My idea of proper mathematical education may be different from that of most other people, or I may be biased because of my experience getting a Ph.D. in mathematics. Whatever the issue may be, I have an uneasy feeling that most gifted math program focus too much on acceleration and too little on difficulty and exploration. I am not against acceleration. In fact, educating a mathematically talented daughter who hates repetition and "boring" stuff, I am acutely aware of the importance of cruising through the basics as fast as possible to get to the "fun" and "interesting." Unfortunately, I have yet to find an elementary school program that uses difficulty and exploration systematically. I find this disturbing because it may be impossible to get truly good at math without solving increasingly hard problems and learning to explore by asking what-if questions. The key question here is what parents can do to foster the problem solving talent of their children? I don't have a wholly satisfactory answer. All I can do is describe the problem and offer suggestions. I am not an education expert, but I am smart and educated enough to realize that conventional methods don't work. This blog post is as much about my observations and ideas as it is about asking for suggestions from those who have gone down this path before me. I am passionate about and always happy to discuss this subject. Hit me by email at Pablo_A_Perez_Fernandez@yahoo.com if you have an answer to my question.
What do I mean by difficulty vs. acceleration? The easiest way to describe it is by example:
- The Mirman School for the Gifted – When first looking for the right school for our daughter, my family went through the application process at the Mirman School for the Gifted. It looked like the ideal place for Paulina until we got to the last step. While she was escorted to a placement test, I waited in the library along with a group of other eager and anxious parents. Mirman's head of school took the opportunity to spend an hour or so answering questions from the group. Fifteen minutes into the Q&A, I asked how Mirman taught math to kids. I was told that kids work at their own pace. If they are ahead of their peers, they could move to more advanced "rooms." I remarked that this was great and then asked what else was done besides letting kids progress faster than their peers. I got a blank stare. I asked if the school used custom curriculum or specialized books. I was told that they used standard mathematics books but allowed kids to work faster than normal and are encouraged to participate in competitions. I did not ask any more questions.
- EPGY and CTY's Distance Education Courses – Both programs use Stanford's adaptive software for K through pre-algebra. My daughter started in K and now is in the middle of 6th grade. I find EPGY to be carefully thought out, rigorous, and complete relative to the California's DEO standards. EPGY does a good job teaching concepts like variables, equations, and the representation of English statements as mathematical equations. However, I would not characterize EPGY as challenging. Paulina so far has cruised through the program, and I know that she is working below her problem solving potential. I am disturbed by this.
I investigated this issue a few months ago. I discovered that EPGY provides software for non-gifted school programs, and it is identical to EPGY's gifted track. The only difference between the gifted and non-gifted tracks is a teacher-controlled flag that triggers acceleration. There is no switch for difficulty or depth.
- My Yale University Experience – Let's fast-forward to my freshman year at Yale University. There were three tracks for freshman physics and math. Each subject offered easy, traditional, and advanced paths. The easy classes were also known as physics and math for poets. They introduced the basic ideas without the "torture" of really difficult problems. The traditional tracks resembled a traditional university course. The advanced courses were much more difficult. They covered much more material and from a far more theoretical perspective. They also required killer problem sets that few students could finish on their own and on time. Bear in mind that the students taking these advanced classes were some of the best in the world. A number of my classmates participated and won honors at the International mathematical Olympiad and other top-level competitions. The biggest difference between the advanced courses and the others was the combination of acceleration and problem solving difficulty.
I hope it is clear by now what I mean by the difference between difficulty and acceleration. Gifted kids need both. It is not okay to facilitate one but not the other. So, what can we do to help? This question is difficult to answer. Here are some suggestions:
- Use Problems to Teach Material – There is no sense in explaining things through endless lectures. This has the potential to bore the most enthusiastic students. One learns math best by doing math. Some of the best math classes I ever took asked me to discover math my solving problems.
- Challenge the Student – Arithmetic drills are rarely challenging for gifted students. This suggests that increasingly difficult problems are necessary to push these kids toward their potential.
- Ask Open-Ended or Broad Questions – This is the only way to truly challenge a smart kid. Give them an open problem. See how far their minds can go. See what questions they come up along the way.
I hope this post gives you a few ideas and helps you ask the right questions when thinking about your kid's education.