A little help might go a long way to make students better at math…

May 18, 2010

Fear of and failure in math has had a profound effect on my life, and I know that I am not alone.

But my discomfort with math prevented me from going straight to college when I got out of high school, and, in fact, it even kept me from enrolling in a college prep program when I signed up for high school.

I did eventually complete my four years of college well into middle age.

But whether we go to college or not, we all need a good working knowledge of math.

As far as I know, it’s a settled fact that some of us are math oriented and some of us are not. And I am pretty well convinced that I am not. But that does not mean I do not understand any of its concepts or how to work out relatively simple problems.

In fact, I noticed early on that I was pretty good at word problems, with my main hang-up being I might get lost in the actual mechanics of calculations (such as long division, or worse yet, fractions, or even worse, fractions and long division combined).

So, if I could just do better at the mechanics of it, I think I’d be as good or better than some who whiz through already printed out problems. That’s because I think in some instances I might be able to interpret word problems quicker than some who speed through problems already laid out for them.

Beyond not being math oriented, I think my initial problem in the lower grades was that I was somewhat lazy about the whole thing — all those rows of problems we were always given.

Also, like so many pupils, I was intimidated by fractions — they looked so strange. And it didn’t help that the tone from most of my teachers was that fractions are hard.

(And let me break away from my main point to say that as far as teaching things like fractions, I think a little real world practice could help — have pupils use a ruler to measure things and let them get used to using those lines between the numbers that represent fractions — that way they form a mental picture of what a fraction is. Pictures of pies are nice, but cutting up a real pie and relating the pieces to the fractions they represent could help. )

Also, it seemed that we did not stay with fractions for any length of time. We’d do them for a couple of weeks or so and then never see them again until the next year when they again reared their ugly head.

And did you ever try to get your folks to help you? Oh, my God! I wouldn’t advise it for anyone.

A few times my sister was forced into helping me and that helped. One of my brothers did too, and that helped. But they had their own work to do and did not have the time nor interest to be my constant tutor, and they may have not had confidence that I was really paying attention. And I was the pesky little brother, baby of the family — still am at 60.

But let’s stop right here. That’s the key for people like me (and again, I know that I am not unique in this). We need tutoring. Of course we have to want to be helped too. But I think the easy availability of help encourages most of us to seek it out.

In all public schools, from the lower grades to the higher grades, as well as at junior colleges, there should be fully-staffed tutoring centers, and staffed with professionals, as well as student helpers. I think that might be more important than new teaching methods or endless worksheets.

(And it does no one any good, the individual or society as a whole, for students to be passed on from grade to grade without proper mastery of the basics, of which math is one.)

I would not have been able to get through my minimal requirements in beginning algebra without some tutoring help from the junior college I attended. That help allowed me to go on and complete intermediate algebra, for which I had no tutoring, except from some fellow students. But by this time I was well into middle age and motivated to complete college. (Motivation always helps.)

I’m not trying to write some sob story here and say boo hoo for me. I’m hoping that some teachers and some school board members and some parents and some voters might read and identify and get something out of it and that in some way it might contribute to the improvement in the way we teach math in this country.

I should mention here that things may have changed drastically since I was in school, but from what I have read and observed, not that much.

By the time I got to eighth grade I was still treading water in arithmetic. We added, subtracted, multiplied and divided and did some word problems, to include some fractions. And I’ll always remember my math teacher. He would just shake his head at how poorly most of us did (the better students were in a different class) and then say things like: “I don’t know what you’re going to do when you get to high school and have to take algebra”.

Not only was I doing poorly at math, I was getting no encouragement whatsoever, and not extra help either — teachers had no interest or time to help you after class.

I was supposed to take college prep classes in high school. But I told my counselor of my fear of math and he let me slip by. You see, to take college prep classes, I would not only have to take higher math (algebra and so on), I would have to take biology and chemistry and such. Instead, I took something called “General Math”, nothing but grammar school level work. I took a science class but had difficulties, not because I was not interested, quite the contrary — but math is an integral part of science. (I took ag science, but in my day that was a misnomer, since real science was only touched lightly.)

In my senior year my counselor put me into a class called “Senior Math”. I think all the kids that took algebra but flunked algebra were in it. They at least knew how to begin. The teacher refused to help me. He said I was too far behind and he did not have time.

