48 votes
Accepted

Future educators writing nonsense questions

You might try starting this kind of lesson with an assignment where you provide a list of different responses to the prompt "Write a variety of word problems which would require the student to ...
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  • 7,686
22 votes

teach that $\frac10$ not defined properly

What is $\frac 1 a$? It is the unique (real) number such that $a\cdot \frac 1 a=1$. Does there exist a real number that multiplied by $0$ gives $1$? No. Why is this? Because if $0\cdot b=0$ which ever ...
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20 votes

Teaching indefinite integrals that require special-casing

I'd avoid giving problems like that to students first learning indefinite integrals (either by not asking it at all, or specifying the range x>1 in the question). It's a subtle algebraic trap, and if ...
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20 votes
Accepted

Is there a place where I can buy well made calculus 2 and calculus 3 lesson plans and power points?

Assuming you are newly part of a department, ask someone in the department if they have anything you can use. They may direct you to publisher-provided materials or just give you a big pile of things. ...
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13 votes

Best form for slide / beamer presentation: display items in a slide as they are discussed or all at once?

A style which I really like is to have all the material on the slide, but have the material which you haven't reached yet in light grey. Then, as you move forward, advance your slides to turn light ...
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12 votes

Devising backup plan to become HS teacher as a late undergrad

Undergraduate students should be aware of their academic advising offices. Essentially every school employs full-time academic advisers to answer questions precisely like this one. If you go to a ...
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  • 19.1k
12 votes
Accepted

Explaining mathematics, giving talks, and using the blackboard as a support

I struggled with this as a new lecturer, and I found a few ways to manage the process of using a big blackboard: Observe people lecturing When I first started lecturing, I visited the lectures of ...
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12 votes

Teaching indefinite integrals that require special-casing

This is a hard question, because students are so used to manipulation of this kind. I have found you are right that absolute values can cause the worst of these examples. Here is an example I ran ...
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  • 5,752
11 votes
Accepted

Is multiplication by zero clear for and understood by K-3 students?

Turning my comment into an answer as per request: I think the graphical approach gets the idea across. You could represent $3\times 1$ by a row of three dots; likewise, $3\times 2$ is two rows of ...
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11 votes

Teaching indefinite integrals that require special-casing

You are right to be concerned that the students are "missing something", but IMO the real problem here is that the question is completely artificial. In any application of this type of integral, most ...
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  • 879
11 votes
Accepted

Graph theory teaching materials for young students

One of the charms of graph theory is that people of all ages often enjoy learning graph theory ideas and tools. One place one can read about these ideas is in the book called For All Practical ...
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10 votes

Future educators writing nonsense questions

Partial answer regarding an approach to fix this problem. First: Don't tell them (criticism), but lead them to find out themselves (insight). Now comes the fun part. Don't let them write just the ...
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  • 201
9 votes

Grad school backup: high school teacher

tl;dr do a ton of research first before making any decisions IMHO, you shouldn't just whimsically pursue teaching as a "backup plan" if your current plan doesn't work out. Teaching is A TON of work ...
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  • 4,840
9 votes
Accepted

How should I introduce the concept of a function to a precalculus student?

When introducing functions to a student, I usually give thought to two main methods, each with its pros and cons. Method 1: Use the set definition of the function. This is what you're attempting to ...
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  • 296
9 votes

Future educators writing nonsense questions

You might start out by giving them a test in the kind of arithmetic they are supposed to teach. This article in the Guardian from 2010 reported that many primary school teachers in the UK were unable ...
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8 votes

Teaching indefinite integrals that require special-casing

To me, the key point here is that the integral runs over a singularity. If you naively calculates a definite form that runs over the singularity you get the wrong answer. This is something I have ...
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  • 81
7 votes
Accepted

Regarding AMATYC's draft position statement on the academic preparation of mathematics faculty at two-year colleges

After writing an email, I received a response from Ernie Danforth, the NE regional vice president of AMATYC which answer my question. Keep in mind these are GUIDELINES, they are not hard and fast ...
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7 votes

How can a math teacher manage a class when unprepared?

As JoeTaxpayer suggested, my comment is more of an answer than a comment, so I'm copying my comment here. Maybe this will get others to answer, although I realize that appearing to admit that ...
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7 votes

Best form for slide / beamer presentation: display items in a slide as they are discussed or all at once?

Ultimately, I think that this is a matter of taste and presentation style. You should create documents which allow you to present in a way that feels natural to you. My preference (and this is a ...
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6 votes

How to: Learn how to solve a simple equation...in one hour!

It takes a few seconds to download Dragon Box 12+, then your job is just about finished. It will take her a few hours to go through, but it will teach her well. It is also a game, so it neatly ...
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  • 2,588
6 votes

Mathematics in UK vs Central Europe

Part of the answer to your question is that the statement 'mathematics is considered good in the UK and USA' refers, I believe, to research mathematics, not to undergraduate teaching. I don't have ...
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  • 5,540
6 votes

teach that $\frac10$ not defined properly

A little late to the party, but I wanted to add my two cents. The students should understand that they are looking at the value of $1/0$ as a limit. This is good but it's not the entire picture, and ...
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  • 314
6 votes

Is there a place where I can buy well made calculus 2 and calculus 3 lesson plans and power points?

As noted in a comment, most major calculus textbooks at this time (or more generally: almost anything in the standard undergraduate track, at least freshman-sophomore years) comes with slideshow ...
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5 votes

How should I introduce the concept of a function to a precalculus student?

Input-output machine is the most intuitive thing to first give, especially to a weaker student. Ideally, you eventually want to have multiple frames of reference for a function, but to start with......
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  • 1,758
5 votes

Mathematics in UK vs Central Europe

First off I would like to point out that at least one of the things you're comparing is a bad comparison. Mathematical Physics (or in my country just mathematics for Physics majors) will have a ...
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  • 906

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