Daniel J. Brahier
Department of Educational Curriculum & Instruction
Bowling Green State University
Bowling Green, OH 43403

OCTOBER 1998

While recently paging through some "old" issues of the Mathematics Teacher and Arithmetic Teacher journals, I ran across articles detailing the results of the first and second NAEP tests (National Assessments of Educational Progress).  The tests were administered in 1972-3 and 1977-78, respectively.  The first item that caught my eye was on the second NAEP test, where Fourth and Eighth Graders were asked to "Subtract 237 from 504."  On this item, 28% of the 9-year-olds got it correct, and more than one-fourth of the 13-year-olds missed it as well.  In fact one out of every three Fourth Graders made a reversal error in doing the computation (meaning that they 'took the 0 from 3,' rather than the '3 from 0' in doing the calculation).  Similarly, when Fourth Graders were asked to compute "36 - 19" on the first NAEP in 1972, only 55% of the students were able to find a correct answer, and about one in four could calculate 38 x 9, despite two years of practice in multiplication.

More recently, on the achievement testing portion of the Third International Mathematics and Science Study (TIMSS), Eighth Graders in the United States, on average, got 59% and 48% of the items correct in the areas of Fractions/Number Sense and Geometry, respectively, while countries such as Japan, Korea, and Singapore scored from 74% to 84% in the same two areas.  But the TIMSS data were collected in 1995 and 1996.  And, many educators were shocked by the 1992 NAEP on which less than one-fourth of 9-year-olds could reason-out why half of one person's pizza could be more food than half of someone else's pizza.

Maybe it was ironic, or maybe it was just destiny that I happened to be reading the famous book Why Johnny Can't Add:  The Failure of the New Math at the same time as I ran across these journal articles.  The book was published in 1973, but the issues are so relevant that I had to keep reminding myself that the book was 25 years old.  Paging through the journal articles and reading this book made one thing clear to me:  There have always been problems with teaching and learning mathematics, and it is difficult to point a finger at a specific reason for the difficulties or to identify a definitive solution.

The results on computation items from standardized tests over the past 25 years are simply not impressive.  How is it that barely half of the Fourth Graders on the first NAEP could find the answer to a simple subtraction question, and less than one in four could solve a simple problem involving subtraction?  If those results had appeared on a test last month, rather than in 1972, many would jump to one of two conclusions:  (1) Students are relying too heavily on calculators, and they're not learning how to do simple computation by hand anymore, or (2) the Standards place so much emphasis on understanding and problem solving that children don't get enough experience doing computation.  While both arguments appear plausible, we can immediately dismiss the first one because calculators had barely been invented at the time this test was given.  In fact, the scientific calculator didn't get introduced into even the high schools until the late 1970's, and at that point, they still cost $75 or more!  So, what about the second explanation?  Well, it's possible that one could draw a parallel between the New Math of the 1960's and the Standards movement of the late-1980's, since both emphasized mathematical thinking and problem solving.  However, the scores did not significantly increase on the second NAEP, and it was administered five years later, in the midst of a "backlash" back-to-basics movement.

Recent performances on NAEP and TIMSS tests have left many educators and politicians pining for "the good old days" when life was simpler, children didn't have access to calculators, and teachers didn't buy into a constructivist theory of teaching and learning.  Of course, this pining is only justified if we assume that there actually were good old days.  We have a long road ahead in terms of reforming mathematics education in the United States.  Several reform movements have come and gone over the years, with researchers continually searching for answers to questions about how students learn best and how teachers can most effectively help their students.  But the next time we find ourselves pining for the good old days, let's be careful and recall the words of Will Rogers who was once quoted as saying, "Schools aren't as good as they used to be . . . but, then, they never were!"

What is your "take" on this?  Has anything actually improved or deteriorated in mathematics education over the past three decades, or are we simply doomed to repeat history again and again?  How can we blame the skeptics who say, "the Standards reform will pass ... the pendulum always swings back"?  We would like to hear from you!  Take a moment to drop an email to Daniel Brahier at brahier@bgnet.bgsu.edu, and we will continue the discussion with your thoughts included in the next newsletter issue.