractional form 5/2? If yes, how would you describe this ratio as 5/2?
Monika's user avatar
  • 7
6 votes
3 answers
236 views

What to do with "wild goose chase" or "quantum leap"-types of incorrect solutions when you ask students to prove/show something?

So in an advanced mathematics course for engineers, there are often problems of the type: Prove claim A. Given equation A, show that you can obtain equation Z. I am frequently faced with a problem ...
Fraïssé's user avatar
  • 737
12 votes
11 answers
4k views

Does a proof by induction have to explicitly refer to the principle of mathematical induction?

I teach high school math. Some of my colleagues insist that a proof by induction should explicitly refer to the principle of mathematical induction, i.e. it must include the words "by the ...
Dan's user avatar
  • 771
0 votes
5 answers
250 views

Are logic textbooks wrong to teach ‘unless’ = ‘or’? How to motivate?

Most times in English, it’s ungrammatic to swap ‘unless’ with ‘or’! Aren’t the textbooks below wrong? My undergrads can master Truth Tables, but still fail to intuit why ‘unless’ = ‘or’. How to ...
user726n98e09t's user avatar
10 votes
12 answers
3k views

Fixing wrong ideas about coefficients (e.g. subtract 3 from 3x to isolate x)

I tutor a student (9th grade, United States) who is in an algebra class. She consistently makes mistakes when dealing with coefficients. The most common one is attempting to subtract away a ...
bobble's user avatar
  • 363
0 votes
2 answers
204 views

What will happen if someone doesn’t make it to the IMO team?

I am highly interested in mathematics, and solving Olympiad maths problems has been a type of hobby for me. But due to my age, I will never be able to give the olympiads a go again. I want to know ...
Soumyadip Das's user avatar
1 vote
1 answer
2k views

How does a math Olympian fare in undergraduate maths courses?

I am a maths enthusiast and have been exposed to maths olympiad problems for some time. I wanted to know how does a math Olympian do in undergraduate courses of mathematics, statistics or computer ...
Soumyadip Das's user avatar
1 vote
1 answer
101 views

Speed math appropriate for middle-school students

There are many "rules" for speed arithmetic. List of some reference links showing speed methods or rules: https://ofpad.com/multiplication-tricks-for-mental-math/ https://ofpad.com/mental-...
EngrStudent's user avatar
-4 votes
2 answers
205 views

Order of operations pemdas

Why was the order of operations established in mathematics with multiplication taking precedence over addition, as dictated by the PEMDAS rule? What historical or practical factors influenced this ...
Humberto José Bortolossi's user avatar
5 votes
4 answers
2k views

How can we explain intuitively the convergence and divergence of these two series?

It is known that $\displaystyle\sum_1^{\infty} \frac{1}{n^{1.000001}}$ converges while $\displaystyle\sum_{n\text{ is a prime number}}\frac{1}{n}$ diverges. Though we can logically prove these results,...
Zuriel's user avatar
  • 4,245
8 votes
3 answers
1k views

Is there a standard convention for interpreting ambiguous absolute value expressions?

Consider the expression $$|x + 2|x + 3|x + 4|.$$ One way to interpret this is that there are two products being added together: $$|x+2|x \hspace{1cm} + \hspace{1cm} 3|x+4|$$ But you could also ...
Justin Skycak's user avatar
-4 votes
1 answer
104 views

PROBABILITY QUESTION [closed]

How to solve this probability question?f a, b, and c are in the range [0, 1], what is the probability that the quadratic equation ax^2 + bx + c has real solutions? justify your answer! This question ...
Humberto José Bortolossi's user avatar
3 votes
11 answers
3k views

Importance of complex numbers knowledge in real roots

Many students question the importance of complex numbers in real life. We can find many important applications of imaginary numbers in Engineering field and physics. This question is not related to ...
Janaka Rodrigo's user avatar
1 vote
1 answer
86 views

Summer or Semester Programs which bridge to Graduate Mathematics

A few years back I had a student attend the MASS semester at Penn State. It was a fantastic experience for my student and it certainly helped him find a place in graduate school and I would wager it ...
James S. Cook's user avatar
6 votes
11 answers
5k views

How can I teach intuition why ‘If P then Q’ and ‘P only if Q’ mean the same, to first year undergraduates?

