You probably already know that the current state of mathematics
education in this country is very bad. What you may not know is exactly
how bad. Harvard recently released to the news media the results of a
study about mathematics. Their findings: (1) the US currently ranks 31st
out of 56 countries, and (2) only 6% of our high school students take
higher level math courses. Another statistic you may not have heard
(except from me) is that the failure rate for first year Algebra
students is a deplorable 50%. That statistic has direct bearing on the
Harvard results; and, as if these statistics aren't bad enough, you need
to understand that the 50% failure rate was true in 1972 when I started
teaching and it is still true today. Doesn't this just make you want to
shout "Why isn't anyone doing anything about this?"
In reality, mathematics educators, education specialists (seems like an oxymoron, doesn't it?), and universities have been trying for over 40 years to make positive changes. During my lifetime I have experienced, to varying degrees, at least six different methodological changes. (1) I grew up using the "skill and drill" of the old days. This method produced temporarily strong basic skills but very weak application or understanding; and without the latter, the former fades quickly. (2) In 1972, I started teaching just after the pendulum swing to "New Math." All math books started with a chapter on set theory, out went rote memory, and in came understanding. In theory, if students understood the why of mathematics, then they would create the skills on their own. Of course, none of that happened, and mathematical understanding actually decreased. It is now universally agreed upon that "New Math" was a miserable failure. Fortunately for me, I was raising a family during most of those years and didn't have to teach it very long; but I often wish that we could apologize to the students of the 70's and early 80's. "New Math" caused you more harm than good. That shouldn't have happened.
Since the final death of "New Math" in the early 80's, there has been no overriding mathematical philosophy for the country. Instead, different states--even individual school districts--have been searching for that perfect solution. (3) Some school districts returned to "skill and drill" by adopting the Saxon method. Of course, the problems that existed with "skill and drill" the first time still existed. Returning to a method that was unsuccessful before is not logical. Math people should know better. (4) In 1983, the University of Chicago conducted a great deal of research into why Algebra students were failing in large numbers. Then they created an entirely different approach to teaching mathematics. In 1988, I was very fortunate to have been working in Colorado Springs when my district (Air Academy School District #20) adopted the UCSMP (University of Chicago School Mathematics Project) textbook series. UCSMP was truly revolutionary and inspired. To learn more about how it came to be and how it was different, read my article "Frustrated With Everyday Mathematics/UCSMP? Why Is It So Different?" For the first time ever I saw large numbers of students improve both their basic skills and their understanding of mathematics. UCSMP continues to this day in various parts of the country, although the extreme difference in approach coupled with the fact that our society is now highly mobile have caused major difficulties, especially for parents. For UCSMP to have a positive impact on the country, it would have to be adopted by all schools. And we all know that will never happen.
Two other approaches bouncing around the country are (5) Project-based and (6) Activity-based programs. Project-based programs give classes a "situation" and that situation is worked on for weeks or months. The Pit and the Pendulum is the project I have heard the most about. This approach works well with certain students, but you haven't read anything about startling success because that hasn't happened. Activity-based programs are similar to project-based programs except for length of time spent on the activity. The activities might last a day or a week, and then change to another activity. In both of these methods, the math skills are taught as they are encountered in the situation. Classroom management issues arise with both of these methods. And, again, you aren't hearing shouts of joy over the positive benefits to mathematical understanding.
In addition to the philosophical changes, there have been many smaller changes in teaching techniques and classroom changes. Some still exist in some places, but most have been replaced with the newest and improved techniques. Cooperative learning was all the rage for a time and it is still a useful technique. I have lost count of how many of these teaching fads have come and gone over the past 40 years. You will notice, however, that the failure rate remains unchanged. So where are things now? Floundering. While school districts and states are bouncing around trying to find that magical solution, No Child Left Behind is slowly but surely destroying what little enthusiasm for learning still exists. No Child Left Behind may very well be the final death knell for mathematics education in this country.
In reality, mathematics educators, education specialists (seems like an oxymoron, doesn't it?), and universities have been trying for over 40 years to make positive changes. During my lifetime I have experienced, to varying degrees, at least six different methodological changes. (1) I grew up using the "skill and drill" of the old days. This method produced temporarily strong basic skills but very weak application or understanding; and without the latter, the former fades quickly. (2) In 1972, I started teaching just after the pendulum swing to "New Math." All math books started with a chapter on set theory, out went rote memory, and in came understanding. In theory, if students understood the why of mathematics, then they would create the skills on their own. Of course, none of that happened, and mathematical understanding actually decreased. It is now universally agreed upon that "New Math" was a miserable failure. Fortunately for me, I was raising a family during most of those years and didn't have to teach it very long; but I often wish that we could apologize to the students of the 70's and early 80's. "New Math" caused you more harm than good. That shouldn't have happened.
Since the final death of "New Math" in the early 80's, there has been no overriding mathematical philosophy for the country. Instead, different states--even individual school districts--have been searching for that perfect solution. (3) Some school districts returned to "skill and drill" by adopting the Saxon method. Of course, the problems that existed with "skill and drill" the first time still existed. Returning to a method that was unsuccessful before is not logical. Math people should know better. (4) In 1983, the University of Chicago conducted a great deal of research into why Algebra students were failing in large numbers. Then they created an entirely different approach to teaching mathematics. In 1988, I was very fortunate to have been working in Colorado Springs when my district (Air Academy School District #20) adopted the UCSMP (University of Chicago School Mathematics Project) textbook series. UCSMP was truly revolutionary and inspired. To learn more about how it came to be and how it was different, read my article "Frustrated With Everyday Mathematics/UCSMP? Why Is It So Different?" For the first time ever I saw large numbers of students improve both their basic skills and their understanding of mathematics. UCSMP continues to this day in various parts of the country, although the extreme difference in approach coupled with the fact that our society is now highly mobile have caused major difficulties, especially for parents. For UCSMP to have a positive impact on the country, it would have to be adopted by all schools. And we all know that will never happen.
Two other approaches bouncing around the country are (5) Project-based and (6) Activity-based programs. Project-based programs give classes a "situation" and that situation is worked on for weeks or months. The Pit and the Pendulum is the project I have heard the most about. This approach works well with certain students, but you haven't read anything about startling success because that hasn't happened. Activity-based programs are similar to project-based programs except for length of time spent on the activity. The activities might last a day or a week, and then change to another activity. In both of these methods, the math skills are taught as they are encountered in the situation. Classroom management issues arise with both of these methods. And, again, you aren't hearing shouts of joy over the positive benefits to mathematical understanding.
In addition to the philosophical changes, there have been many smaller changes in teaching techniques and classroom changes. Some still exist in some places, but most have been replaced with the newest and improved techniques. Cooperative learning was all the rage for a time and it is still a useful technique. I have lost count of how many of these teaching fads have come and gone over the past 40 years. You will notice, however, that the failure rate remains unchanged. So where are things now? Floundering. While school districts and states are bouncing around trying to find that magical solution, No Child Left Behind is slowly but surely destroying what little enthusiasm for learning still exists. No Child Left Behind may very well be the final death knell for mathematics education in this country.
