In January, I wrote about WolframAlpha iPhone apps for algebra, calculus, and music. There also exist astronomy and multivariable calculus apps.
Your humble correspondent could finally test two new "course assistant" apps described at the WolframAlpha blog. They help users to master and solve:
There are also lots of details that make the experience more pleasant and the usage more effective. One of them is good for testers such as myself: whenever you're using a tool in the app and you have to enter something, there are always pre-filled input parameters that produce an interesting enough output. You may modify them or discard them but you're never lost by having a tool with no idea how to get an interesting answer from it.
For another example, when you're supposed to enter an element, more general chemical formula, or a mathematical expression for a function, you always get a new relevant keyboard. This is just an example of the screen when you're trying to get the electron configuration of silicon.
You can imagine how many hours one could have save at school - and not only at school - if he had (and was allowed to use) these apps. I am convinced that if you are a student who hasn't memorized all of precalculus and general chemistry or if you use these things in your job or if you know a kid or someone else who needs to solve similar tasks, you should buy the $4.99 apps.
Let us look at the precalculus app. The first thing you will find is a menu with 8 categories; combinatorics didn't made it to the picture below.
Some of them have submenus. You enter your problem. Depending on the context, you write the expressions with a certain kind of a keyboard. And of course, the application solves your problem in an appropriate way.
In this case, you obtained a plot. Of course, in many other cases the result is more "talkative". When you're solving a trigonometric equation, it may have many solutions.
Sometime in the past, I would be tutoring all these things - how to draw vectors, compute their sums, dot products, other products, how to draw functions, solve sets of linear equations, and so on. This app would have surely been useful for "my" student who hadn't really learned those things and gave up. ;-)
In March, in the article called Michael Green: Math Classes Are Boring, I have been thinking about whether or not the math classes should be made easier and whether the hard work should be eliminated. My answer was essentially No.
These apps show that there are lots of mechanical things that students are required to do and that may be fully replaced by software - such as the apps based on WolframAlpha. (Yes, the apps need to connect to the Internet.) However, I would much happier if the buyers were not using the app just to cheat - whenever the teacher allows it. They should play with it and see what happens. They should learn.
An app may make learning more efficient but I don't think that it should replace it. When you don't spend enough time by doing hard mechanical work, you won't understand what's happening inside similar apps. Consequently, you will be unable to even formulate the right questions.
If someone uses the Precalculus App to cheat, he will experience some fun things. In most cases, the solution is given with the full treatment that a high school or elementary school teacher may expect. But sometimes it just spits the right result. If a student copies it, it may be suspicious how he got it.
The suspicions may turn into a self-evident fact once an otherwise problematic basic school student copies some trigonometric results that involve exp(ix) or combinatorial results that include the Gamma function - and be sure that the app naturally returns them (at least as one of the ways to express the result) in several cases because the underlying Mathematica is assuming functions of complex variables at the end.
The general chemistry app is divided into 9 main categories; the 3 that didn't get to the picture below are acids & bases; the nucleus; units & chemical properties. Many of them have subcategories and even subsubcategories but the hierarchy is natural.
The problems it can solve deal with as simple things as unit conversions, counting of protons in elements, simple inorganic compounds as well as many complicated things such as finding the equilibrium concentrations in chemical reactions etc. Even some of the simple graphs and tables you get are revealing.
For example, I would be sure that the (first) ionization energy of elements - alkali metals have been marked as red by the user (and they have a very low ionization energy) - has to look like this but I don't think that this graph has been shown to us in chemistry classes. Of course, you will find lots of others.
In the example above, the user enters a particular compound and some information that determines how much of it you have in a solution and the app describes the properties of the solutions in many other ways.
The examples above are somewhat obscure but there's a lot of the typical calculations, table data, conversions, lists of elements and acids and other things that belong to various groups - whatever you would expect from a good "intelligent textbook".