# Tag Info

Accepted

The student changed something which was indeterminate ($\infty-\infty$) into something which was not ($\infty\cdot \infty$). How does that not merit a perfect score? Changing indeterminate expressions ...
• 5,733
Accepted

### How rigorous should high school calculus be?

Not very rigorously at all, but that doesn't (and shouldn't) mean just memorizing calculations. (I should add that I'm basing this on my experience teaching calculus to non-major college students, ...
• 11.6k

### What do you do in order to drag out lectures?

What you are describing is so far outside of my, and I suspect most educators, experience that it appears to be literally incredible. The very strongest Universities in the country, with some of the ...
• 25.6k
Accepted

### Is there a canonical name for a polynomial-like expression allowing for negative powers?

There is also the term "Laurent series", where we allow an infinite number of terms... $$\dots +5x^{-3} + 2x^{-2} + 3x^{-1} + 2 + 4x - 7x^2+\dots$$ So perhaps yours is a "finite ...
• 7,607

### Why are calculators not allowed in post-secondary exams?

As a professor/teacher I have some insight. You just answered your own question: "my level of math right now is not basic. So, like many, I tend to forget the basics of math, like adding fractions, ...
• 836

### Do I really need to cover solids of revolution in my Calculus I class?

An operation is born when we recognize the regularity in repeated reasoning. Take multiplication for example. If we are living lives which involve even a modest amount of arithmetic thinking, we will ...
• 25.6k

### Why is differential calculus often presented before integral calculus?

While there are no theoretical difficulties with developing integration first ("from scratch" measure theory books demonstrate this), it presents some pedagogical challenges. Most problems ...
• 25.6k

### What is the best way to intuitively explain the relationship between the derivative and the integral?

You start by noticing that the Riemann sums (multiplication followed by addition) and the difference quotients (subtraction followed by division) undo each other. Their limits -- the integral and the ...
Accepted

• 586

### Tutoring a recalcitrant/awkward/exasperating student---special needs?

How do I reach [this] kid? Let me be blunt: You probably don't. This is a person who is so intransigent that you effectively need to black-tag them. A hard lesson is that you can't save everyone. At ...
• 26.1k

### Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs

Sadly, these students seem to think of math as a bunch of rules. You have done great work, and probably gotten them a little closer. But they are resisting the reasoning that can't easily be put into ...
• 20.8k
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### What are some rationales to teach Computer Science students Sequences and Series?

Big O and related notations relate closely to these notions. They are often defined using limits. Although it is also possible to define them without using limits, the style of those definitions is ...
• 286

### How to properly define volume for beginner calculus students?

It depends somewhat on the style of the course, but the majority of calculus students do not need a formal definition of volume or area, in my experience. They have studied geometry and (usually) ...
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• 4,845
Accepted

### An introductory example for Taylor series (12th grade)

One practical reason for choosing a Taylor Series approximation of a function over the function itself is if you are able to compute using only the four arithmetic operations. For example, if you are ...
• 10.8k

### Why are calculators not allowed in post-secondary exams?

In addition to @BobaFret's answer I'd like like to point out following: You said: Before you downvote this question, I actually want an answer to this. Is the calculator going to give me my ...
• 409

### How shall we teach math online?

Instructor at University of Washington here - we were one of the early closures, so I feel like we're starting to get the hang of it. Here's what I'm using: Zoom: Zoom is similar to Skype, with ...
• 1,994

### I'm worried that my struggles with calc 2 mean I won't be able to become a professor later

A lot of students seem to make it through high school and well into college with the idea that school is supposed to be easy, and that having to work hard, or being confused at times, or struggling ...
• 11.6k

### Tutoring a recalcitrant/awkward/exasperating student---special needs?

This is a student who doesn't understand social cues. He only knows that if he is rude you keep trying. If acts disruptive, he will get the answer without working for it. As long as you reward him ...
• 8,017

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