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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 ...
Amir Asghari's user avatar
  • 4,438
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 ...
Chris Cunningham's user avatar
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 ...
Justin Skycak's user avatar
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 ...
Jon Bannon's user avatar
  • 6,173
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 ...
Reese Johnston's user avatar
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. ...
James's user avatar
  • 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 ...
Tommi's user avatar
  • 7,368
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 ...
Boyd's user avatar
  • 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 ...
guest's user avatar
  • 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 ...
Eric Towers's user avatar
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 ...
Dmitry Kamenetsky's user avatar
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 ...
Jessica B's user avatar
  • 5,832
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 ...
Daniel R. Collins's user avatar
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 ...
user52817's user avatar
  • 11k
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 \...
Steven Alexis Gregory's user avatar
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. ...
Matthew Daly's user avatar
  • 5,629
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 ...
J. Plencner's user avatar
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 ...
James S. Cook's user avatar
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 ...
MadScientist's user avatar
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 ...
user52817's user avatar
  • 11k
8 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 "...
guest's user avatar
  • 105
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 ...
Alias K's user avatar
  • 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 ...
Daniel R. Collins's user avatar
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 ...
user1815's user avatar
  • 5,760
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 ...
JRN's user avatar
  • 10.9k
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 ...
Opal E's user avatar
  • 4,043
7 votes

How much does it cost to develop an online course?

I am using zoom, and getting better attendance sometimes than in my face-to-face classes. Modified tools for getting interaction: I ask students to put a number from 1 to 5 in the chat to rate their ...
Sue VanHattum's user avatar
  • 21k
7 votes

Why do we teach the Rational Root Theorem? (high school algebra 2)

I would reluctantly agree that it's not a particularly powerful tool if you have electronics at your disposal. But I might double down and say that you should be teaching synthetic substitution as ...
Matthew Daly's user avatar
  • 5,629
7 votes

Is there a math curriculum that is aware of CAS and the internet?

You could look at https://neilstrickland.github.io/maths_with_maple/. This is a full set of material for a CAS-based course which is mostly calculus but has some precalculus. It was originally ...
Neil Strickland's user avatar

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