While the onus is on the student (along with his or her parents), someone at the school level needs to take time. And if there is no time, we need to find out why and do something about it (like forcing some of those so-called math teachers who spend more time working as coaches do the job they are supposed to be doing).

My main complaint against many math teachers is that they like to help students who do not need help and do not have patience to help those who do.

We need quality teachers and we need enough of them and we need support from those who make the policy, such as school board members and legislators and those who vote for them.

Please, any math teachers who read this (to include one of my brothers), do not think I am indicting all teachers. But I’ll bet you good teachers know what I am talking about.

I only present this from the perspective of an ex-student myself and of someone who is intelligent enough to understand math but who is not math oriented.

P.s.

Please don’t tell me calculators and computers have eliminated the hard work. You need to know what you are doing and not have to depend upon a machine that could turn unreliable. And calculators do not solve problems by themselves — garbage in, garbage out.

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High school and college too long; elementary learning pace too slow…

April 7, 2009

I don’t really know what goes on in high schools these days and I don’t think I really want to.

And to be honest, it probably is no worse than when I was in high school (‘63-‘67).

And maybe that is the point I want to address.

It needs to improve.

In fact, I think we need to revamp our whole system or format.

For one thing, I think the standard four years of high school is too long. And perhaps even the standard four years of college is a tad long too.

There is too much repetition. The first two years of college are often basically a repeat of high school – something like everything you should have learned in high school but didn’t.

Now I should note right here I am not addressing the problems of gifted and/or motivated kids. These folks often forge ahead despite the best efforts of parents and teachers and fellow lame brained students to get in their way.

No, I’m talking about everyone else.

While I know my attitude differs from the long prevailing thought that young people need infinite freedom and time to make up their minds about life, I really am convinced that a lot of our social problems and unemployment problems (Wall Street excess economic disasters perhaps notwithstanding) could be alleviated if people did make up their minds sooner about what they want to do when they grow up. You can change your mind if you change your mind or if things don’t work out a lot easier than you can come up with something after procrastinating well into adulthood and finding yourself in the unemployment line with little to no marketable skills.

I am going by the California model of education since I am intimately familiar with that. I went from kindergarten through four years of college in the state’s public system. Also, I covered schools as a beat for more than one California newspaper. And I spent one fun (not really) month serving as a substitute teacher in one large urban school district in the state. I know what goes on in the state’s schools (a lot of administrative stuff, a lot of disciplinary problems, not so much teaching and learning). I have not been in the schools for more than a decade, but from what I read and hear, things appear status quo.

Starting in elementary school, we need to up the quality of teaching and promote learning at a faster pace. Year-round classes would probably help in that they alleviate the problem of long vacations in which pupils forget and then have to start over on the old material when school resumes.

And maybe even in the lower grades individual teachers can’t be expected to handle all subjects together. Just like I’ve heard lawyers joke, “I went to law school because they promised there’d be no math,” maybe some otherwise adept and knowledgeable teachers need help in some subjects.

This could also apply to all subjects, to include English and social studies, but I would imagine, though, that in the lower grades the biggest demand for single subject teachers would be in the area of math and science.

By the time a student reaches high school, he or she should be able to have a good handle on what general career goals are practical. Those who plan to go into careers where academics is stressed need to be allowed to follow that path and not be held back by those who seem to have no use for wider knowledge.

Those who think they would be better off at what we have called vocational training should be allowed to do so and should be provided the most up-to-date facilities and training. And this is where real-world help could be used. The problem has been that career educators, through no real fault of their own, because they have lived in the sheltered environment, have little concept for what goes on in the outside world of work.

Probably high school does not need to be more than three years, whether the vocational or academic track is followed.

And I do not for a second suggest that those who follow the vocational route should be short-changed on academics. In this modern world people need to be more highly educated. But the emphasis for them would still be more directly related to hands-on work.

Now all of this might seem a kind of stifling and a straight jacket approach, but I think there could be room for some flexibility. I am only presenting a general concept. But there has to be more structure than there is in the conventional U.S. approach, because even in good economic times employers complain there is a lack of skilled labor for both the trades and upper scale work. That’s why we import labor from say Mexico and India (that and the fact employers can get cheaper labor, but that is another subject).


Algebra can be taught, but it’ll cost you…

January 29, 2009

(Copyright 2009)

If algebra is so important for our school kids to learn why aren’t most adults knowledgeable in it? Why is it so hard to find teachers competent to teach it?

Math teaching or lack of it is a pet peeve of mine – one I will likely take to the grave.

