Dr. Stat

Dr. Stat is a Statistics Professor. This blog is his opportunity to share ideas and opinions about education (especially math education), politics, and whatever else comes up.

Monday, November 26, 2007


Let's face it. The presidential election is a farce. The only people who can win are those who have lots of money backing them and a good share of the media as well. In order to get elected, politicians either have to lie or sell out.

I wish I could be president. Of course, I don't have any of the qualities. I'm not a schmoozer. I have been known to say stupid things in public. I'm not rich. I don't have political experience. I don't have an "organization." I have principles.

I wouldn't take any money. (Meaning, of course, that I couldn't win.) As soon as a candidate takes money, he owes somebody, and principles are out the window. We Americans have dug this hole for ourselves. We refuse to listen to principled candidates. We let the media drive the campaign, and the media runs on the sensational and the novel, not the principled. We make decisions on sound bites and perceived personality traits (i.e., who is the best actor).

Oh, how nice it would have been if we had listened to the founding fathers. They TOLD us not to elect the president through popular vote. They TOLD us not to tax individuals directly. They TOLD us that powers not enumerated in the constitution were reserved to the states, in order to keep the national government from becoming too strong. They TOLD us to maintain balance of power between the branches of government. They TOLD us to protect our nation's sovereignty. We are on the verge of losing everything. There are voices (other than mine) sounding the warning. For some reason, not many people are truly listening. They will pay--we will all pay--for this. We will pay with our lives and treasure. I fear time is growing short.

Thursday, November 15, 2007

No Child Left Behind is a Failure

as many of us have known, suspected, predicted, preached, whined, cajoled, cried, complained, and generally tried to get anyone to notice.

But, you know, anytime you have a big government program that "benefits the children" no one will pay any attention to the fact that it is bad, wrong, useless, harmful, inefficient, or even unconstitutional--which NCLB clearly is, as the federal government has NO AUTHORITY in the area of education. Paul Weyrich, in the linked article, explains again what is wrong with NCLB. The idiotic measure of "progress" have nothing to do with real progress or real education. Teachers all over the country know what we all should have known to begin with--the program causes wasted efforts to prove the school is proficient which, in most cases, only takes resources away from other important areas. Yes, some math and reading scores are up. A little. But they were on their way up before NCLB, and who knows if the trend would have continued or not? Meanwhile, science, history, geography, music, and art are shunted to the side. I know reading and math are most important. But not to the exclusion of all else, IN PARTICULAR, when reading and math can so readily be taught WHILE teaching science, history, geography, and maybe even music and art.

Local schools and local teachers can figure these things out, but large bureaucracies (expensive bureaucracies) can't. So more teachers are "highly qualified?" I wouldn't believe it. Maybe. Giving attention to teacher qualifications is important. But so many are receiving spurious or nominal certificates that come from completing some busy-work program that likely does nothing significant to improve their actual teaching performance. Good teachers have to be SMART. You don't get smart by attending a certificate program. Good teachers have to be GOOD WITH KIDS. This is an innate quality that I don't think anyone can be taught, certainly not by taking a few evening classes from an Ed. School.

I wish somebody would give me a chance to fix the schools. The first thing I would do is give the federal government the boot, right where it belongs.

Thursday, March 29, 2007

Don't teach the Bible in public schools

Christopher Ruddy (Don't teach the Bible in public schools) said, "Let's go back to the Bible in the classroom issue. Would you want public school teachers interpreting the Bible for your kids? In some schools teachers may promote the Bible because they are believing Christians. In other schools teachers with a secular humanist bent will undermine its legitimacy. The best place for faith to be taught to kids is in the home, church, and private schools."

Would you want public school teachers interpreting history for your kids? In some schools teachers may promote the a view of history that emphasizes the struggle for freedom and liberty and individual rights, together with a positive view of western civilization and the contributions of America. In other schools teachers with a socialist bent will undermine western civilization, denigrate America, and focus on issues of social justice and the benefits of socialism. The best place for history to be taught to kids is in the home, church, and private schools.

Would you want public school teachers interpreting literature for your kids? In some schools teachers may promote the classical literature because they believe it contributes to the development of the human spirit and timeless values. In other schools teachers with a secular humanist bent will use literature to undermine the noblest achievements of man and promote a pessimistic and defeatist attitude about modern and contemporary life, with a goal of eliminating the influence of religious belief and conditioning children for life under an all-powerful state. The best place for literature to be taught to kids is in the home, church, and private schools.

Would you want public school teachers interpreting mathematics for your kids? In some schools teachers may promote basic skills and fundamental knowledge that is useful in everyday life and serves as a base for advanced mathematical understanding such as our best scientists and engineers will need to have if we are to remain competitive in the world. In other schools teachers with a progressive bent will undermine the legitimacy of fundamental mathematical knowledge, if in fact, they understand it at all. They will teach fuzzy concepts and use of calculators and computers to do "advanced" tasks for which the students have no structural understanding. The best place for math to be taught to kids is in the home, church, and private schools.

