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To the student who wants to know why he or she should learn addition/multiplication/other mathy thing when they can use a calculator or computer:
It is a matter of independence. You will not always have access to your preferred tool. Being able to compare prices in a store without shamefully pulling out a calculator will boost your confidence that you can ...
42
First, a little background. I switched to slides a few years ago when teaching a 3rd year course at my university. Because of how teaching works at my university, this course is one of the first where as a lecturer I can assume that the students taking it are interested in mathematics as a subject in its own right. That is, they aren't students from ...
37
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 try to give an answer from a different angle based on a recent experience I had in a numeracy class with adult students. One of the questions I asked was inspired ...
32
Under the laws in most countries, a work such as a book is automatically copyrighted as soon as it is written down. Putting the copyright notice in the book isn't what makes it copyrighted. The notice just makes it easier to sue for copyright violation, because it's harder for the person who copied to claim they didn't know the work was copyrighted.
For this ...
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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 sometimes combine nicely with technology tools. I'll provide an example of this.
Consider the following algebra puzzle:
Solve for $x$:
$7x^3 -39x^2+52x+30 = 0$.
If ...
27
I think the issue fundamentally is about a student's comfort with symbols and notation. A student who relies on a calculator thinks of it as a magical oracle that returns an answer to the question being asked. So, when that same student is asked to solve even the simplest of algebra problems, since the calculator can't answer that problem, the student is ...
26
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 computational technique as a way to see.
As a researcher, I find one of the main values of manual calculation is as error correction for reasoning, and a source of ...
24
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 functions here: sawtooth, triangle, partial cubic)
Fourier transform time and frequency domains
Continuous Fourier transform of rect and sinc functions
22
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 better support for many-participant calling and additional features. It has a built-in whiteboard you can write or type on, mechanics for allowing students to "raise ...
17
People who ask why calculators don't resolve the (very low-level) issues well enough are quite accurate in their skepticism, I think, which makes it hard to present an "absolutist" defense of alternatives. For that matter, seriously (!), why is it ok to use Hindu-Arabic numerals and the weird associated algorithms, rather than "honest" manipulations of hash-...
17
The reason we teach strategies for multi-digit operations is (in a large part) because students are learning to manipulate the symbol system we use to represent numbers, and they need to see that there is meaning behind these strings of digits. That understanding carries through not just for subtraction, but for anywhere they'll use multi-digit numbers.
To ...
16
I've created roughly 40 videos for an online course and a flipped course in biology, so I've got some experience making videos. I researched the maker of your videos, and he deliberately does NOT reveal his process. So I don't know if this is his method, but I'm comfortable that this would produce something very similar.
Supplies:
Computer (I use a ...
16
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.
Another answer recommends YouTube to upload source material but I feel this might be inadequate interaction. Other alternatives:
Discord
Recently in response to ...
15
In terms of free software, a large portion of the available choices are based on a Gnuplot backend; I however would probably not recommend directly using Gnuplot. Instead, your choices are mostly between the various front ends. In terms of the front end, depending on what your students are familiar with and are willing to learn, there are many options.
...
15
For undergraduate level, Gnu Octave is probably what you want. It is open source, cross-platform, and syntax-compatible with MATLAB. It's very useful for 2D and 3D plotting and for numeric linear algebra, and it's a tool that will be beneficial for students to know.
Also, GeoGebra is excellent plotting software, and has recently added 3D graphing support. ...
15
One technique which is fairly obvious, but (at least for some of us) surprisingly difficult to implement consistently, is to just model for them in class what you expect them to write on their own. When I solve a problem in class, I try to show the same work and write the same explanations that I expect them to show. I also try to talk about it as I do it, ...
15
Brief Remarks: It is difficult to find longitudinal studies on calculator use as specified by the OP. One of the reasons for this is that tracking students from, e.g., high school till college is quite complicated. Another reason is that studies on technology use are often fodder for theses, which are completed in too short a timeframe to provide such an ...
15
Never.
I think that in 2014 we can teach students to use opensource projects: Sage does a very good job: Sage Notebook is couple times better than Wolfram Alpha since you can use it with no subscription, save your worksheets and it's based on much better programming language than Alpha is.
You will probably very likely find some other free (really free, ...
15
My answer would be neither. A TI-89 is \$80, which is a lot of money for many families, and the functionality it provides beyond that of a \$5 calculator is hardly ever needed. I don't own a graphing calculator myself, so I can't see forcing my students to buy one. A tablet is even more money and even more overkill.
If this is a public high school in the US,...
15
The best thing you can do for your daughter is to talk to her and especially have her talk back to you. You noted that she doesn't like doing exercises. If you want her to like math, and she doesn't like doing exercises, more exercises are not going to help her like math. She is already intrinsically motivated to do certain things. People learn when they are ...
14
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 one to say, at-risk or remedial students has been a failure over and over again. Some links that you should consider:
Recent overview of the field, "The MOOC ...
14
I know a lot of people use slides to teach, but I cannot imagine doing so myself. Here's why:
Slides are boring. It's vital to good teaching to keep the students interested in what's happening, and one of the best ways to do this is to keep things spontaneous. Slides kill spontaneity.
Slides are one-way. They are entirely about the professor conveying ...
14
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 engages the game-playing, obsessive nature in us.
Main use case - Homework engine
The two biggest features of a VLE/LMS are the presentation of materials and ...
13
You might want to look into Geogebra. The current beta version (Geogebra 5 Beta) has a 3D mode and allows you to create 3D plots of a function of the form f(x,y) and a graphical interface for rotating, zooming, etc. It is also open-source, free, and cross-platform.
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All of math is a logical progression. One should master a type of calculation before turning it over to a calculator or computer.
Can I multiply 4386x934754 by hand? Of course I can. And it was important to learn to do this in 4th (?) grade, but soon after, no need for long multiication or division.
Every day, I'm intrigued at the disparity between the ...
12
I'm very happy to see this discussion here, because all of you are saying exactly the things that led to the project I and my collaborator (Ken Monks, Univ. Scranton) are working on, Lurch. It's free, open-source, and cross-platform, so there's no barrier to trying it out any time.
It was mentioned briefly in one of the comments above, but it's so directly ...
12
I TA'd a first course in abstract algebra during my senior year of undergrad. The professor wanted a computational flavor to the course, so we introduced Magma right off the bat. We wanted to allow the students to experiment with permutations without needing to actually do large computations themselves. As part of my contribution to the course, I was put ...
12
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 practice.
Some help with intuition. If the students can see how the ideas could be of use to society as a whole (say through higher-dimensional calculus), even if ...
12
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 to how in calculus, one uses first derivative test, second derivative test, concavity, asymptotes, intercepts, end behavior, etc., all at once, in some ...
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If you type a function into a Google search, you get a pretty nice graph. In order to get interactive 3d graphics, you will need a WebGL enabled browser (with WebGL actually enabled, of course). Try these for starters:
y=sin(x)/x
z=-x^2+y^2
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