The Early Years,  1971 - 1987

Since I began teaching, I have always taken pride in the success of my students, especially those with learning disabilities and those who previously  have had a difficult time with math. For over thirty five years I have taught the entire curriculum from Basic Algebra to Calculus and Differential Equations.  Student success has always been a major goal in my career.  This page summarizes some of my projects and efforts to facilitate learning for students. 

When I first began teaching at the then Seminole Junior College of Florida in 1971, I was looking for a College Algebra book that could be read and understood by students.  When we could not find one, I wanted to write my own, one that would eliminate lengthy explanations that students were not reading anyway, and instead to use carefully selected examples and tightly organized exercises to teach the concepts in a discovery format.. My plans were laid aside in favor of a more pressing problem, developing materials for our liberal arts math course of the late 1970’s called MS 101 Fundamental Math.

About the time I completed my first book, Math is Fundamental (1979), the math curriculum changed in Florida.  Instead of one 3-hour liberal arts math course for an Associate of Arts degree of the 1970s, in the early 1980’s the State required a passing score on the Florida College-Level Academic Skills Test (CLAST) and a 6-hour math requirement was introduced.  Also in the early 1980’s, I began work on my doctoral degree, which I completed in 1987 with a dissertation study related to the CLAST. 

Basic, Intermediate, and College Algebra: One Step at a Time

Upon completion of my doctorate and my CLAST study, I immediately realized that for most students, the real problem was not so much passing the CLAST, but learning algebra.  My goal was to write materials for Basic Algebra that would be easier for students to read and understand.  The explanations and examples were integrated into the exercises, and the skills would be presented one at a time in a step-by-step format.  The book, called Basic Algebra: One Step at a Time, was laid out in the form of a work-text, where students would show their work in the space provided.  Moreover, in the first exercises of a particular skill, partial steps were provided to help students learn not only what to do, but where to do it on the page (like a parent who, after taking off the training wheels, holds the bicycle while a child begins to ride for the first time).  Eventually, exercises are given in which there are no helpful hints, and the student must work exercises on his/her own (like the parent who, after holding the bicycle while the child gets started, releases the bike!).  A former student who later enrolled in classes at Rollins College told me that at Rollins they call this “directed learning” and “independent practice.”

In 1991, after about three years of writing and improving Basic Algebra: One Step at a Time, I hand-wrote a “draft edition” of Intermediate Algebra, covering about two-thirds of the hardest skills in Intermediate Algebra.  This draft edition was used as a supplement to the traditional textbook for about seven years while I worked on the more pressing problem, College Algebra.  It was not until 1997, when I finally completed Intermediate Algebra: One Step at a Time, which I had begun six years earlier.   The following year (1998), I wrote Introduction to Algebra, a Basic Algebra book in the One Step format for Kaplan Educational Centers.

In 1991-92, the math department selected a particularly difficult College Algebra textbook.  In my College Algebra class in Spring of 1992, I had only 10 of 25 students (40%) complete the course with a C or better.  This was unacceptable to me, so in the summer and fall of the 1992, I began writing College Algebra: One Step at a Time, beginning with the hardest sections first.  As I completed sections, I replaced the ones in the traditional text, and my student success rate leaped to 69% in Term I of 1992-93. For the next few terms, my success rate ranged from 70 to 80%, and a couple of semesters in excess of 80%. 

My latest project in the One Step series was a major revision of my Basic Algebra: One Step at a Time (2001).  In more than 10 years since the first writing, I had so many improvements to make, based upon my own teaching from the book, so many pages of the original work to be replaced by supplements.  Finally, I had my NEW improved Basic Algebra book!   Students seem to like it, and my success rate increased to 74.4% for the first year of use!

Graphing Calculators

In about 1995-96, the math department changed the College Algebra  to  College Algebra with Graphing Calculator.  I immediately wrote a 30 page handout that my students have used for 8 years instead of the Texas Instruments Manual, a thick book suitable for mathematicians, but hardly appropriate for students who are just beginning to learn calculator skills.  In the following year, I wrote an 80-page calculator supplement to accompany my College Algebra book, in which explanations and examples explain calculator techniques to solve particular examples from the book.  This handout is currently a supplement at the end of the College Algebra: One Step book.   Now, we not only must teach the College Algebra skills, we need to take some class time (varying from instructor to instructor, of course) to explain the graphing calculator. 

In Term I of 2003, the math department began conducting FREE calculator workshops on the campuses of Seminole Community College.  It was my privilege to conduct the Hunt Club sessions on the first Friday of each semester.  In this workshop and in my classes, I now have a new 12-page user-friendly handout for the TI85/86 that seems really effective to replace the old handout that I have used for the past 8 years.  Students seem to like the idea of the workshops, and they respond with attendance and enthusiasm about learning to use this somewhat intimidating calculator.  They REALLY like the handout!  They actually read it!  