In every of my ten years as course instructor introducing first year undergraduates to proofs, I always project this quotation on the lecture screen, then dictate the whole caboodle word for word! But ...
user1110341's user avatar
2 votes
3 answers
164 views

Engaging Mathematical Riddles for Classroom Enrichment: examples and impact studies references

Hello fellow educators and math enthusiasts, I am on the hunt for entertaining and thought-provoking mathematical riddles suitable for a classroom setting. My objective is to find riddles that not ...
Humberto José Bortolossi's user avatar
6 votes
3 answers
147 views

Game project using linear algebra

Throughout this year, I have been in charge of a linear algebra course aimed at engineering school. In this course, I asked my students to work on a final project involving finding a winning strategy ...
Gabriel's user avatar
  • 61
9 votes
6 answers
1k views

Intuition for order of operations in compound transformations

This is a close cousin of the previous question asked here about transformations inside and outside a function and how they switch things around. I think some of the perspectives there will help here, ...
Kevin P. Costello's user avatar
1 vote
2 answers
72 views

Online Probability Simulation for Compound Events

I'm teaching Grade 9 Probability. We need to compare Experiment Probabilities (Relative Frequencies) with Theoretical Probabilities for Simple and Compound Events. I want to come up with and Online ...
pdmclean's user avatar
  • 957
4 votes
4 answers
327 views

Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?

Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
Justin Skycak's user avatar
3 votes
0 answers
69 views

Examples of Financial Institutions that Compute Interest Atypically?

Are there examples of financial institutions that compound their interest more frequently than once-a-month? Are there examples of financial institutions that consider continually compounded interest ...
Mike Pierce's user avatar
  • 4,606
0 votes
1 answer
102 views

Chinese and Japanese most important high school textbooks

I would like to know the best high school math books from Japan and China. Can you suggest some books or free resources? I would like to compare the different approach betweeen China and Japan and ...
ryuk's user avatar
  • 101
13 votes
18 answers
5k views

What are some "deep" questions to explore in elementary school math?

My first grader is very advanced in math. Rather than doing more and more math and making school math even more boring for him, I recently decided to start going "deeper" rather than "...
Akdinv's user avatar
  • 373
1 vote
1 answer
106 views

Idea of using LLMs to help communicate ideas in math

What do you guys think about the ideas presented in this short text: https://github.com/yougetyourmanwww/AI-for-math/blob/main/AI.md The text is about how LLMs like chatGPT can be used for when doing ...
user23248's user avatar
9 votes
8 answers
4k views

Why do most Analysis textbooks overlook, and fail to teach delta-epsilon proofs, using the K-ε principle?

When writing $\delta$-$\varepsilon$ proofs, it's common that the ''natural'' choice of $\delta$ leads to the final inequality in the form, say, $|\ldots| < \varepsilon+\varepsilon+\varepsilon$ ...
user27289's user avatar
  • 139
8 votes
2 answers
150 views

Cognitive activation vs cognitive load reduction

During my teaching training in Germany and in many professional development sessions, there has been repeated emphasis on the importance of cognitive activation and challenging tasks for effective ...
Julia's user avatar
  • 1,128
13 votes
5 answers
4k views

Role of human math teachers in the century of AI learning tools

In view of recent developments of AI-based adaptive math learning systems like Squirrel, Aleks, Knewton Alta, or Math Academy: Does a human math teacher play any reasonable role, or will those systems ...
Julia's user avatar
  • 1,128
2 votes
1 answer
353 views

Feedback from AI based learning to human based learning in math?

