Something in me tells me to not talk about myself. I don't want this website to come across as an ego trip. However when I read what others write, I find I would like to know something about them. So I have no doubt that at least some of the people who read something I have written would like to know something about me. Click here for "About Me"The articles below are mostly the result of long and careful effort, sometimes years. But I also have thoughts and ideas on a much smaller scale that I would like to get into print. Click here for my blog space. (last updated 11/30/14, with the post, "Thoughts On Inequality") "Thoughts On Cultural Sharing" is an article prompted by an article on the internet about belly dancing. The author of this article doesn't think white women should belly dance. That prompted me to spend a lot of time thinking about it, but my conclusion is pretty much the same as what I thought when I first read the article. Click here for Thoughts On Cultural Sharing. Posted 3/5/15 The "Romantic Fallacy" is an idea that has formed part of my thinking for most of my life. I should have written this article many years ago, but better late than never. Click here for "The Romantic Fallacy And Doing Good". (posted 10/15/12) These next two articles are related, and both about language. The first article, Suspicions of Language Learning was started many years ago and was prompted by a situation which I describe in the article, two cases of bilingualism. My thoughts there led to other thoughts and resulted in this article. The second article Some Doubts About Learning By Immersion is a result of effort and thought in the last six months or so. Language learning by "immersion" has been a popular educational idea for at least fifty years, and perhaps much more. I always thought it needed some careful thinking through, and this article is the result of my thinking. (Posted 6/4/12) I came across a video clip on the internet about a week ago that got me to thinking about the teaching of arithmetic. It's a humorous clip, a young man is trying to explain a simple problem concerning speed to his wife. It led me to some thoughts that I thought might be worth putting down on paper. Click here for "Explaining MPH And Other Things". (Posted 3/28/12) The following article is already on this website. I put it in my Blogspace on Sept 7, 10. But thinking about it recently I decided it's worthwhile as a separate article. It's my take on the cause of the start of our present economic problems. It is not the cause of its continuation by any means. That is another sad story. Click here for "Buying Trash". (posted 11/1/11) Click here for my "Good Songs" page. You'll find no math education writing here, nor anything academic or analytic. It's just a collection of songs that I like. Posted 7/11/11. (and hopefully to be updated now and then) Should divisibility rules be taught in elementary school as a regular part of arithmetic? I really don't know. There's not enough time to teach everything we would like. If divisibility rules are taught, then should they be taught for understanding? Again I don't know. I don't know if enough time is available. But here's a few ideas about the divisibility rules and how they can be explained and understood by children in elementary school. click here for "Understanding Divisibility Rules". (posted 6/19/11) Music has always been an important part of my life, and I have learned a lot over the years, but music has never been easy for me. A few years ago I started putting down a few ideas on musical talent, and I finally finished it. I thought it would be a short article, but it didn't come out that way. Click here for "Can't Carry A Tune in A Bucket". Posted 10/5/10 There's nothing very exciting or important about this article, but I thought it might be worth writing. It's a simple description of an experience teaching by computer, one form out of many that computer instruction might take. Computer instruction might or might not be very important in the future. Perhaps my short description will be useful to someone. Click here for "Teaching With Aleks". Posted 8/10/10 In another article below, "The Lack Of Description In The Study Of Education" I argued that we need more simple description of teaching and learning. I have tried to do that in several of my articles below, "Thoughts On My Teaching at . . ". Here's another approach to that, a snapshot of what I do on a typical day in my job. It's short, and not meant to be analytical. I hope others will consider doing something similar. Click here for "Teaching Snapshot". Posted 4/17/10 I have developed some ideas about teaching fractions in the past year or so, after I discovered that many of my college algebra students don't know fractions very well at all, and after discovering that that handicaps them in learning algebra. I have no way of knowing if these ideas have much applicability to teaching and learning of fractions in elementary school. Anyway click here for "Some Ideas On The Teaching Of Fractions". I have long said that teachers, and educational researchers, should study what is, not what should be, and to do that we need a lot more description of what actually goes on in real classrooms. To that end I have often said that teachers should put down in writing what they do in their classrooms. And I've tried to practice what I preach as best I can, by giving descriptions of what I do. Here's something I did in 1975-6. It's about individualized instruction, an idea that never quite goes away, but never quite seems to arrive either. Click here for "An Attempt At Individualized Instruction". (Posted 12/30/09) I have written about math education before, and I've got a lot more left to say. Hopefully this article wil be the first of a number in which I focus rather narrowly on teaching different topics. Click here for "Teaching Written Problems In Algebra". (Posted 7/13/09) Here's an article on motivation in the classroom that I started about twenty years ago. My thesis is simply that the willingness to be taught, which mostly means the willingness to follow directions, is very important in schooling. Click here for "Motivation And The Willingness To Be Taught". (Posted 4/5/09) Problem Based Learning And The Nature Of Mathematics is my latest foray into math education. It is the result of my gut reaction against one of the trendy