Would you want public school teachers interpreting the sciences for your kids? In some schools teachers may promote understanding of a wide range of ideas and important issues, in some cases because whatever their religious beliefs, they believe that scientific thinking is best served by examining conflicting hypotheses rather than teaching current speculations as facts. In other schools teachers with a secular humanist bent will undermine free inquiry, and demand that students accept the currently-dominating views of what is legitimate science. The best place for science to be taught to kids is in the home, church, and private schools.

Tuesday, March 20, 2007

Fixing Math Education 3


Whenever you mention testing, there are people who get up in arms with all kinds of objections. Testing isn't fair. Testing doesn't really measure what kids know/understand/can do. Testing is biased. Testing is racist. Testing takes time away from real education.


Well, math is, probably more than any other subject, amenable to testing, fair and unbiased. We need to have meaningful standardized testing that is not just "high-stakes" for schools but for individuals. There has to be a way to require a certain skill level be achieved in each grade or the kids don't pass. The students have to be personally responsible for achievement, and the teachers have to be responsible if their students don't pass. They need to contribute the extra time needed to get their students up to speed when they don't pass. The tests should be comprehensive up to each grade level, the questions should not be known in advance, and they should be changed every year. Let's put the students and teachers together on the same team, fighting together to beat the tests.

Monday, November 27, 2006

Fixing Math Education 2

The Back-to-Basics vs Constructivism feud

AKA "Drill-n-Kill" vs "Inquiry Based"

AKA "Traditional" vs "Progressive"

Notice how some terms just naturally sound better than others? Does that have anything to do with the substance of the ideas?

So there's really no general agreement on what constructivism is. Some people argue it's not curriculum or pedagogy, it's brain science. I simply use it to refer to those approaches of teaching mathematics that require students to develop their own mathematics from scratch. It might include "Problem Solving," "Discovery Learning," and "Inquiry-based Learning (IBL)." My apologies to those who will claim that I do violence to their pet definitions here. But there do seem to be two general camps. On the one hand we have those who think students should learn efficient, time-tested methods of solving problems, and learn them to mastery (automation). These I call "traditionalists." On the other hand, we have those who emphasize that students should learn to think creatively, develop strategies to solve novel problems, and develop deep insights into mathematics. These I call "constructivists."

The answer is actually simple. We need both. However, when sacrifices must be made, there is one approach that is essential, and one that is merely desirable. Unfortunately, reasonable people will disagree about which is which. This, however, is my blog, so my opinion is right.

The much-maligned traditional method is essential. We must first realize that there is a great deal of disinformation floating around about the traditional method. Its opponents claim the traditional method teaches rote memorization without understanding or thinking. Except perhaps in some isolated enclaves where stereotypically poor teaching took place, this has never been the case. All the widely used math textbooks of the 19th century, for example, emphasized "mental arithmetic," that is, the ability to think through multiple-step problems "in your head" and give the solution, not only without a calculator but even without a pencil. The kinds of thinking and understanding that were required differed from what is expected today, because the skill set expected of an educated person has changed. So in those days, being able to carry sums in your head was far more important than, say, sketching the graph of an exponential function. In honest debate, we must realize that "Back-to-the-Basics" or "traditional education" does not imply restricting ourselves to the content or objectives of a bygone era.

The primary features of the traditional method include: 1) Understanding a mathematical concept, e.g. "What does it mean to add two numbers?" 2) Memorization of basic facts/definitions/results, e.g. "the Times Tables." 3)Application of memorized knowledge to novel problems and more advanced concepts. 4) Review and maintenance of memorized knowledge.

The traditional method results in efficient learning and provides the foundation necessary for creative thinking, even if it fails to sufficiently address that objective, according to its critics. And yes, even educators from Singapore, whose students smoke the Americans in international tests, are looking with envy at the creativity of some of our students. This demonstrates that a commitment to the essential objectives may not produce all the results that are desirable.

It is well documented in cognitive science that the brain has a limited capacity to manipulate objects in "working memory." It is often said that we cannot process more than seven memory objects at once, which supposedly explains why phone numbers have seven digits (only now they have 10, but that's OK, because the phone remembers all the numbers for us). The working memory is where problem solving and creative activities take place. The working memory can access permanent memory for information it needs. However, any new information that must be taken in to solve a problem must occupy space in the working memory, thus taking away from the space available for creative activity. That is why we quickly become frustrated when trying to follow assembly instructions that include many terms with which we are not familiar. Even if the actual steps in the process are simple, if they involve several terms that are not defined in our permanent memory, those terms require space in our working memory which is then not available for solving the problem. This explains why the pedagogic fad of "learning to learn" is a failure. We do indeed need skills for learning--but such skills are utterly dependent on a reliable bank of information which can be accessed instantly and does not require the use of working memory. The first step in problem solving or creativity must be putting as much relevant information as we can into permanent memory.