Another posting of something I wrote over the summer while starting my teacher education program.
A Brief History of My Experiences Learning Math
Math has never been a favorite subject of mine and I have never been the insightful mathematician; I struggle even today with challenging, abstract math problems. I excel at math problems that require use of traditional problem solving methodologies though. My passion is to help those who might shy away from math, or feel like I used to about math, so they can build confidence in their own mathematical capabilities, at some level. Ideally they will far exceed the minimum necessary to pass the UC “A through G” requirements; however, even for those who may not succeed passing those requirements, for whatever reason, I hope to enable them to increase their self-image concerning their math skills and when ready, confidently tackle problems of a mathematical nature they may face in their lives.
For me personally, math was mostly a necessary evil required for graduation and a pre-requisite to college coursework; it provided a toolbox for problem solving in many areas, however, I viewed it as providing the equivalent of a hammer, screwdriver, wrench, or other for the job at hand. It is not until recently, that I have allowed myself to consider the softer side of math – math as art or even method of philosophical exploration. I am currently watching the DVD course, “Zero to Infinity: A History of Numbers,” by Prof. Edward Burger; I find it very interesting and it is helping me to see another side of math.
My first recollection of math takes me back to second grade in Rhode Island in 1972. Apparently, completing workbooks with various colored pictures of blocks, coins, and other objects had already taken root in our educational system. I do not recall any specifics about that modality of learning, however.
My first detailed math memory takes me to 1976 in a combined 4th, 5th and 6th grade classroom where I was a newly arrived sixth grader. I clearly remember using self-paced learning in southern Virginia. A series of booklets for both math and grammar instruction were arranged in a cardboard container on a desk which was slotted to hold and show the booklets. Students started out at an assigned level, I presume as a result of a pre-assessment, and progressed from unit to unit as guided by the booklet. Upon completion of a particular concept / unit, a test was administered and if you passed it, you moved on to the next level and so on until completion of all math concepts; if not, you repeated the self-guided unit until mastery was demonstrated.
I must have done well since I was selected to take Algebra I the following year as part of a gifted and talented program offered at Crestwood Junior High School; I was bussed to Crestwood, along with hundreds of other students throughout the city as part of the school desegregation efforts of the time. I remember my seventh grade class well: the room, desks, layout, location and teacher (Mr. Shucker). Direct instruction using an overhead projector and chalkboard was the primary means of instruction. I do not recall any group work or projects; they may have been utilized though.
I fared OK in Algebra I, although I remember struggling at times with some of what seemed like very abstract concepts at the time while simultaneously tripping up on elementary number operations. Looking back, I believe the self-paced instruction in elementary school was not a sound method of instruction. Students may have advanced quickly, with little imposition on the teachers who handled a varied level of student understanding and maturity across three grades, however retention and recall faded quickly, at least for me. I suspect that the instruction modality apparently was limited in integrating prior concepts or retesting for retention at various checkpoints in the program. Nonetheless, I advanced to Algebra II the following year, 8th grade, at the same school, in the same classroom, with the same instructor. My recollections of that year are no different than for 7th grade.
The following year, 9th grade, initially at the same school, in the same classroom, with the same instructor, again, was very different. There were only four students in our Geometry class. All of whom were students bussed to school whereas for the prior two years, there was a mixture of local and bussed students. Most of the local students struggled with poverty, crime, broken homes and their associated impacts on learning while more than a few young girls attended school pregnant. Why no others advanced to geometry was not apparent. I do not recall any discussion of why amongst the five of us starting the year: four students and Mr. Shucker although I do recall feeling very special for having such an intimate class. We put our four desks in a semi-circle at the front of the classroom in front of the teacherʼs desk. Instruction included much deeper dialog about math, and I recall struggling occasionally with the concept of proofs.
About halfway through the first semester, we moved to a rental house requiring us to enroll in a new school. Brandon Junior High School was newly built with state-of-the-art facilities, new textbooks (which we had to purchase at around $150-$200 total which was a significant sum for my parents in 1979) and a different socioeconomic profile than Crestwood. My geometry class was filled with other students and it followed a classic direct instruction pedagogy with periodic dialog by the teacher to ensure understanding. I excelled at geometry, and all of my classes that year, which were considered to be part of a gifted and talented track at the time. While I do not recall anything other than direct instruction for geometry, I do recall other classes employing extensive use of group work, projects and reports.
