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.
- Name: Dr. Stat
Saturday, April 30, 2005
Friday, April 29, 2005
R.L. Moore Conference
Everyone interested in Math Education should know about the Moore Method, or, as it is sometimes called, the Texas Method.
I first learned of the Moore Method when I was a Secondary Math Education major taking my "transitional" course, which was called Set Theory. We were required to read the autobiography of Halmos, "I want to Be a Mathematician," in which he briefly describes the method.
Some people refer to the Moore Method as the Discovery Method, but it seems to me these should be kept separate. They are similar in philosophy and purpose, I guess, but for me, the Discovery Method applies to Elementary School (maybe Secondary too), while the Moore Method is appropriate for upper level college and graduate studies. The lines are no doubt blurry. I asked some of the presenters questions about the difference or distinction between the methods, which generated some discussion but ended without any clear answers.
Let's see, what did I learn today?
One of the first presenters gave us a problem to work on while he was getting set up. He called it the "McDonald's Problem." Say Chicken McNuggets come in boxes of three and boxes of 20. What is the largest number of nuggets that you can't get?
We heard from Cathy Seeley, President of the NCTM, who talked about how important we are to restoring the glory of American Math Education (my words, not hers) and Rodger Bybee, Executive Director of Biological Science Curriculum Study (an organization going back to the 50's which is apparently responsible for introducting evolution into the curriculum). Bybee gave us a copy of the organization's journal, "The Natural Selection" which has articles about the TIMSS and PISA studies of 2003 (international assessments).
Hyman Bass talked about "Mathematical Knowledge for Teaching." He has been doing research on specific knowledge that teachers in K-12 need to do their jobs--not mathematical content, but profession-specific stuff, like how to analyze wrong answers and quickly recognize what the problem is. Also, he said they have to analyze right answers to see how students are arriving at solutions. Another thing is how to craft questions that reveal what the teacher wants to know about the student. An example was given of arranging 4 decimal numbers in order. Two of the choice could have been done correctly if the student ignored the decimals. Another point was that teachers need to use definitions that "don't lie later." He talked defining even numbers as an example. You might say "A whole number divisible by 2" but what happens when the students get to negative numbers? He has been working on assessment tools to measure teachers' strengths in these types of knowledge. Some of the stuff he said reminded me of what Liping Ma wrote in Knowing and Teaching Elementary Mathematics, and also Hung-Hsi Wu on teacher preparation, but I wondered if he was familiar with these works.
Peter Jipsen talked about using online tools for teaching. He uses "Moodle" which is a free software like WebCT or Blackboard. He has written a couple of java utilities that make it easy to post mathematical equations and graphs in web pages. They are apparently downloadable and are called "ASCIIMath" and "ASCIIsvg." I will be checking these out.
Well, there was more (Moore) but I think that's all I'll say for now.
On Religious Tolerance
Excessive tolerance necessitates embracing falsehood.The fact that various competing and mutually exclusive truth claims exist does not prove that they are all false.
Religions are not equal (in validity or truth). However, they are all complicated. None of them can be understood in sound bytes or short quotes. It is possible to evaluate the relative merits of religions logically and historically, by careful study. It is probably not possible to come to a conclusion of truth by this method.
Western Civilization values religious tolerance, and that idea of tolerance was promoted by Christians and enshrined in the laws of the United States by Christians. It was not easy for the colonists to realize that tolerance was good or necessary, but they did it, in spite of their deeply held religious beliefs. However, tolerance for others to believe and practice as they like does not extend to agreeing with their beliefs. Many liberals require that we treat all religions as equally valid (but implicitly they mean "except Christianity") but to do so is to insult them all, because if they are all equally valid they are all false.Christians who are actually living their faith do not persecute others, but they do seek to share the Good News that constitutes their religion. If this is offensive, so be it. Seriously, now, what kind of friend would I be, if I knew my friend was going to hell, but refused (out of "respect") to tell him how to avoid it? Only by denying the truth of my own religion could such a thing be considered! But there is absolutely no point in "forcing" someone to become a Christian. The historical claims that such things happened are either false or the events were orchestrated by someone for political purposes who did not understand Christian faith.
On the other hand, Muslims have a long and rich history of forcing people to become Muslims. Atheists also have a long and rich history of coercing people to become atheists--that is to say, persecuting them in an effort to make them give up their religion. The current work to promote atheism in the American educational system is incredible.
