There are many methods of organizing math classroom activity. Some, such as the lecture method where appropriate and in skillful hands, have proven successful while others have established a record of failure.
There are many reasons why an instructor might want to spend class time on in-class student activity (group projects and individual manipulative work and exercises.) These things might engage bored students. They might be used to break up a class period into logical components. Obviously the impulse to reach more students is a dominant motivation. The activities do take large chunks of class time and must be carefully weighed against that which they displace.
Another motivation is the desire to seem "with it" and "at the cutting edge" with one's colleagues. Fashion has power without respect to merit.
Still another motivation is boredom. I am not referring to student boredom here. I am referring to the plight of a teacher fifteen years into a forty year career who finds that he or she simply cannot bear to deliver the canned lecture 357A on the quadratic formula ONE MORE TIME without screaming.
It should be remembered that the students themselves have not heard 357A dozens of times. They may need, exactly, lecture 357A. An excited teacher delivering 357A might well knock socks off.
An instructor who thinks of him or herself as teaching MATERIAL might lose focus and forget that it is fresh to new students each quarter.
An instructor who thinks of him or herself as teaching STUDENTS is less likely to fall into this way of thinking. Students change each quarter and present a kaleidoscope of challenges. If 357A is the one that works and creates success measured in performance by students on tests then that is what a student-centered instructor will use (with 357B, C and D in the background in case multiple approaches seem in order.) The goal-dynamic in the classroom is one that allows as many students as possible to learn as much as possible as measured by performance indicators during the quarter or semester. Since each class dynamic is formed by the personalities of class members in contact with the instructor and focussed to learn a specific body of material, the situation is fascinating and NEVER the same two quarters in a row. What could be more interesting?
We teach STUDENTS not only the MATERIAL of the course.
But there are other reasons some experiment on our students.
In many grade schools and high schools in the United States teachers have found it necessary (in some school districts this has been an order by school administrators) to curtail most of the school work to be done by students outside the classroom. In an environment like this, practically all learning must take place in the class room itself. In this circumstance the lecture method of instruction cannot be used to a significant extent. As a side effect, students never learn well the skills of efficient note-taking and concentration for more than five minutes at a time, or the skill and pleasure in mastering from a book -but otherwise on your own- a new idea.
It takes a few years of practice to master the skills. Even the best students progress slowly when the home work hours are not there. They have serious problems adapting when they get to the much faster paced environment at a college. They have not been prepared by the people they trusted to make them ready.
They are even denied the thought that these are worthwhile skills.
At lots of schools instructors are threatened in various ways if they don't achieve certain popularity goals with students and parents.
Some schools have ordered teachers to submit a certain average GPA whatever the performance level of the students. Students know this of course and this - finally - disconnects student performance from grades.
Often teachers try "group work" methods very early swayed by the claim that real world projects in corporate environments succeed as a result of team effort. That is usually or at least often true. The problem with this point pushed too early is that team members must bring many skills to the pool to be an addition to the team. What is the point of adding a team member whose only skill is an ability to "play nicely with the other children?" When a hard, deadline-coming-up job needs to be done, there are words for team members like that. Whatever their charm and enthusiasm and "self-esteem" they are eventually found to be "dead wood" or "parasites" and people want them OFF THE TEAM so the job can get done. Real team participants bring many REAL skills to the table. These come first. When push comes to shove team members will bend over backwards to accommodate a contributor who can help MAKE THEM ALL LOOK GREAT, even if he or she lacks a few of the social graces.
Some teachers avoid "rote memorization" of skills such as knowing the times tables or adding fractions or long division or decimal arithmetic and rounding and approximation. They claim that any practical person or "anyone in engineering or the sciences or anywhere else uses a calculator." True.
But how could a sales clerk with no number sense prevent embarrassment when asked by the boss "About how much business did we do today and what fraction was Nike shoes?"
What about some fictitious engineer who knows numbers only through a calculator? How could such a person do the endless seat-of-the-pants estimates that comprise engineering intuition? How could he or she know if a little factor of three error was made that would cause a bridge to fall? Does the engineer remember that the intuition regarding changing phenomena - "When I change this quantity it projects to a change in that." - has SOMETHING to do with his or her hard work in Calculus class? The good ones know this very well. The "lawsuits-waiting-to-happen" look it up in the standard manual and trust it will all work out OK.