ideas we sometimes hear about the teaching of math - the idea that we should make math relevant to students by starting with problems, "real life problems". I felt there was something wrong with this idea, and have tried to figure out and explain just what that something is. (posted 10/28/08) Here's some thoughts on college freshman and what they don't know about fractions. I first posted this last spring, but have now revised and extended it considerably. Click here for "Fractions My Algebra Students Can't Do". (posted 10/3/08) Browsing the internet for articles on educational matters resulted in finding a book, "The Trouble With Ed School", by David Labaree. I don't recommend it as a really good book, but it certainly catalyzed my thinking on schools of education and related things. I've never been much of a fan of ed school, but I didn't know I had so much to say until I started writing. What was supposed to be a short essay came out to be my longest article ever. Click here for "A Personal Indictment Of Ed School". (posted 11/20/07) My eleventh grade English teacher once told us that communication is very hard. I didn't believe him at the time. I thought communication was pretty easy. You just talk. But he was right, and every year I realize that more and more. Here's another article about verbal communication, again from 1974. Click here for "The Value of Straight Talk". (posted 5/22/07) Click here for "The Lack Of Description In The Study Of Education". I think simple, accurate, comprehensive description is an important basic to any science, but is woefully lacking in education. I give some examples, both bad and good. (posted 2/5/07) Click here for "The Value Of Surplus Information". Giving and getting more information than is absolutely needed can be very beneficial in many areas of life. This article is rather old. I think I could write it a little better today, but I would not change the ideas presented. I did not write this with teaching in mind, but I think it applies. (posted 2/5/07) Click here for my Guitar Page. This is not meant to be of interest to advanced guitarists. It consists mostly of a collection of guitar music that I used a few years back for teaching beginning guitar students. In the near future I also will include an article or two on the subject of teaching and learning to play the guitar. (posted 10/18/06 ) I have an article (see below) about health insurance and how it has caused health costs to rise in the last few decades. I do not accuse insurance companies of being greedy in this article. Doctors also, in my humble opinion, have a lot to do with sky high health care costs. I do not have such a benign opinion of doctors. I not only accuse them of being greedy, but that is the whole point of my next article. Click here for "The Trouble With Doctors". In this article I briefly mention what I call the "doctor knows best mentality". I think this could be a separate article. The idea needs a lot of explanation and elaboration. But that will have to wait for another day. (posted 8/27/06) Click here for "The Mathematics Curriculum - Some Personal Observations And Preliminary Thoughts". In this article I have managed to clarify and put in words some thoughts that I have had for many years. I discuss why numbers are, and should continue to be, the basis for the mathematics curriculum. Perhaps the most important idea in this article is that "conformity to reality" is the type of proof we use in arithmetic. This is an important type of proof all through elementary school. Very early in learning arithmetic informal deductive logic is combined with conformity to reality. (posted 4/30/06) I have managed to complete Chapter 17 in my book (see link below for the rest of this book which I have tentatively titled "Principles Of Teaching And Learning"). I have always considered this book to be the most important thing on my website, although some other articles are read a lot more, and this chapter is one of the important ones. Click here for Chapter 17, Everyday Classroom Practice. (posted 12/30/05) Some people think we ought to have a national conversation on race. I have generally thought that discussing race only aggravates people, with no benefit. However after much thought I decided to put on this website an article I wrote many years ago about prejudice. Click here for "Profiles In Prejudice". (posted 11/27/05) Political discussions tend to be negative experiences. Some time ago I started putting down ideas on how to talk politics more productively. I thought I could have it finished before the election. I believe it was probably the 1988 election I had in mind. But the ideas seem as relevant now as when I first started this article. Click here for "How to Talk Politics". (posted 11/13/05) In the sixties and seventies I did some reading in the field of ethology. Ethology is the study of animal behavior. The writings of Konrad Lorenz, particularly his book, On Aggression, impressed me greatly. I was convinced that the field of study he started would have a great future. I still believe that. Indeed Lorenz won a Nobel prize for his work in 1973. However the word "ethology" seems not to have entered into either popular culture or academia as I thought it would by now. Sociobiology made a bit splash a few years ago. I never learned too much about sociobiology, but what I did learn seemed to me less basic and valuable than ethology. I wrote this article, "A View Of Instinct" in 1975 to summarize a bit of my thinking on the subject. I haven't kept up with the field, and I have no doubt it has advanced a great deal in the last thirty years. To those who actually know the subject, this article may seem very unimpressive. However I think I present some important and valuable ideas. So I'll print it. Click here for "A View Of Instinct - Part One, Rationale". Part two will be on mechanisms of instinct, which is equally important to the rationale of instinct. Unfortunately I never got around to finishing part two. But I did start it, and will get to it when I can. (posted 10/15/05) Bureaucratic frustrations are a fact of life, which prompted me in 1977 to analyze things a bit. My central idea is that it is the good bureaucrat that frustrates us, not the inept. Actually bureaucratic frustration seems less a part of life now than it did when I wrote this. But I think the analysis is