Claims that all religions are equally war-like, that is, that people make war because of religion, are incorrect. Some religions do this (Islam being the most prominent example), but most do not. There is nothing in Christianity that would encourage starting a war for religious reasons. The Christian religion was explicitly pacifist for the first three centuries, agreeing to war only after Constantine mingled the Christian religion with politics. Most Christians now believe that they may support defensive military actions, which are sometimes mis-characterized by the detractors of Christianity as offensive. However, political people have always used religion to their advantage in promoting their causes. This must not be attributed to the religion itself, except where the religion truly is the source of the aggression.
Thursday, April 28, 2005
The system for too long had just shuffled children through and just hoped for the best. And guess what happened? We had people graduating from high school who were illiterate -- and that's just not right in America. It wasn't working.
If you've read any of my blog you know I'm not very positive about our education system.
You also may know how I feel about NCLB.
But I'm starting to get really teed off about Bush's own illiteracy. Let's just get right down to it. How many, really, how many high school graduates in, say, North Dakota, South Dakota, Montana, and Wyoming are illiterate? Go ahead. Find one if you can. (I'm sure there are a few--the exceptions to prove the rule, though.) So what business is it of the Federal Government, really, to interfere in the successful workings of state educational systems, where they are doing fairly well? What right is it of the Federal Government, to burden these rural states with inappropriate, ineffective, misguided regulations that actually take money away from budget items that help students??
Oh, "It wasn't working." Like in Texas? Where Bush's state program achieved a statistical success because schools figured out how to manipulate the results? (9th graders who didn't pass a subject were "held back" and didn't have to take the statewide test in 10th grade, then they were promoted to 11th grade after making up their failed subject, and again avoided the test.)
See also NoNCLB. I disagree with lots on that blog but we have a common enemy.
More good stuff at Shut Up and Teach.
Byron Dorgan's Comments. Go For It!
Wednesday, April 27, 2005
How to fix education
Teachers (including professors) have always complained about the quality of students, and it is difficult to fairly ascertain whether there has actually been a change, but I am convinced that there has. Unfortunately, I think that the causes of the problem have been misdiagnosed. There have been major changes in the maturity of high school graduates. Compared to high school graduates of the 1950’s, many no longer know how to set goals and work toward them, and most no longer take responsibility for their own learning. In fact, there is a widespread attitude that education is something the teacher/professor does to them or for them.
This is unfortunate both because it is false and because it hinders the student's ability to obtain a true education. Students essentially want to be entertained for four years and then be given a diploma for it. These are attitudes they learned in K-12 education. In the last 20 years, K-12 education has become far more entertainment-based than it ever was before.
I used to review teacher-ed students' portfolios, and time and again I would see that their educational philosophy was that "learning should be fun."
I'm not against having fun in school, since it is a great motivational tool.
But what students really need to learn is not that learning is fun--rather, that hard work is rewarding. It is no different than being on the football team. When you go to practices, the coach says "No pain, no gain." He makes you work hard, he makes you exert yourself to your maximum potential--and from that you learn, grow, and ultimately you find that the struggle itself is fun. K-12 has missed this point by a mile. This is the true meaning of education--learning how to exert your mind to reach new heights, new capabilities, and doing it because it is both rewarding and necessary.
Some people talk about the class differences as a factor in education, but I would argue that they often miss the point of class differences. There are no fixed classes in America. By far most people do not finish life in the class they started out in. We have class mobility. However, what keeps people in the lower class is not the lack of opportunity; it's the lack of attitude. As long as people think of themselves as victims, being held down by society, or the dominant race, or some such thing, they will fail to address the true problem and thus fail to solve it. People's attitudes about education have to change. That's priority one. Neither NCLB nor any other major player in the education game is addressing this, mainly because you always run into problems with "political correctness." Telling the truth here becomes racism.
And of course, racism is a "killer word," an epitaph that kills any idea no matter what its true merit or worthiness.
NCLB is defended on the basis of achieving equity in education between the races or classes. I have been asked how any government founded "for the people" could allow inequity in education. That's a good question. A better question is, how dare the government step into the people's lives, take the responsibility for education away from the parents by force, make the kids go to schools that teach things the parents do not believe in and would not tolerate in their own homes, destroy the religious basis of the society, and finally, destroy the work ethic of an entire generation by teaching that you should feel good about yourself no matter how lazy you are or how little you accomplish? Anyone who is concerned about the education of black children (or lower class children) ought to take a look at how black people a hundred years ago taught their children to succeed and contrast that with what is happening today. The contrast is stark, to say the least. It is black and white, to risk a bad pun. Look at George Washington Carver. What were his educational opportunities? What did he say black people should do? Look at the statements of all the leaders right up to Martin Luther King, Jr. They all stated that it was the hard work and perseverance of the individual that mattered. I think King called it the "Quality of our Character." Today's black leaders don't say that at all.
They keep talking about getting the government to step in and straighten things out. But government won't succeed, because government can't get at the root of the problem. Simply put: individuals have to take responsibility for their own education. There is no other way. K-8 is the time when these attitudes are formed. If you haven't done it by then, it's unlikely that it will ever be done.
Wednesday, April 13, 2005
I saw a bit of a certain children's show this morning. I don't know if I'm spelling it write* or not. Honestly, I have problems with most children's TV that I see. Maybe I'm too cynical. Anyway, apparently they portray different people in the neighborhood as heroes in every show. This time it was the grocery store clerk who turned out to be a hero because he helped the kids find star-shaped noodles.
OK, I'm glad he could help the children find their noodles. But is that heroic? Don't we want the word "hero" to actually mean something out of the ordinary? If everyone is a hero for doing his or her day-to-day job, then we are creating a situation where all are special and therefore none are special**. So the children are learning that to be a hero just means to be a nice person doing a job in the neighborhood. What, then, do we make of people who make great personal sacrifices in service to their communities, or risk their lives on the battlefield to bring freedom to others? What about the people who died to give us a lifestyle that enables us to expend energy worrying about the shape of our noodles? What about the people who go to far away lands and risk their lives to help the poor and sick in inhospitable environments (natural and human)? Are they heroes too, just like the grocery store clerk? Just like the grocery store clerk, who risks...what exactly?...to find us our star-shaped noodles. And now, we have no word to honor a "real hero" since the term "hero" has been taken by...everyone.
I highly suspect, however, that the children's program in question would hesitate to apply the term "hero" to many of the people I consider "real heroes." Forbid that a hero might carry a gun... Let's not forget that a hero is supposed to be a person who sacrifices himself, without expectation of reward, for the benefit of others. The grocery store clerk is getting paid to "be a hero."
And to round off the insult, they have to include a dose of grammatical nonsense, as they sing the theme song with the line "so we can be a Higgleytown Hero, just like you."
Oh...and of course the clerk sings his own praises calling himself a hero. A tale of mediocrity, bad grammar, and pride thus comes to a greating* conclusion.
*intentional mispelling :-; (in case you didn't get it)
**paraphrase of a line from "The Incredibles," a show I was surprised to find I liked very much. See also Metaphilm's story.
Monday, April 11, 2005
The American educational system is one of the last experiments in socialism left on earth and, on its present course, it will take its place in the succession of socialist wreckages that litter the highway of human history."
Friday, April 08, 2005
Daylight Saving Time is a Peeve of Mine
"The more daylight we have, the less electricity we use," said Markey, who cited Transportation Department estimates that showed the two-month extension would save the equivalent of 10,000 barrels of oil a day. (In an April 7 AP article quoted rom CNN.com.)
The California Energy Commission has a nice article called Saving Time, Saving Energy which explains the history and advantages of DST.
It seems convincing, but I'm not yet convinced. First of all, it is not true that changing our clocks changes the amount of daylight available. Therefore, it is not automatic that extending DST would save oil. Second, the statement, "The more daylight we have, the less electricity we use," appears to be false. I obtained monthly electricity usage data for the US for the years 2001 to 2004. The amount of daylight available varies across the country, but as an operational "average," I used the number of minutes from sunup to sundown in Omaha, Nebraska on the 15th of each month. A simple linear regression of electricity usage to minutes of sun shows a significant (p=.03) positive relationship of 66 million kwhrs per additional minute of daylight! (That's about .02% of the monthly average). The explanatory power of the model is poor (R-square=.0981).