The approach to math teaching that would shield children from the awful tyranny of accountability for understanding basic arithmetic has really hurt lots of kids.
It will hurt us grievously as a nation when these hundred million products of flawed education theories turn into adults and there is a massive shortage of people with real management and technical skills. We are becoming a nation of "I'm a people person" folks (this might be translated as "best suited for retail sales") as distinct from DOERS.
There is nothing wrong with being a sales clerk. We just need people with lots of other skills too. Must we rely primarily on our immigrant citizens?
The many experiments that have been performed on our students during their years at our primary and secondary schools by teachers desperate to improve performance have left them with a patchy and disorganized information and skill base.
It should come as no surprise that our average rankings of pre-college student achievement put us among the non-industrialized nations. What is equally distressing for those concerned about the future of our collective home place is that our best 10% when matched against the best 10% of other nations fares no better.
Currently we have the finest collection of Colleges and Universities of any nation on earth and the very most pathetic average instruction level in primary and secondary schools among the industrialized nations.
I have been involved in dozens of experiments in education over the last twenty years. The ideas that would move the "Sage On The Stage" off his or her pedestal tweaked my egalitarian impulses. I have seen these experiments run their course and watched the results (our students) succeed or fail and disappear from view. There has been success and failure in all these methods but I have been profoundly disturbed by the casual way the experimenters (myself among them) have bartered and spent the lives of our experimental subjects in our curiosity and ambition and desire to seem "au courant."
A medical doctor who experiments on a flock of human test subjects is governed by the strictest scrutiny. Even with the noblest of intentions, centuries of experience have taught us that the impulse to try new procedures which the physician hopes or believes will be beneficial overwhelms judgement and has resulted in innumerable disasters. Laws are in place to prevent premature or casual experimentation in the medical professions.
WE HAVE NO SUCH RESTRICTIONS PLACED ON US. Power without control leads to excess. More than that, we don't even have the sensibility that our experiments place our experimental subjects at risk. We run experiments that, if we were medical doctors, would see us tried and convicted in a court of law and imprisoned.
You may say that the mistake of a medical doctor costs limbs or organs or even lives while our mistakes do not. I suggest you reconsider.
Our experimental subjects are people with dreams. They have a few chances before them and decisions to make and, mostly, are not sure which way to go. They have to decide on a technical career or something in business or whether to bag it for a few years and work for Uncle Fred. Returning students have to decide if the big dream of coming back to school is something they can continue to justify with the spouse and family.
We put them in our experiments without their real understanding of the consequences. These are not even deliberate, carefully planned events. Some enthusiast pushes and it happens. Maybe it works and maybe it doesn't. If our experiment fails for them it absolutely will direct them down a life path that WE determined. Make no mistake - we are changing and making big decisions about the lives and futures of our experimental subjects.
We experiment. When an experiment doesn't work they pay. They pay with squandered opportunities and careers henceforth directed away from anything technical.
And the funny thing is many never do understand what has been done to them. We don't advertise in our class schedule that we are running an experiment and "any of you who sign up will just have to take what you get." When the experiment doesn't work we usually still give out credits. The credits just don't mean anything and the student will not be able to pass the next class up the line. They are stuck and usually don't know why.
But we know why.
We look the other way and, in a couple of quarters, the sources of any guilt we may feel have moved on. It must be time for another experiment!
It is time to take a hard look at what is working and with what methods. We must also look at what is not working. We must find out exactly at each institution which individuals promote theories that demonstrably do not work. It is time to take the gloves off and shift into new careers those well-meaning but foolish education theorists who have guided (as principals or other administrators and as teachers) our primary and secondary schools down a path that has led to our current disgraceful and pathetic state.
It is not foolish to run with a great and cherished idea that turns out to be wrong.
It is foolish and culpable to squander the lives and resources of millions of young people in the service of a collection of theories about how people learn that are, by the clear evidence, simply wrong.
And we who are stewards of the Colleges and Universities must guard the door and make sure that this sorry hopeless rot, promoted by the foolish and the culpable, does not creep farther into our halls.
There should be no more squandering of the precious years and opportunities and futures of our children.
It must stop right now.
Larry Susanka
The Mathematics Department Pages
More From the Teaching and Learning Page
 |