still valuable. My article on mediation (see below) ties in with this. click here for "Bureaucracy". (posted 5/1/05) We expect too much of logic. Good logic applied to uncertain premises leads to uncertain conclusions. Good conclusions require knowledge. Click here for "The Limits Of Logic", which I wrote in 1974 and see little need to change now. (posted 4/10/05) In 1979 I had a book (Tactics And Strategies, see below) published by a subsidy publisher. It didn't work out too well. I didn't sell many books. But I figured the experience was worth writing up, which in 1981 I did. Click here for "My Encounter With Subsidy Publishing". (posted 4/3/05) It was disappointing, but not unexpected, that The Mathematics Teacher rejected my article, "Some Disagreements With The Standards" (see below for a link) Click here for "My Disagreements Shot Down", in which I present a few thoughts about math education. (postsed 12/19/04) Click here for "NDSU Math". This is rather long, and a long story behind it. I am not satisfied with it yet, but decided to post it anyway. Perhaps I'll be able to figure things out a little better as time goes on. (posted 12/05/04)
Click here for "Chicago Math", written in 1996 from a parent's perspective. I had this article posted before, but apparently I let this link slip off my home page someway for the past few months, but here it is again. (posted 12/05/04)
Click here for "The Case Against Incidental Learning". We learn a lot of things incidental to other things we learn and do, but just how much does this amount to. Can we depend on incidental learning for things that are really important? The project method and activity method assume so. I disagree. (posted 11/21/04)
I'll be accused of heresy again perhaps, but some years ago I got tired of hearing about the scientific method. There are many scientific methods, and the method of "contrived experimentation" is not the most important. Click here for "Rules And Methods Of Science". (posted 9/13/04)
Click here for "Hydrogen, Nitrogen, and John Q. Public", which is a short lament on how much science the general public does or does not know. It's purely anecdotal, which I realize doesn't prove a thing, but perhaps is food for thought.
Parenting As Reality Interpretation is a few conjectures on how parents can fail to teach their children some of the subtleties of social behavior, and how the kids suffer for it all their lives.
I added Chapters Six and Seven in my "Tactics And Strategies Of Classroom Discipline". (See below.) This completes the book.
Click here for "Some Thoughts On Constructivism". Constructivism has been popular among educators for a few years now. I don't know just what it means, but that doesn't stop me from conjecturing.
Click here for The Case For Long Division. More math ed. It has been suggested that we consider getting away from "paper and pencil" algorithms in the teaching of math in the elementary school. Apparently some of the newer math programs do that. My argument is that learning long division, and lots of other topics in arithmetic that students have always learned, are needed to develop a useful knowledge of arithmetic, which is second only to reading as a life skill.
Click here for "The Bump School Of Driver Training". I wrote this in the seventies. I don't find much to change in it today. I think accident rates have fallen over recent decades, probably mostly due to increasing awareness of the problem of drunk driving. But tailgating, it seems to me, has gotten worse in recent decades. I no longer have any illusions that I'll ever be able to test out any of these ideas.Click here for "Some Disagreements with The Standards". The standards I'm talking about have to do with the teaching of math. They were published in 2000 by the National Councel of Teachers of Mathematics. They're more concerned with ideals of math teaching, it seems to me, than about standards to actually be attained. I wrote this last year after reading the NCTM's standards and deciding there was much to disagree with. I sent it to the editors of "The Mathematics Teacher" hoping they would publish it. As time went on I learned a lot about the California math wars, and learned that NCTM is interested in implementing the standards, not discussing them. Since I'm putting it on my web site now, I wrote to "The Mathematics Teacher" withdrawing it from their consideration.
Click here for a bit more info on math teaching (especially in California) and a few links of interest.
The following two articles are short descriptions of my math teaching. I wrote them out to send along with job applications. I have argued for years that one thing that is missing in the field of education is simple accurate description of what actually goes on in the classroom. Description is not very sophisticated science, but it is a starting point, and I think a starting point so far omitted in the field of education. Click here for a description of my experience at St. Cloud State in Minnesota, and click here for a description of quite a different situation at North Dakota State.Click here for "The Trouble With Insurance", about health insurance and why we're in such a mess. Click here for Let's Do It Together , a rather long article about how "groupers" and "non-groupers" don't understand each other.
Click here for the table of contents of the book I've been working on for many years about teaching and learning. Click on the chapter titles that are in blue. Chapter titles not in blue are not yet ready.
Click here for the table of contents of Tactics And Strategies Of Classroom Discipline, a book I wrote in the 1970's. I got it published by going to a subsidy publisher. It sold a few copies, but few enough to decisively end any further hope of publication. But I think its still the best nuts and bolts, nitty-gritty analysis of classroom discipline in existence.The Rationale For Laboratory Exercises In the Teaching Of Science from 1978. We learn by doing, don't we? So obviously rattling glassware is the way to understand Avogadro's number. (See Chapter Eight of my book.) Mediation is not a discussion of conflict resolution. Rather it is a discussion of mediation in a broader sense. There central idea is that one acts differently when the consequences of one's actions are mediated, rather than one does when consequences are automatic.
More to come as time permits.