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 ...
  • 4,324
30 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 ...
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 ...
  • 5,887
24 votes

Fourier Animation

Wikipedia always has some great animations, often by User:LucasVB or User:Cmglee. A few Fourier transform–related ones: Approximating a square wave with a Fourier transform (more of these for other ...
  • 341
23 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 ...
17 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. ...
  • 271
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
14 votes

Experiences with online courses, specially MOOC?

A year after this question was asked, the bloom is definitely off the MOOC rose. The primary finding is that the majority of people who finish one already possess a prior bachelor's degree; offering ...
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 ...
  • 5,634
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 ...
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 ...
  • 8,133
11 votes

Is it morally acceptable to complete math homework with a program oneself has written?

TL;DR Yes, as long as the teacher didn't explicitly forbid it, you wrote the mathematical core of the program yourself, the technique you are using doesn't twist the intent of the problem. Teacher ...
  • 8,777
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. ...
  • 5,559
11 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 ...
  • 111
11 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 \...
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 ...
10 votes
Accepted

Statistics Class Held in a Computer Lab

I have been an IT/maths teacher, so I have spent several years teaching in a computer lab, and watched others use the room, sometimes very effectively, sometimes not so much. I have recently seen ...
  • 2,598
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 ...
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 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
10 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 ...
9 votes

Appropriate ways/sayings to discourage undergraduate students' overreliance on calculators

Modeling mental math strategies as part of your teaching is important. I make a show of the fact that I'm not pulling out a calculator. I also show them how I think through certain calculations: "36*...
  • 18.3k
9 votes

Fourier Animation

The Wolfram demonstrations project has several, including: http://demonstrations.wolfram.com/FourierSeriesOfSimpleFunctions/ See here for the full list: http://demonstrations.wolfram.com/search....
9 votes

Fourier Animation

I would suggest using a freely available program to generate and analyse signals. Audacity is a freely available program that can generate various waveforms (sine, square, triangle, sawtooth) and can ...
  • 290
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 ...
8 votes

Appropriate ways/sayings to discourage undergraduate students' overreliance on calculators

I think one reason students reach for their calculators so readily is out of fear. They are afraid that they will get the answer wrong, and would rather rely on an oracle which "always gives the ...
8 votes

Statistics Class Held in a Computer Lab

I see you teach university level courses, however, I think that my experience in a high school classroom may offer some insight. I teach an introductory applied statistics class at my high school ...
8 votes

How to create a misuse of calculator!

Reminds me of a story a friend (who is a math teacher) told me. Student comes to him and says his calculator is broken - it shows (-5)^2 = -25. ...
8 votes
Accepted

Is it morally acceptable to complete math homework with a program oneself has written?

I put my recommendation first, with my reasoning about the moral basis of school and homework underneath if you are interested. Recommendation It is not cheating and is probably more moral than doing ...
  • 2,598

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