MGF 1050 Math Thinking Skills

In 1991, I wrote a proposal to introduce a new 1-hour course MGF 1050 Math Thinking Skills., a course designed to teach students how to develop study skills, learn test-taking techniques, and overcome the fear of math.  I wrote most of the materials to be used in the course, and I taught the course several times before moving out to the Hunt Club Center.  Several years later, increased enrollment at Hunt Club enabled me to offer the class again, this time using my own book Achieving Success in Math as the text.  Scheduling problems have temporarily discontinued the offering of this course even at Hunt Club.  

Achieving Success in Math

One of my more recent projects was the book Achieving Success in Math (2000), which can be obtained by request from my office, in which I attempted to summarize everything I had learned about students and success in math.  Written in a frequently-asked-questions format, this book summarizes study strategies and helps students locate resources to help them succeed.  Chapters addressing topics of math anxiety, test-taking skills, and sample topics from Basic Algebra are included.  

As I wrote the Achieving Success in Math book, I recalled some of my own students and the trouble they had with math.  So many of these students overcame incredible difficulties and succeeded in math classes.  Student Success Stories, many of them written by the students themselves, are included to give hope and encouragement to other students.  Some of the stories are so good that one of the reviewers of the book did not believe the stories were real.   Nevertheless, to the best of my knowledge all the stories are true.

As I begin each of my classes, I raise the question:  “What would it take to succeed in a math class?”  The first and most important requirement is prerequisite skills.  The algebra courses we teach are in sequence, and a student must have a solid foundation in one level before attempting the next.  Without a solid background in Basic Algebra, a student has little hope to succeed in Intermediate Algebra.  Without a solid background in Intermediate Algebra, a student has little chance to succeed in College Algebra, and without a solid College Algebra, a student has NO chance to succeed in Calculus. 

The second important requirement for student success in math is the instructor of the class.  It is the instructor who sets the agenda for the semester.  It is the instructor who establishes the environment of the classroom, gives the explanation of the necessary math skills, and evaluates the performance of the students.  For over 35 years I have worked to become the best instructor I can be!  My goal is to give the best explanations I can give, to make class worth attending, and to encourage students to do the homework.  Students should enjoy class and succeed, but not at the expense of preparation for the next level.  After completing any math class, students must have the confidence and skills to continue to the next class and succeed there as well.

The third requirement for success in math involves student study skills (see Chapter 3 of Achieving Success in Math). Many students who are not successful in math classes are not successful because they simply do not spend enough time on the homework.  It is a busy life for nearly everyone, but there are strategies, including time management and personal discipline, that enable students to succeed in math class—if they spend enough time on the homework!

Mathematics Learning Center (1986-1991)

In busy times, it is important that students locate resources  (see Chapter 4 of Achieving Success in Math).  Of course, the instructor is probably the most important resource.  Like life-lines on Who Wants to be a Millionaire, learning centers, friends in the class, friends and family members are all important resources to students who need help with math.  In my first years at Seminole State College of Florida, Mrs. Lucy Spencer and I proposed the original “Math Lab.”  We staffed it with our own students whom I remember by name after all these years:  Debbie and Bernard.  In 1986, when Mrs. Spencer retired, I became the coordinator of the Mathematics Learning Center, until 1991, when all the learning centers at Seminole State were consolidated into what was later called The Learning Center (TLC), and now called The Academic Success Center.  During those years, with the help of paraprofessionals, I supervised the tutors, helped with the tutoring (especially in Calculus and Differential Equations), and contributed a lot of  handouts, many of which are still in use today. 

Videotapes

In those last years at the Sanford/Lake Mary Campus before my office was moved to the Hunt Club center in 1994, several videotapes were made of some of the more difficult sections in my classes.  A total of 12 videos were made—they are not fancy, just me teaching my class—but they are still on reserve at the circulation desk of the library and also in the Learning Center at Hunt Club.  Now, after more than 10 years of use by my students, they still find them a helpful resource.

Success Rates

From 1995 to 2003, 322 out of 529 (60.9%) of my students were successful in Basic Algebra (since my NEW Basic Algebra, that rate is 94 out of 135 or 69.6%).  In Intermediate Algebra, 672 out of 1098 (61.2%) were successful, and in College Algebra 706 out of 1030 (68.5%) were successful.   Most importantly, I have observed a phenomenal correlation between homework and success in the class.  Because of the work-text format of the One Step books, I can quickly grade homework during exams, which allows me to know who is doing and who is NOT doing all the homework.  Students who DO the homework have an incredible success rate in the classes! 

