# Tag Info

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 ...
• 9,639

### 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 ...
• 1,715

### 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 ...
• 11.6k
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. ...
• 21.7k

### 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 ...
• 5,332

### 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 ...
• 5,976
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 ...
• 1,872

### 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 ...
• 889

### 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 ...
• 211

### 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 ...
• 201
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 ...
• 296

### 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 ...
• 3,120

### 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 ...
• 81

### 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 ...
• 8,225

### 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 ...
• 11k

### 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 ...
• 324

### 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 ...
• 5,822

### 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 ...
• 26.1k

### 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 ...
• 1,018

### 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......
• 1,828

### 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 ...
• 29.8k

### 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 ...
• 5,869

### 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 ...
• 49

### 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 ...
• 20.8k