38
votes
Accepted
How to solve the problem of Wolfram Alpha?
First of all, I believe this question is quite similar to the question "How to give homework for integration technique?". I avoid the temptation of repeating my answer for that question. Instead, I ...
- 4,418
33
votes
Why do we teach the Rational Root Theorem? (high school algebra 2)
I would say the standard implementations of the Rational Root Theorem (make a huge list for the sake of making the huge list) indeed feel like a complete waste of time. However, the theorem can ...
- 21.2k
28
votes
Role of human math teachers in the century of AI learning tools
I'm the Director of Analytics & Algorithms for Math Academy; of particular relevance to this question, I also spent about a decade teaching/tutoring math human-to-human, as well as several years ...
- 6,171
27
votes
How to solve the problem of Wolfram Alpha?
Imagine you had to look up every word you wanted to use, because you had a poor vocabulary. This would get old, very quickly.
The trouble is, many people don't have a genuine need to internalize ...
- 6,045
24
votes
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 ...
- 1,984
18
votes
How shall we teach math online?
Already put two comments but ideas keep coming to me so I'll just package them here. Keep in mind I'm not an educator, I'm just trying to think of practical solutions to the problem as a whole.
...
- 281
16
votes
Role of human math teachers in the century of AI learning tools
Many (most?) mathematics learners benefit immensely from social, mathematical discussions, and often multi-modal ones where people speak, write, point at things, explain what is happening by using ...
- 6,741
15
votes
How shall we teach math online?
The case for WeBWorK
tl;dr - use WebWork as an easy way of giving students as much practice solving problems as they can handle. Learn by doing lots of problems with a tight feedback loop. It ...
- 171
13
votes
Why do we teach the Rational Root Theorem? (high school algebra 2)
Agreed...it's one of the less useful parts of high school algebra. But not because "you could use a computer"--you could say that about almost everything. And then we get some of the same ...
- 131
13
votes
Why do we teach the Rational Root Theorem? (high school algebra 2)
The RRT is not taught in isolation. It is taught as a collection of tools for (partially) factoring polynomials. It should be taught with Descartes' rule of signs and some form of polynomial ...
- 641
13
votes
Role of human math teachers in the century of AI learning tools
I joined this community just so that I could answer this question.
I work in AI and I am big proponent for it. However I do not believe that it is ready to replace math teachers, nor do I think it is ...
12
votes
How to solve the problem of Wolfram Alpha?
It doesn't exactly solve the problem, but one way to make positive use of Wolfram would be to use some Wolfram Demonstration Projects.
There are some that attempt to gamify calculus calculation ...
- 5,762
12
votes
How shall we teach math online?
I gave a presentation to my department about this today. Like you, as I see in a comment, I am also at a CUNY math department. I haven't done all-online classes before, but I've used Blackboard ...
- 24.3k
12
votes
Why do we teach the Rational Root Theorem? (high school algebra 2)
I think an important learning outcome of this part of high school Algebra 2 (theory of polynomials) is developing mathematical capacity to juggle several disparate abstract tools all at once, similar ...
- 10.3k
12
votes
Why do we teach the Rational Root Theorem? (high school algebra 2)
Let $x = \sqrt 2 + \sqrt 7$ prove that $x$ is irrational.
\begin{align}
x - \sqrt 2 &= \sqrt 7 \\
x^2 - 2\sqrt 2x + 2 &= 7 \\
x^2 -5 &= 2\sqrt 2x \\
x^4 -10x^2 +25 &= 8x^2 \...
11
votes
Algorithmic thinking problems
One well-known source is Project Euler. The concept behind it is that each problem is mathematical and designed to be solved by an efficient algorithm on a "normal" computer in less than a minute. ...
- 5,599
10
votes
A study comparing effects of calculator usage on later math skills?
Studies such as Suydam (1979) indicate that there is not an adverse effect. However, most of the cited studies on the effects go back to the late 70's or early 80's. Anecdotally, as a high school ...
- 101
10
votes
Accepted
Sliderule for teaching logarithms
Anecdote: For some years I've been trying to get my hands on a slide rule and I can't find any vendor who sells them.
This highlights the fact that for general purposes the electronic calculator has ...
- 24.3k
10
votes
How shall we teach math online?
I like You Tube for posting videos. Once you get started it's pretty simple. There are various levels of privacy possible which you can read about. If your school has a convenient way to post videos ...
- 10.7k
10
votes
How much does it cost to develop an online course?
The Lone Ranger had escaped many dangers, but this time, the situation was hopeless. Back to the wall with 200 wild Indians surrounding him.
He turned to his faithful sidekick, Tonto, and said "...
- 109
9
votes
Are there any video games/app to teach children at age 3-4-5?
Not formally an answer (so if you have one, do not let this prevent you to post it), but I think challenging the implicit assumption that it would be good to have your kid use any such software ...
- 9,079
8
votes
Sliderule for teaching logarithms
As Daniel's answer states, the most likely reason why slide rules are rarely used to teach logarithms boils down to them being hard to come by. As they have been replaced by electronic calculators, it ...
- 921
8
votes
How to solve the problem of Wolfram Alpha?
You can also use Wolfram Alpha to look up definitions of words. So by reductive reasoning, there is no need for infants to learn vocabulary because when they are old enough to use a smartphone, people ...
- 10.3k
8
votes
Writing mathematics in real time for lectures using Latex
I believe Overleaf would be your best bet. I am currently taking a class right now where the lecturer writes up the contents of the lecture using overleaf and it's very feasible. Even though you don't ...
- 251
8
votes
Worth introducing a mandatory short module on $\LaTeX$ into a mathematics degree?
I do think that having an introduction and primer to LaTeX in the course of a college math/computing degree is appropriate and beneficial.
For example, I work this into my discrete math course, and ...
- 24.3k
8
votes
Role of human math teachers in the century of AI learning tools
I'll address a narrow aspect: Access to quality, minimum-standard instruction in math. Two hundred years ago, access to quality math instruction was limited, at least in the US. General public ...
- 5,345
7
votes
Do iPhones help students in their math class?
Some anecdotes. I have volunteered with 5th grade math students for a few years. The general rule is, they do not use electronics unless instructed to do so.
We came to a problem where it says to ...
- 7,369
7
votes
How to solve the problem of Wolfram Alpha?
Show your students some simple questions that Wolfram Alpha cannot answer.
Wolfram Alpha currently cannot satisfactorily answer some problems stated in words. For example, the query "find the ...
- 10.8k
7
votes
Algorithmic thinking problems
Any puzzle game which requires students to plan the entire problem before executing it might help. Also, there are physical puzzles which can be solved algorithmically much more neatly than if they ...
- 3,996
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