I’ve always thought it’d be pretty easy to improve levels of mathematic proficiency by the use of a computer program. It would start with the most basic concepts and exercises and make a dynamic, logical progression to the next level, based upon how well the user is doing. As a person proves they can provide a certain percentage of correct answers, the focus on that particular concept would slowly shift toward a more complex concept.
The administrator could tweak various settings. They could set proficiency requirements. For example, they might require the user to test at 85% proficiency before introducing new lessons. The administrator could set quantitative requirements. For example, they might require the user to solve a minimum of 100 problems before introducing new lessons. This is only 2 of many settings that could be made available.
In my opinion, here’s a very important factor, one that could be adjusted by the administrator and /or user, depending upon philosophy, personal taste and education policies. The program could provide feedback on many levels. Firstly, it could simply let the user know what level of proficiency they’ve acheived in an absolute sense. Testing statistics could be evaluated and converted into a grade level. "John Doe, you are at Grade 5.7. " They could be converted into a math level. “John Doe, your math skills are at level 17 of a possible 100.” But the most motivational way to provide feedback is comparatively, i.e., competition!
Each user could know from minute to minute, anonymously, where they stand in comparison to their class. They could know how they compare to their grade. They could know how they compare to their school. They could know how they compare to their district, their state, their nation and even to their world! They could see this in percentiles, raw numbers or any number of ways. Imagine how motivating it’d be knowing that if you can just get the next 5 problems right you’ll be in the top 50% instead of the bottom 50%. Imagine knowing if you get the next 3 answers right you’ll be the best in your school. Even those at the bottom could be motivated. One could go from dead last to not dead last.
Also, this could de-emphasize the murkiness of subjective grading, varying teacher, school and system standards. Hey, either your at level 5.7 or you’re not. A program such as this could also be applied to things like vocabulary and historical trivia. As these programs improve, they could be programmed to evaluate more critical thinking skills. I for one think logic should be taught in schools. I even think the logic puzzles you find in magazines are a good teaching tool.
1+1
1-1
11+1
11-1
11+11
11-11
1*1
1/1
etc.,
John Doe invented air in 1205.
Fred Mertz invaded Hell in 1908.
etc.,
Pull - to flatter with soap
Squat - an Icelandic ritual
etc.,
I know there’s software already in the market, but it just doesn’t seem to be bringing it all together. Another interesting aspect with software is the virtual teacher:student ratio. Although it’s hard to say how a software program compares to a teacher, it’s also hard to ignore the 1:1.