What brings the subject up this time is an article by political columnist Thomas Elias that mentions that a California Superior Court judge has blocked a controversial plan aimed at requiring all of the state’s school children to be tested in algebra in the eighth grade at the latest. While the article does not explain what the consequences of failing are, I’m sure it would mean kids flunking and/or schools losing funding.

But that, what the consequences are, is not my concern. My concern is this sudden push to get all kids to learn algebra when for decades most have not and grew up to be adults who still did not and nothing has been done to rectify the situation, if indeed it needs rectifying. I graduated from high school in 1967 after taking nothing more than general math (adding, subtracting, multiplying, and dividing) as a freshman. Yes, about two decades later I had to pass intermediate algebra to get a four-year college degree, and if I had been a little quicker at getting that degree I would not have been required to do that.

Some of us find math difficult. And if no one will teach it to us and if no one even requires that we learn it, then chances are we won’t learn it (and I was finally fortunate enough to have some first-rate math teachers at the community college level).

I personally think math is extremely important and I think any educated person ought to at least be able to master intermediate algebra and probably more. I have noted, however, that most adults who have taken algebra often faintly recall it as an unpleasant memory, something they worked hard to master and then immediately forgot (even those who liked it, usually admit they forgot it). I think, however, they learned something along the way and probably subconsciously developed a somewhat better understanding of the relationship of numbers. For one, you work with a lot of fractions in algebra.

The afore mentioned judge apparently realized you can’t just mandate that math instruction will happen from a court bench and it will magically be done. The will of the public and the will of the taxpayers (which really are one) has to be there, and the will of the education establishment has to be there too.

And most any math teacher I am sure would tell you that education has to begin early and can’t let up.

I have seen that at least a lot, if not all, schools these days are attempting to introduce higher forms and /or more complex forms of math at much earlier ages. How well they do this, though, is dependent upon the knowledge of the instructors available.

Usually in the lower elementary grades pupils have only one teacher who has to teach multiple subjects.

When I was in my late 30s I was sitting in a community college class taking introduction to algebra and sitting next to me was a kindly old woman who was a veteran school teacher. She had to master rudimentary algebra to pass a state teachers’ test, one that was just then being mandated. And, really, the level she had to pass was barely algebra (I know. I later took that test and it was easy, believe me – I did not become a teacher, though). No offense to her, but why was she allowed to teach children arithmetic all those years when she was lacking in proficiency herself? And that my friends is why we are still trying to figure out how to get our children to learn algebra.

(I was taught what probably was third or fourth grade level arithmetic in high school by a gym teacher. My oldest daughter had an athletic coach for a high school algebra teacher, who refused to help his students ; maybe he didn’t know the subject himself.)

I have observed enough now at age 59 to believe that a working knowledge of some level of algebra would be quite valuable for all adults. It’s not the algebraic method itself as much as the need to understand math (which you do when you master some level of algebra) that rules so much of our life, from using recipes to cook at home, to doing home repairs, to balancing our check books, to figuring out how much interest we are paying or are receiving, to understanding the wonders of science, to master job skills and so on. Without that understanding we are all at the mercy of those who do. And please don’t tell me all that you need is a computer or hand-held calculator (garbage in, garbage out).

But if it is so important, then why have we not built up our math instruction after all these years?

It’s partly a question of money. Those who allocate the funds and some taxpayers don’t want to admit that it takes some expertise to master and teach the subject, so in that way they can avoid paying the bill.

P.s.  So, do I remember any algebra? Not too much. Do I have a solution to the math teaching problem if there is one? Maybe: Math may be challenging enough that we need single subject specialists to be introduced into the lower grades. Also, while adequately training current teachers who may be deficient in the subject may be problematical, certainly we must up the standards for those going into teaching. If the standards become too high and the pay is seen as too low, it will be difficult to recruit new teachers. Legislators and school boards will have to figure out what they want and whether they are willing to pay for it. Simply paying existing teachers more without requiring that they demonstrate proficiency will not work. I took the California teachers test, known as CBEST, many years ago. Hopefully, they have strengthened it. When I took it, you only had to demonstrate a rudimentary knowledge of arithmetic (using some basic algebra) to pass. Had the test of been adequate, I would not have passed it.

And finally, my apologies to any teachers or former teachers who might read this and think I am criticizing them. There are a lot of good and qualified teachers out there – just not enough.