Desmos Graphing Caluclator

Desmos Graphing Caluclator

Desmos is an education startup, currently with one major offering – an online graphing calculator. Graph any equation, cartesian or polar coordinates, exponential and trigonometric functions, and multiple equations at the same time. Using MathQuill (a what-you-see-is-what-you-get LaTeX editor for HTML5) and/or a built-in key pad users can easily enter and seamlessly edit any equation.

Users can also create a free account to save graphs and use a projector mode to display on in-class screens.

Desmos Graphing Calculator - On Screen Controls

A screen shot of the calculator in-browser, here you can see the on screen controls.

Aesthetics: 7
Entertainment: 2
Usability: 10

I am currently trying to rebuild my own mth skills after years of neglect, starting from precalculus on through multivariable calculus. My main tool for this has been Khan Academy, which has a great set of exercises arranged in a knowledge map, but a TERRIBLE calculator interface. I haven’t had a chance to play with the two simultaneously yet, but I strongly suspect that Desmos’s calculator is going to be a hugely useful tool for visualizing and manipulating complex functions.

Desmos Graphing Calculator Screen Shot 2

In this screen shot you can see the display options, including a projector mode that makes everything a little bolder for better display on class room projectors.

Additional awesomeness include the explorations, where users can explore graph-able functions ranging from different forms of linear equations, through derivatives; and the graph gallery, where users can peruse other users recently saved graphs.

Desmos Online Graphing Calculator - Trig. Functions Exploration

Here is one exploration, which graphs any/all of the trig functions. On the right some points of intersection have been selected showing their coordinates, on the left is the menu for selecting different explorations.


Khan Academy

I almost feel like reviewing Khan Academy is unnecessary, it has been so prominent over the past few years. However, it is one of the most impressive online resources for learning, and I like it, so this site would be incomplete without it. Khan Academy is an enormous, diverse, and free collection of online lectures across an equally enormous number of subjects – in their own words “from math and finance to history and art.” Plus math exercises, an interactive computer science section, and the potential for much more. Khan Academy is a rapidly growing . Because they are constantly adding new lessons, and expanding features, this article will probably be out dated by the end of the year, if not the week.

Aesthetics: 8
Entertainment: 6
Usability: 9
Bonus: Huge number of subjects!

Note: Almost exactly the day after I posted this Khan Academy updated their interface. I have updated the first image, but the rest of the screen shots below still show the old interface.

If there is a subject you want to learn about, it is probably here. The majority of the material is video lectures – usually 4-10 minutes. In the videos, the teacher, often Salman Khan himself, speaks over a visual presentation to explain the subject. While I haven’t seen many, those I have seen are quite good. There has been some back lash (see the links at the bottom of the page), and it is key to note that Salman is not a professional teacher, nor a certified expert in every subject he covers. However, he is smart and he speaks in common language that I think is accessible and accurate. Khan academy shouldn’t replace school, or college, but these thousands of lessons are a great place to start with any subject. But wait – there’s MORE!

Khan Academy Home Screen Shot

The home page – look at all that stuff! In the top left you’ll see a drop down menu, with a link to the knowledge map.

Mathematics exercises, with a map! These can be accessed by searching for the material, or via the knowledge map (see above to find your way to the map; look below for a picture of the map).

Khan Academy exercises are great for sticky subjects students are stuck on, need to review, or just practice. Problems come as straight numbers, and sometimes word problems, with randomly generated values. In my experience one of the most mechanical and time consuming tasks for a teacher or tutor is generating problems that make sense and solve with a clean/neat answer. Not only do these exercises vary the numbers, they include “hints” that gradually walk though the problem, and then reveal the answer.

Khan Knowledge Map Screen Shot

Look at all that knowledge!  One complaint I have is that the knowledge map doesn’t zoom out very far – to get this screen shot I zoomed out by pressing Ctrl and the minus key, use Ctrl + to zoom back in.

The problems come in “stacks,” illustrated by the stack of cards (see below, top right).  Student can score a 1-3 leaves on each card. 3 leaves for a correct answer on the first try, 2 for a second attempt or with hints, 1 if the answer has been revealed by showing all the hints. At the end of a stack the number of leaves is shown, plus the number correct in a row, plus the number answered “quickly”.

A Khan Exercise Screen Shot

The Scratch pad allows students to do work on the screen, and then they enter their answer on the right. Here I have shown all the hints to the problem, just to illustrate, but showing all the hints results in a maximum score of 1 leaf.
Khan Results
The fire cards shows the number answered quickly, while lightning indicates the longest streak of correct answers, and leaves shows the number of points earned.

For more information on Khan Academy check out the links below.

If you like Khan Academy, you might also like:

Some of coolest videos on Khan Academy – under construction – suggest one in the comments!

Criticisms of Khan Academy

Among teacher and education innovators there is a huge amount of criticism of Khan academy. The reason for this is the mainstream media’s unchecked exuberance for the site, which overlooks major flaws and growing pains inherent to the website. Some examples below: