A short article in the Transforming Education through Technology journal caught my eye last week. It was called “Math Course Takes ‘Real Life’ Approach to Algebra”, and described a new courseware program integrating real numbers into algebra problem sets.
Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, “What does algebra have to do with real life?” The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to “real life.”
It’s no wonder that interest in algebra and other mathematical areas is not higher, despite their usefulness to everything from home repair to catching the train on time. After all, while communication in general becomes increasingly integrated and “just in time”, high school math students still must deal with word problems with numbers plucked from thin air. Yes, these numbers might be realistic, but that’s far different from them being real.
And while the A+nyWhere Learning System’s use of real world numbers is a welcome development, it’s really only a superficial one. The numbers in question are being manually inserted into the word problems, so for all practical purposes they’re no better than fake numbers.
The major step we should be pursuing is directly embedding queries for real world numbers into equations. For example, let’s say that an algebra word problem is something like the following:
“Residents of Cityville (population 2.2 million) and Countrytown (population 580,000) often move from one of these places to the other. Because there are triple as many jobs in Cityville, the rate of migration from Countrytown to Cityville is 2.5 times greater than the rate of migration from Cityville to Countrytown. Assuming that the 12% of the population of Countrytown moves to Cityville annually and this rate increases by 2% every year, what will the population of Cityville and Countrytown be in ten years?”
Now imagine that instead of given the numbers of population and migration, we were instead asked to modify this problem to be about real local towns, and form queries to request and retrieve real local numbers to make the problem more interesting. For instance, we could use a simple query like { Population:Cityville } to resolve the most current possible population of Cityville.
This allows two immediate distinct benefits. The first benefit is personalization. The numbers being pulled could be changed to familiar entities that are easily visualized and abstracted. Working with local, familiar entities would undoubtedly make students more interested in their coursework and more likely to continue pursuing math and science.
But the even more important benefit would be that learning how to construct and modify such queries is a skill that is just as important, if not more important, than the math itself. After all, math in the real world never exists in the vacuum, and by using real numbers, it’s conceivable that math students could make real contributions back to their community by crowdsourcing calculations and publishing research.
Of course, this is all dependent on having a query interface that is easy and accessible enough for mainstream use covering a sufficient amount of real world data. Once such an interface is available, the search engine usage patterns that are growing increasingly longer and more complex will make the leap into actual data queries, and math class will never again be the same.
This is why I’m so, so, so excited about Wolfram|Alpha.