A Ship of Fools

I want to address what I see as a disastrous movement in math education. I believe we must understand the damage being done because too many states and school districts have moved toward “constructivist” or “discovery” math curricula especially in elementary grades. Do the new curricula work? YES and NO. Yes, they do work for a subset of the total math problem set. They work to allow students to do basic arithmetic with the aid of four-function calculators. However, they don’t work in providing the foundational skills required if the students will ever face the need to study algebra or higher math. Thus, my indictment of the “constructivist math” programs is that they waste time on an alternative method to solve the easy problems when they should be studying the optimized over centuries algorithms and skills that work for the easy problems but also work for the more difficult problems as well. This makes “double work” for students who want/need to take algebra and higher math because they have to learn the old algorithms anyway. This makes algebra much more difficult for students who have been exposed to constructivist math curricula.

You may ask, “Why did the educators decide to go this way, they are the experts, after all.” First, they are not generally expert in subject knowledge. Fallacies have begun to show in the methods area as well but that is a topic for another time. While there are certainly educators who have a good understanding of the math they are teaching, the vast majority do not. This is not only true of math but most subject areas because the education schools focus the majority of their curriculum on “methods” classes. It is not hard to understand why educators who don’t understand the subject but are under achievement testing pressure would like a curriculum that makes the “teacher” into a “facilitator” helping the kids “discover” the subject matter. That is so much easier in their eyes than having to take the remedial classes they would need to increase their subject knowledge to the required level. So, who’s to blame if the scores come in lower than the standards? Must be the kids who are teaching themselves, it couldn’t be the teachers.

So who are the fools on the ship? The educators? Well, because they are acting in their self-interest, fools may not be the best description. The students? They are doing as they are expected to do, so we can’t blame them. How about US? Do the parents, legislators, dept of education, school boards, the general public, etc. have a role to play here? Yes, we do. Is our performance any better than the educators? Not really. We are accessories to the crime that is being committed against our kids. We are far too gullible. When we have a health problem and go to a doctor, we often ask for a second or third opinion. If we have a serious problem like cancer, we will likely do self-study on the internet, in the library and other sources. Do we tolerate half-truths and propaganda about the healthcare system’s performance on the problem?

But if the subject is our children’s future wellbeing we don’t seem to be concerned at all. When our schools turn in poor results do we get involved? It has been easier for us to participate in the delusion that the education system is well run and effective so that we can avoid the work of digging for the truth and demanding better performance of our schools. When our kids shy away from higher level math because they didn’t receive the appropriate foundation in their early schooling do we investigate the reasons the system didn’t prepare them properly? Do we demand the truth of school performance in the context of how are the kids being prepared to cope in the more and more competitive global economy? The truth is there to be seen and it is scary. Our kids score near the bottom in math and science and near the middle in literacy in the three major international achievement tests that compare us to our competitor nations. Is that OK when high paying jobs are leaving the country because companies have to go where the educated workforce is?

Do we bat an eye when the educators take the low and easy road to make it easy for themselves? Do we complain about the huge amounts of money being spent to implement harmful curricula like Everyday Math, when the schools are always asking for more money, more money, more money? Perhaps we should say no more money until you can prove you are not spending a lot of it irresponsibly.

It’s time to get off of the fool’s ship and start demanding much better performance from our educators. We must start by getting to the truth in spite of the propaganda and misinformation being put out by the education entities. If we don’t our kids and the nation will have a very difficult time competing against nations where education is far more rigorous and effective in providing the skills kids need to compete in the new global meritocracy.

Ammunition

1. If an educator says the new constructivist math programs have been research based and are approved, tell them that much of the research in education is slanted to support the vested interest of the sponsor of the “research.” Also, much of the rest of education research is poorly done from a statistical rigor point of view which makes the conclusions highly suspect. Mention the What Works Clearinghouse on the US Dept of Education website which details their findings on ed research.
2. Ask an educator, esp. math teacher to compare the old standard algorithm taught to most of the adults when they attended school to the new “magic seven” or partial quotients algorithm taught in Everyday Math, one of the most popular constructivist curricula. Everyday Math is widely used in this area and districts are working hard to spread it across all elementary schools. Next ask them to explain why the old algorithm works for dividing polynomials in algebra and the magic seven algorithm does not. Then ask them if they expect that none of their students will ever want or need to take algebra in middle or high school. If they truly understand even relatively elementary math they should be able to do this. Don’t be surprised if they babble without a clue.