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49 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 ...
Nick C's user avatar
  • 9,639
21 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 ...
Nicola Ciccoli's user avatar
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 ...
Henry Towsner's user avatar
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. ...
Chris Cunningham's user avatar
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 ...
David E Speyer's user avatar
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 ...
kcrisman's user avatar
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11 votes
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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 ...
Joseph Malkevitch's user avatar
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 ...
alephzero's user avatar
  • 889
11 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 ...
jvb's user avatar
  • 211
10 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 ...
Paul Johnson's user avatar
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 ...
mmdts's user avatar
  • 296
9 votes

Elementary Teacher Math specialist/ Basic Math Minor

The top priority should be ensuring that elementary education majors have a deep and mathematically-sound understanding of elementary school mathematics. They need to (re)learn the core mathematics ...
Justin Hancock's user avatar
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 ...
Andrew's user avatar
  • 81
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 ...
Xander Henderson's user avatar
  • 8,225
7 votes

Why is calculus important for pre-service Math basic school teachers?

When the undergraduate curriculum for preservice teachers does not include mathematics beyond middle school (say grades 6-9, algebra 1 or algebra 2 in the US), then what can happen in some cultures is ...
user52817's user avatar
  • 11k
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 ...
CosmoVibe's user avatar
  • 324
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 ...
Jessica B's user avatar
  • 5,822
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 ...
Daniel R. Collins's user avatar
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 ...
DRF's user avatar
  • 1,018
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......
guest's user avatar
  • 1,828
4 votes

Graph theory teaching materials for young students

Here are GeoGebra materials: Graph Theory for Kids, inspired by Joel Hamkins' notes, to which @A.Goodier pointed.                     Four-color ...
Joseph O'Rourke's user avatar
4 votes

Teaching indefinite integrals that require special-casing

This sort of example is not artificial and needs more careful treatment than it often receives. The inherent difficulty of the example is compounded by the tendency to discuss primitives without ...
Dan Fox's user avatar
  • 5,869
4 votes

Why is calculus important for pre-service Math basic school teachers?

As Tommi commented, the question is a bit imprecise, but attempting to address it: I don't think lower level teachers (early grades) [IN GENERAL] are required to take calculus. If they are as part ...
guest's user avatar
  • 49
3 votes

teach that $\frac10$ not defined properly

If the students can think about graphs, you can graph y=1/x. So if 1/0 = ∞, this should approach ∞ as x -> 0. It does on one side. But on the other, it approaches -∞. Since it doesn't approach ∞ from ...
Sue VanHattum's user avatar
  • 20.8k
3 votes

To what extent is MSE reputation an indication of potential in education?

I'm not a tenured faculty member so take this with a grain of salt: No one is going to care, your reputation in the field and job prospects will almost certainly be based on your PhD work. Many people ...
Nate Bade's user avatar
  • 1,941
3 votes

To what extent is MSE reputation an indication of potential in education?

It's an imperfect correlation. The best athletes are not always the best coaches. Sometimes those who struggled to perform can teach better than the star athletes that did it all naturally. The ...
guest's user avatar
  • 1,828

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