Hunt Club’s One Step for SuCCess Scholarship

Since there is no external publisher for the One Step books, the books are printed in the Seminole State Print Shop and sold in the Seminole State Bookstore, without publisher expenses, profits, or royalties.  However, in lieu of royalties, a donation (currently $10) is made to the Seminole State Foundation for each book that is sold in the College Bookstore.  Money generated from the sale of the One Step books together with matching funds from the State of Florida (when available!) is used to fund the One Step for SuCCess Scholarship.  The scholarship, presented each semester to the top student at each level of math, consists of a three-hour (in-state) tuition waiver, a $100 stipend, and a free One Step book for the next level of algebra.  Since the scholarship was first awarded in 1996, we have awarded scholarships to over 130 different students totaling about $50,000 (as of January, 2007).  In addition, eighteen “Continued Excellence Awards” , which is currently a $300 stipend, have been presented to repeat winners, including three “Triple Crown” winners, students who won the award at all three levels.

Webpage

My latest project, now that I have accumulated 36 years of experience and materials, is to make many of these materials, the ones that would be most useful to the most students, available to them via the Internet.  My website, http://www2.seminolestate.edu/rrapalje/, is not fancy yet, but this is a great opportunity to use the technology of the day to improve student success by making materials available to them at little or no cost to me or  the College.

Use of Color in Teaching and Learning Math

The following example, first presented in black and white then secondly, exactly the same explanation is presented in color.  Notice how color-coding can be used to emphasize differences and similarities.   Life and television, for the most part, are full of color.  Why not math? 

                F =First · First;  O =Outer · Outer; I =Inner · Inner;  L =Last · Last

Product of Binomials              “F   OI   L”

                                                  F       O        I        L

Example 1.      (x + 4) (x + 3)     =     x²  +  3x  +  4x  +  12

                                                    =        x²   +   7x   +   12

                                                           F       O        I        L

Example 2.      (x + 6) (x + 4)     =     x²  +  4x  +  6x  +  24

                                                    =        x²   +  10x  +  24

 -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -  -

F =First · First;  O =Outer · Outer; I =Inner · Inner;  L =Last · Last

Product of Binomials             “F   OI   L”

                                                            F       O        I        L

Example 1.      (x + 4) (x + 3)     =     x²  +  3x  +  4x  +  12

                                                    =        x²   +   7x   +   12

                                                             F       O        I        L

Example 2.      (x + 6) (x + 4)     =     x²  +  4x  +  6x  +  24

                                                    =        x²   +  10x  +  24

Looking Ahead

For 36 years—over half of my life—I have been a mathematics professor at Seminole State College of Florida.  My main goal  is and has always been to provide the best possible classroom activities and curriculum materials for my students.  Unfortunately, most of the textbooks from which we teach are not written for the non-traditional students in our classes.  Many of our students enter math classes with weak backgrounds, negative attitudes, low self-esteem, and high anxiety in math. 

Since my first year at Seminole State, I have been writing handouts and books attempting to present math on a level that can be understood by students, especially those who have not previously been successful in math.  My own students are unanimous that the One Step books from which I teach are somehow easier to read and understand and the homework is easier to do than traditional textbooks.  I have found that, when these students are presented with the simplicity of math and helped to overcome the intimidation of it, most of them who do the homework will rise to the occasion, overcome their fears, and succeed after all.  It has been a rewarding career!   Now I am in my last weeks at Seminole State!  Given that so many students still need help with math, what can I do in these last years to maximize my efforts to help students succeed? 

In the future, I hope to expand the use of my One Step books and other materials from my own classroom to the rest of the College and the community.  I propose to convert significant portions of what I have already written to html (for use on computers) and to develop new and improved materials.. These materials will be placed on the Internet on this website to be accessed by anyone who may find them helpful!  

Once materials are available on the Internet, the work could be freely used by math instructors and students, especially those at other community colleges, secondary schools, and even middle schools.  Students and instructors can supplement and enrich their own textbooks by downloading and using free sections of One Step.  Those who try the free samples and like them can purchase the entire book from the College Bookstore for about half the price of a traditional textbook, while generating a $20 donation (including matching funds!!) to the Seminole State Foundation for the One Step for SuCCess Scholarship. 

Endowed Teaching Chair

In the spring of 2003, I was nominated for and awarded an Endowed Teaching Chair.  Now, as I near the end of my career as a full-time instructor at Seminole State College of Florida, I am so grateful to the hundreds of students, faculty, and staff who have allowed me to be a part of their success stories, and to those who so generously have given me so much credit for their success.  I am flattered, almost embarrassed, by the letters I have received from my former students and esteemed colleagues that were submitted in my application for this Endowed Teaching Chair.  My passion at the moment is to finish my last years at Seminole State with a flourish, then to continue my last years after formal retirement helping other teachers develop and improve their teaching skills.  Perhaps I will have the opportunity to continue developing and improving the One Step curriculum, which is still a work in progress.

I have been blessed, and I have really enjoyed my career at Seminole State.  I have loved going to work each day, and I love going home every night.  You can't ask for a better life than that!!