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 ...
- 8,558
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 ...
- 1,715
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 ...
- 11.4k
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.
...
- 20.3k
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 ...
- 4,760
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 ...
- 5,856
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 ...
- 1,862
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 ...
- 889
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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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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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 ...
- 296
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 ...
- 4,900
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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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 ...
- 341
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 ...
- 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 ...
- 7,118
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 ...
- 8,550
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 ...
- 314
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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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 ...
- 21.6k
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 ...
- 1,008
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......
- 1,792
4
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 ...
- 18.9k
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 ...
- 28.7k
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 ...
- 5,670
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 ...
- 49
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