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Integrated Mathematics after 25 Years

by Lynn A. Richbart
January 2001

lynn New York State developed an integrated mathematics program in the early 1970s. The committee that developed the integrated content included teachers, college mathematics educators, and mathematicians. The program includes an integration of algebra, geometry, trigonometry, logic, probability, and statistics over the first three years of high school. In New York, the final three-hour examinations, known as Regents Examinations, are produced by state committees of teachers and are kept secure. They are sent to the schools in locked boxes and are administered to everyone in the state at exactly the same time. The first New York Regents Examination on the new program was offered in June 1975, a quarter-century ago. During 1979, we worked with Educational Testing Service (ETS) to evaluate the program using Preliminary Scholastic Aptitude Test information. The following year, the State Education Department conducted a study using Scholastic Aptitude Test (SAT) information. We also monitored SAT Achievement Tests (now called SAT II) and numbers of students who took and were successful in Advanced Placement calculus. The results showed that students were and continue to be quite successful on those measures.

A description of the program appeared in The Secondary School Mathematics Curriculum (Paul and Richbart 1985). When the NCTM's Curriculum and Evaluation Standards for School Mathematics appeared in 1989, we were quite pleased to see that our then-14-year-old program met most of NCTM's recommendations.

Over the years, the content has been slightly modified; the testing process has been revised to two examinations rather than the three originally developed. The new Regents Examinations, known as Mathematics A and B, still cover the content of the three years.

Another change over the years has been the use of calculators on the examination. We first permitted four-function square-root machines, then scientific calculators; the new tests permit graphing calculators on the first test and require them on the second.

As in most states, a major change has occurred in the population of students taking these courses. One of the purposes of the integrated program back in 1974 was to keep more students in mathematics courses. Before 1974, we lost a lot of students in the sophomore year because they were unsuccessful in a full-year geometry course. The integrated program permitted a good geometry foundation in the first year and a second year that was not totally geometry oriented. The integrated program did what was intended, in that more students made it to the third year of mathematics than in the traditional program.

Today it is not more; it is all. All freshman of 1997, our present seniors, must pass one state Regents Examination to graduate. The only exception is that for the first four years, a special education student who fails the Regents Examination can use the lower-level competency test.

The integrated mathematics program has come of age. The program lends itself to a problem-solving approach taken by many of the newer National Science Foundation programs. Even most of the more traditional algebra textbooks of today integrate mathematical reasoning, geometry, probability, and statistics topics.

Reference
Paul, Fredric, and Lynn Richbart. "New York State's New Three-Year Sequence for High School Mathematics." In The Secondary School Mathematics Curriculum, 1985 Yearbook of the National Council of Teachers of Mathematics (NCTM), edited by Christian R. Hirsch, pp. 200–210. Reston, Va.: NCTM, 1985.

 

Lynn A. Richbart was a member of the New York State Education Department from 1969 to November 2000 and had responsibility for statewide mathematics curriculum development and assessment. He continues to be an advocate for an integrated approach to teaching mathematics.
 

 

 

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