Prelude to Algebra

“making algebra make sense”

The motivation for Prelude

        The motivation for writing Prelude to Algebra grew out of the very successful remedial math program at Lee University in Cleveland, TN.  Whereas most college remedial math courses are notoriously unsuccessful [Stage; 1995], the Elementary Algebra course at Lee empowers students to continue on in mathematics.  Long-term studies have found that when students complete Lee’s elementary algebra course and continue on to the next math class, they are successful 94% of the time [Lay; 2006b].  How is such success possible?

The origin of Prelude

        The Prelude project actually began about 50 years ago just after the end of WWII.  When the veterans returned to the States, many of them decided to go to college.  Although they were highly motivated, their math skills were largely undeveloped.  This caused a high failure rate in remedial courses in beginning algebra. 

      At this time, L. Clark Lay was head of the department of mathematics and astronomy at Pasadena City College in California.  His department surveyed existing textbooks for a new course in arithmetic, but could find none whose goals specifically included preparing students for algebra.  Convinced that such an approach was needed, Lay began a study of the kinds of mistakes that students commonly make in algebra. 

The study begins

      As Professor Lay analyzed student papers and interviewed students, he found that most of their errors were made with the most basic concepts: working with fractions and signed numbers, evaluating exponents, canceling, and solving simple equations.  He discovered that these errors were often a result of their thinking incorrectly about what they were writing.  This prompted him to look for ways to develop thought patterns in arithmetic that would reduce their errors in algebra.  He realized that students needed better conceptual models for the basic arithmetic operations.  These models had to

· be mathematically correct

· anticipate “algebraic” thinking

· be easily understood.

His work was supported in 1952-3 by a fellowship from the Fund for Advancement of Education (Ford Foundation).

The first book

        The “operator” approach that Professor Lay developed was incorporated into his first book, Arithmetic: an Introduction to Mathematics (Macmillan, 1960).  At this time he also introduced the use of equivalent forms to solve equations—now called the “3-number method” and included in the Prelude to Algebra book in Chapter 6. This first text proved very successful both with college students and with 8^th grade students preparing for algebra [Lay; 1959].  His research led to his receiving a doctor’s degree in education with an emphasis in mathematics from the University of California at Los Angeles. 

More books

      In 1960, Dr. Lay became the chairman of the newly formed department of mathematics education at California State University in Fullerton.  A Faculty Fellowship grant from the National Science Foundation in 1962-63 enabled Lay to pursue post-doctoral research at UCLA.  With his emphasis now shifted to teacher preparation, he wrote The Study of Arithmetic (Macmillan, 1966) to communicate his approach to prospective teachers. 

        As teachers graduated from the Cal State program, they sought a book to use that would incorporate Lay’s effective approach to arithmetic and pre-algebra.  Since his first book was now out of print, he wrote From Arithmetic to Algebra (Macmillan, 1970) for them to use in their classrooms.  This text updated and expanded the material in his first two books.  New insights at this time included the introduction of better definitions of multiplication and exponentiation.  (See Chapters 3 and 5 in Prelude to Algebra.)

        In 1973 he refined his book for elementary teachers, calling it Principles of Elementary Mathematics.  The use of operators, which he had introduced in his first book, now played a central unifying role throughout. 

The early summer institutes

      Having been invited to serve on the Advisory Committee for the School Mathematics Study Group (SMSG), Lay was able to contribute to national efforts to improve mathematics education.  In 1970 he was awarded a National Science Foundation grant to conduct summer institutes for secondary school math teachers in southern California.  For the next three years he trained 30 teachers a year in his approach to preparing students for algebra.

The next generation

      When Dr. Clark Lay retired in 1975, he moved to Illinois where his son Steven was teaching math at Aurora University.  Steven had earned a Ph.D. in mathematics at UCLA and he, like his father before him, was faced with the question of how best to teach remedial algebra to under-prepared college students.  They joined forces and adapted the earlier materials into an intermediate algebra text Principles of Algebra (1980).  Subsequent editions (1985, 1988, 1990) sought to simplify the language and introduced graphical models for expansions and contractions.  (See Chapter 4 in Prelude to Algebra.)  The books were remarkably successful at preparing students for subsequent math classes.  A five-year study documented that 94% of the students were successful in their following math classes [Lay; 1985].

On to Tennessee

      In 1998, Dr. Steven Lay joined the Department of Natural Sciences and Mathematics at Lee University in Cleveland, TN, where a more effective elementary algebra course was badly needed.  By expanding the early material on pre-algebra and omitting the more advanced material, Principles of Algebra (2003, 2006) evolved into a basic math/elementary algebra text that was able to duplicate at Lee the remarkable success that the material had enjoyed at Aurora [Lay; 2006b].

      Both in Illinois and Tennessee as college students used the Lays’ books, they often made comments such as: “For the first time in my life, math makes sense to me.”  “Why didn’t they explain it this way in middle school?” or, “You ought to write an 8^th grade pre-algebra book so that students can learn it right the first time.”

Back to Middle School

      In response to these comments, Dr. Steven Lay completely rewrote the material in 2005 at a middle school level and Prelude to Algebra was born.  The pacing and selection of topics were closely aligned with the TN state standards, and innovations included a simpler explanation of canceling (in Chapter 4) and an easier way of computing with signed numbers (in Chapter 9).  His daughter BethAnn Lay was teaching math at Cleveland Middle School at the time, and Dr. Lay had the privilege of team teaching an 8^th grade pre-algebra class with her while using a preliminary version of the new text. 

      In 2006 the Tennessee Department of Education awarded a 3-year grant of $750,000 to Lee University to begin training middle school teachers in the use of Prelude to Algebra.  The first INAT (Improving Numeracy and Algebraic Thinking) summer institute was held in June, 2007.