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| Reviewed: |
Sep 15, 2009 by Mathematics |
| Overview: |
This site is the mathematics area of the larger Wolfram Alpha project – described as a computational knowledge engine to make the world’s knowledge computable. In response to natural language questions it provides direct answers, explanations, related information and comparisons. In addition to mathematics the main site offers, for example, chemistry, engineering, places and geography, money and finance. Mathematica is used as the underlying software engine.
From the point of view of mathematics education it poses advantages and disadvantages in the way of most technology – but the free availability of a powerful mathematical tool opens up vast new possibilities for students and teachers to explore. For the professional mathematician it’s not clear if it solves anything that their stand alone version of Mathematica could not. |
| Learning Goals: |
Wolfram states that the long-term goal of the project is “to make all systematic knowledge immediately computable by anyone.” It is not designed as a teaching site. The mathematics pages in general compute answers and provide detailed explanation steps. |
| Target Student Population: |
The main site is designed for the general public – albeit those with a certain level of technical sophistication. Mathematics students and practitioners could use it at many levels starting with basic arithmetic. |
| Prerequisite Knowledge or Skills: |
None – depending on the level of the question asked. |
| Type of Material: |
The basic format is search engine style response to questions. But the answers include a wide range of simple, direct answer and extended explanations and related information. It behaves like an intelligent, interactive encyclopedia. |
| Recommended Uses: |
There are a wide range of possible uses with potential positive and negative educational consequences. The site could be used to narrowly answer all the questions on a math test. It could also be used to learn and understand the related explanations. Or it could be used to explore wider mathematical connections and applications. |
| Technical Requirements: |
Works on both Windows and MAC with a wide variety of browsers. |
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| Strengths: |
The mathematical content areas are organized into twelve initial categories: elementary mathematics, numbers, plotting and graphics, algebra, calculus and analysis, geometry, number theory, discrete mathematics, applied mathematics, logic and set theory, mathematical functions, advanced mathematics.
Each of these has a couple of sample problems available on the first page – for example “125 + 375”, or “integrate sinx dx from x=0 to pi” or “find an integral representation for gamma(x).”
Within each of these twelve categories there are subcategories with further examples. But at any point users can type in their own question, regardless of category.
The calculus level examples provide strong material and make nice use of Mathematica graphs to illustrate related ideas. Try, for example asking for the derivative of 2x/sinx
It would also be a useful drill and practice tool for algebra learners and will show graphical interpretations as well as algebraic manipulations of standard topics such as factoring. |
| Concerns: |
Users need to be aware of the sites strengths and weaknesses – it targets “computable knowledge.” Because the underlying software “calculates”, obvious questions on math theory may not produce an anticipated response – for example “four color theorem” yields the message “not sure what to do with input.” Explanation levels seem unpredictable – for example “show steps” on the sample fractions problem ¼ ( 4 – ½) does not produce any steps; on the other hand 2/3 + ¼ shows steps that would be very useful to a student learning addition of fractions with different denominators. |
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Potential Effectiveness as a Teaching Tool |
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| Strengths: |
The material can be used at many levels. It could be used by students to simply obtain the answer to a specific mathematical question. It could also be used to see the standard explanation steps that led to that answer.
But it could also be used as a learning tool to understand the steps and explanations, or to explore new areas using the extensive collection of sample questions.
Answers can be downloaded as pdf documents or as Mathematica files for further work.
Much of this is still a work in progress and the project/site clearly bear watching and participating and sharing with students. |
| Concerns: |
Obviously the first two uses above (direct answers/explanation steps) raise many of the same questions for educators as the introduction of calculators raised for those who teach arithmetic. There is potential for great benefit, and potential for misuse and harm. This site simply extends the scope and availability of material previously available as mathematical symbol manipulation software. It could be used as an interesting resource for discussions of mathematical education and the use of technology.
It seems to be important to know how to ask the question as the “natural language” option doesn’t always work. For example asking for the probability of a z-score greater than 2.37 fails. But just asking for a normal distribution gives the opportunity to input left and right endpoints and make the calculation. |
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Ease of Use for Both Students and Faculty |
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| Strengths: |
The site makes algebraic manipulation software available to those who do not own Mathematica or any of its commercial competitors. This opens an enormous array of possibilities.
The site has many opportunities for user feedback, including a blog area, community forum and the ability to sign up to be an alpha volunteer. Most pages have a direct link to give feedback. There is also a collection of downloadable add-ons and gadgets for a wide assortment of browsers |
| Concerns: |
Some pages are slow to load because of the amount of content. Others seem to have bugs, for example the simple arithmetic demonstration (125 + 375) on the opening page runs a script that makes Internet Explorer stall until the script is manually terminated. It may be the case that “this software is not idiot proof” as the original versions of Macsyma used to proclaim. |
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