Indeed, my calculations are rough and the Transportation Department probably had better data and did more extensive analysis. However, if the real issue in saving energy is the number of hours of lighting needed, it is still not necessary to change the clocks! People who can benefit from a change in rising and retiring times should adjust their schedules accordingly. If businesses can influence this factor, they can change their hours of operation. None of this requires a change in clocks. In fact, we could change business hours at any time throughout the year! NOTHING prevents that. Why not start work one hour after sunrise no matter what time of year it is? Or perhaps time the start of work in such a way that people have to get up eight hours after sunset. It seems to me this would result in the maximum electrical savings. Indeed, it is often managing the peak of electrical usage that is most important to saving energy. This is best accomplished by having different people in the same region on different schedules!
Truck and Barter has some supporting thoughts here.
Thursday, April 07, 2005
University Presidents on Academic Speech
The Power of Family
By the end of the one-hour show, the parents are in awe of the results of fairly stand standard disciplinary principles employed by the "Supernanny," as if to say, "You mean when we discipline our children, it works?"
Why yes you fools. It does.
As the days go by, I am more convinced that almost 95% of our country's problems could be solved in the family. I've said it before and I'll say it again. We don't have crime problems; we have family problems. Family dysfunction spills into the streets, and eventually we pay for it with our tax dollars and more painfully--our time. Rarely do we make that glaring connection. Instead, we collectively throw our hands up in the air, wondering where our society went wrong.
I like to criticize the schools, in particular various forms of progressive philosophy, for their failings, but I am aware that the schools do not exist in a vacuum.
It is self-evident that not all the products of the schools are educational failures. Some children come through the system fairly well, although questions remain about whether even the best are "all they can be," to borrow a slogan. In homes that support achievement goals for their children and give them sensible discipline, we find children succeeding in spite of the quality of their schools. Where schools are failing, there are also significant numbers of families that do not provide such support. This causes deterioration of the learning environment for all students. Without adequate numbers of parents insisting that the school do a good job, there is simply no way it will get done, not in a public institution at least. Church schools have an advantage here, in that they are accountable to the church, which has an important influence on the school environment. Other schools are accountable to parents and the government, so if the parents are not very concerned or involved, we are left with government. And "left" is a great word to use in this situation!
Bad schools (parents) set up a vicious cycle. If parental support is inadequate, the schools will be bad. The students will not get a good education, and most will not develop mature and success-building attitudes from either home or school. Not being "upwardly mobile," most will not leave the neighborhood, and will quickly provide the next generation of children without good parental support and with ever-deteriorating schools. On the other hand, those who do develop mature and success-building attitudes, are not likely to stay in the neighborhood and provide any counter-effect to the declining situation.
So one solution to the school problem is to change families. But don't expect the "outreach" programs of the schools to accomplish that. Don't expect the government to do it, since government interference is also a large part of the problem. Can the church be a positive influence? Yes--but not the various liberal branches, which have also had their hand in undermining the discipline and authority in the family (by starting with undermining the authority of God).
We can make schools better. But if we don't have good parents, I'm afraid the effect will be very limited.
Wednesday, April 06, 2005
April 4th. Border monitoring officially began. Hundreds of volunteers are now monitoring the border. A number of illegal aliens already have been reported to the Border Patrol. A group of 18 were encountered and reported to the border patrol. Earlier this weekend, an illegal alien from Guatemala stumbled into the bible camp where the MMP is operating. He inadvertently wandered into the hornets' nest, but it turned out to be his lucky day. He was tired and dehydrated and MMP volunteers gave him medical attention, food and drink before the Border Patrol was able to arrive.
Yeah, President Bush, just like you said:
I am against vigilantes in the United States of America. I am for enforcing law in a rational way. That's why we have a Border Patrol, and they ought to be in charge of enforcing the border.
Let me join the many voices now being raised in saying, if you were doing your job, volunteers wouldn't have to, but when you to insinuate that civilian volunteers legally helping the (grossly understaffed) border patrol is somehow wrong legally or ethically, you are way out of line. You claim to be fighting a war on terror, yet terrorists can freely enter our country in any number of ways that you have not even begun to address. You said you would fight them on foreign soil so we wouldn't have to fight them here. Then why do you keep letting them in? And you keep talking about illegals doing jobs that Americans don't want--well fine, if that's the case, let them immigrate legally. If they are here illegally, send them back and let them come through proper channels. You are the one making excuses for illegal activity while condemning honorable citizens for doing their constitutional duty to protect our borders.