A math tutor for every child? It's always been a practical and economic impossibility. Historically, we had no choice but to opt for learning in groups, using teacher-centered knowledge transmission. But this model assumes a grade-by-grade sequence of teachers who know math and know how to transmit their knowledge to students. Unfortunately, these necessary conditions are rarely satisfied, and our K-12 math education system is in a chronic state of breakdown.
The sad truth is that the typical American K-12 teacher doesn't know much math. This is especially true for K-8 teachers. Genuine knowledge of math content simply isn't required by our schools of education. They believe in content-independent skills, not the step-by-step buildup of domain-specific knowledge. More importantly, today's educationists reject knowledge transmission. They say teachers should "facilitate" student-controlled "exploration". They want to us to forget that the primary dictionary definition of "teach" is "to transmit knowledge or skills".
There is good news! Now, for the first time in history, there is another way to handle the knowledge transmission function. We can harness the rapidly increasing power of information technology to reengineer K-12 math education and give every child a grade-by-grade sequence of powerful software tutors, with human tutors available as needed through the future "mathnet" dimension of the internet. Each child will be able to proceed at their own maximum speed, not held back by the pace of the slowest child or the fear of public embarrassment. With just one-half hour a day away from sociology and psychology, they will be able to learn genuine math. This is not about firing current teachers. Think of it as the logical evolution of textbooks.
Although we are currently being left in the dust by our international competitors, we now have a rare opportunity to leap-frog over them. Why? Because they don't share our problem. Generally speaking, our European and Asian competitors haven't been sucked into the progressive cesspool. They have genuine national math standards, teachers who know math, and refined methods of knowledge transmission. They don't share our urgent need for a new approach. (For the Asian evidence, see The Learning Gap by Harold W. Stevenson and James W. Stigler.)
But any effort to reengineer American math education is currently blocked by the lack of functional requirements. More specifically, the problem is the lack of genuine math standards. The NCTM Standards are not the answer. They preach progressive teaching philosophy and totally redefine the meaning of "standards", "math", and "learning math". For math standards which do qualify as genuine math standards, see The California Mathematics Academic Content Standards.
Using state-of-the-art information technology, we can educate all our math-illiterate people, not just K-12 students. The key enabler is broadly-accepted standards which clearly identify the required math content. If this can be achieved, there are many benefits. The key result will be greatly increased incentives for software developers. Now that California has adopted genuine math standards, software developers will be attracted. But, if a substantial number of states adopt the same set of genuine math standards, this will trigger a "gold rush" for software development entrepreneurs. The resulting "maximum competition" will result in high quality math tutorial software and the rapid development of the "mathnet" dimension of the internet.
Our current major obstacle is the anti-content mindset of the NCTM and the American education establishment. Our first set of net documents, The Truth About the NCTM Standards, places us in sharp opposition to the NCTM. But we don't underestimate our adversary! They have skillfully redefined the meaning of "reform", "math" and "standards".
While we reject the philosophy of the NCTM Standards, we don't claim perfect vision regarding "the truth" about math standards and information-age math reform. Help us clarify the truth! Help us fight for an effective math education for all our kids. Please E-mail your ideas to wgquirk@wgquirk.com
Alarmed by the breakdown of K-12 math education and the hard-to-believe philosophy of the NCTM, Bill is now working to counteract the anti-content "reformers" and build consensus for genuine math standards and an internet-based reengineering of American math education.
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