There are several AI based adaptive learning environments out there like Squirrel, KNewton or MathAcademy. Are there any studies which try to extract from the (big) data of those learning systems ...
Julia's user avatar
  • 1,128
1 vote
3 answers
497 views

Basic skill requirement suspension

Oregon appears to have suspended the "basic skills" requirement for graduation; see this. What will be the effect of this on the mathematical proficiency of the graduating class? Follow-up ...
Mikhail Katz's user avatar
  • 2,102
4 votes
2 answers
133 views

What are some decent apps for Hasse diagrams?

What options are out there for software that supports interactively constructing, editing, and manipulating Hasse diagrams? Their semantics is significantly constrained, so garden-variety Let’s-draw-...
Paul Tanenbaum's user avatar
2 votes
4 answers
380 views

How can one lone picture prove the Triangle Inequality, $|x−y|≤|x|+|y|$, $|x|−|y|≤|x−y|$, and the Reverse Triangle Inequality?

I always showcase separate pictures of Triangle Inequality, and Reverse, to 16-years-old students in 1st class. I reshow pictures in 2nd class. I preachify Please remember these 4 inequalities. ...
user27289's user avatar
  • 139
1 vote
1 answer
196 views

Identifying Trigonometrical proofs

How can we identify trigonometrical proofs from geometrical proofs, do we have purely trigonometrical proof of Pythagoras theorem as claimed by two high school students ? https://www....
Janaka Rodrigo's user avatar
3 votes
1 answer
93 views

Alternative to Quizlet live that supports latex formulas

With Quizlet Live you can play a flashcard game in classroom, where teams compete against each other. Since Quizlet doesn't seem to support rendering latex formulas, I am looking for a alternative ...
Julia's user avatar
  • 1,128
33 votes
17 answers
7k views

Natural origins or learned habit: Why do students skip concepts before applications?

When teaching elementary mathematics, it takes a lot of time and effort to teach students that our goal is not to learn the examples, but to learn the concepts first, and then apply them to specific ...
Mahdi Majidi-Zolbanin's user avatar
2 votes
3 answers
259 views

Is this a viable Calculus 1 question?

A person is standing next to a hot air balloon. At the same time, the person starts moving away from the balloon at 5 ft/sec and the balloon rises straight into the air at a rate of 12 ft/sec. Is the ...
Maesumi's user avatar
  • 1,084
28 votes
3 answers
7k views

When is it appropriate to warn about the difficulty of a subject?

I've been a TA across every class in the calculus sequence, under the assignment of professors with different teaching styles and curricula. It's often clear to me ahead of time when a certain subject ...
Feryll's user avatar
  • 389
5 votes
13 answers
17k views

To 17 year olds, how can I explain that two numbers with arbitrarily small difference are equal?

$|a – b| < ε, \forall ε > 0 \iff a = b$ resurfaces on standardized tests to 17 year old (y.o.) students, who can memorize and regurgitate the proof to earn full marks. But the glut of duplicates ...
user95017's user avatar
  • 419
0 votes
4 answers
273 views

How to motivate $x^n−y^n ≡ (x−y)(x^{n−1}+x^{n−2}y+...+xy^{n−2}+y^{n−1})$, to 13 year olds?

You can safely presuppose that 13 year old (y.o.) students learned the Difference of Squares and of Cubes identities, before tackling this Difference of Powers Identity ($x^n – y^n$). The glut of ...
user95017's user avatar
  • 419
0 votes
3 answers
282 views

How to explain why we can’t factor $x^n + y^n$ for all natural numbers n, to 13 year olds?

Michael Spivak, Calculus (4th edn 2008), p 13. I know this monograph is aimed at undergraduates (not middle schoolers), but this kind of multiple-part question resurfaces on standardized tests for 13 ...
user95017's user avatar
  • 419
14 votes
5 answers
13k views

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I transcribed this excerpt starting at the 22-minute mark, of Okinawa Institute of Science and Technology’s May 19 2020 podcast with Professor Tadashi Tokieda: For example, this is a bit too ...
user95017's user avatar
  • 419

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