Before the beginning of the next school year, my family moved once again. This time to Maryland, and initially in a poorer town called Glen Burnie in between Baltimore and Annapolis; my friends and I jokingly called the town “Glen Burnout” since drugs were very prevalent. One month into the school year, we abruptly moved out of our rental house neighborhood under police escort after the tires on our cars were slashed, “Move Away” scratched into the carsʼ paint and a BB gun shot into our kitchen window while my mother was holding my four-month old youngest brother.
Fortunately, my father found a place for us in military housing on Ft. Meade where I attended high school. I took trigonometry and analytic geometry as a sophomore; classes that were filled mostly with seniors and some juniors. My teacher, Ms. Klaas, was an excellent instructor, however, she only used the chalk board, which worked fine for me, but my older classmates rebelled tossing bottle caps and other items at her back when she was at the board. I absorbed everything I heard that year and enjoyed the visual, graphical aspects of both subjects. I received straight Aʼs in every class in every grading period that year. In fact, Ms. Klaas suggested I attend a mathematics summer program at the University of Oklahoma to enhance my math understanding, however, my family could not afford the $300 or so fee for the cost of transportation, which was no problem.
As a junior, I started out taking a calculus class, however, I could not wrap my head around limits and derivatives and dropped the class a month or so into the year. I did not take another math class the rest of my time in high school since I had already satisfied the mathematics requirements for graduation.
The nearly two-year gap in mathematics coursework did not prepare me well for college. I ended up failing an entry diagnostic test, partially due to the lengthy period since I last took a math class, and partly being exhausted from the physical and psychological rigors of “Beast Barracks” – a two month program intended to break down and build back up freshly graduated high school seniors into a uniform cadre of cadets at the US Military Academy (“USMA”). While failing the diagnostic test placed me in a remedial mathematics class my first semester, it was a blessing in disguise. It helped fill in the early holes in my understanding of mathematics from my elementary school self-guided instruction; that semester, I ended up the highest ranked cadet in the highest ranked section (known as section “01”) in the several sections of the remedial class.
From a pedagogical standpoint, West Point uses the Thayer method of instruction, first used by Sylvanus Thayer, the founder of USMA, in 1817 (see http://findarticles.com/p/articles/mi_qa3997/is_200203/ai_n9063661/ for an excellent description of the Thayer method at West Point, which is still in use today). His method incorporates varied instructional techniques to include limited direct instruction, student group work, projects, student led instruction and most curious to civilian students, incorporated military commands within the class period ranging from “Class Attention!” to “Take Seats!” to “Take Boards!” to “Dismissed!” as well as periodic ranking of cadets within a course resulting in moving to different sections depending upon whether you were improving or worsening in understanding.
“Taking boards” was an experience in itself: cadets had to use a yardstick to mark off equal sections on the chalk boards surrounding the class on all walls upon which we wrote out our solutions to problems for that day, pop-quizzes and homework. A very specific nomenclature and methodology existed for use while at boards to include use of multiple colors of chalk, double underlines with ANS marked next to your answer, precise and accurate figures, all while standing at attention using a pointer to explain your answer to the class. Similar techniques were required on homework and on tests, formally known as WPRs (Written Partial Reviews); written and oral exams were known as WOPRs (pronounced “Whoppers” and meaning Written and Oral Partial Reviews.)
My knowledge, insight, appreciation and respect for mathematics took root at West Point and grew increasingly through the remainder of my college days: both undergrad and grad. My undergraduate degree was in electrical engineering, which in my opinion is essentially an applied mathematics degree focused on a variety of specific applications of advanced math such as Fourier- and LaPlace transforms, linear algebra, and many other engineering equations requiring extensive use of calculus, trigonometry and probability. My graduate degree, an MBA in finance and marketing, used math for portfolio analysis, forecasting, marketing research, Monte Carlo simulations and many other applications in business.
My experiences struggling with math, overcoming it, successfully applying it in various technical and business fields and now, as a teacher candidate, looking at it as an art, in addition to my experience to date of math as a science (or a set of tools for use in solving problems), provide me with a range of knowledge, applications and techniques to help the most challenged in math to the most gifted. I am excited to learn more about math curriculum and instruction, as well as other content [in my teacher education program], so I can start out as a math teacher for all students: rich or poor, self-confident or self-conscious, struggling or excelling, excited or bored, math hater or -lover, English conversant or not.