Mathography VIII

Another in series. I am loving these this year and the SO illuminate where my students are coming from in terms of math:

Back in the late 1960s I was awarded the math pin for my class at St. Timothy’s elementary school. I was amazed and proud! I didn’t know I was good at math. I still have that pin today and maybe I will wear it to class one night (for extra credit?). Math seemed easy in elementary school and I was happy to excel.

Entering public high school I breezed through Algebra 1. Then came Geometry! I was assigned a young student teacher and for the first time in my life I didn’t get an “A” in math, in fact I got a “C”. I just didn’t get it! My schedule changed the second semester of school and I was reassigned to a “real” teacher. Mr. Grassmeier was such a “real” math teacher that he wore the obligatory black horn-rimmed glasses and a jangling ring of keys from his belt. I was taken. This guy knew what he was talking about. Suddenly I understood geometry and I was back in straight “A” territory. It was the first time I realized that a teacher could make a difference. The next year I enrolled in Algebra 2. The teacher for the class discarded the textbook. He just gave lectures and passed out handout sheets he had created. Without a textbook as a reference I was lost. Within a couple weeks of class I dropped out of high school math forever. My high school math career ended when I was 16 years old. I knew I was a dumb math failure.

Two years later I went off to college. My university was mainly a liberal arts school but I continued to feel frustrated by my math failure. I tried to make up for my deficits. I took a class called “Nature of Mathematics” for liberal arts students. It was okay, but I wanted to be good enough in math to take calculus. I had some making up to do. I was going to Massachusetts to stay with my uncle for the summer and decided to sign up for a math class at Boston College. I wrote to the instructor of the pre-calculus class and gave him my math background. He wrote me back a long handwritten letter explaining the course in very beautiful cursive writing. I signed up. I took the course. It was not easy, but I worked hard and got a straight “A”. I was thrilled. In the fall, I went back to my university and signed up for calculus. I was a junior. The other students were freshman and I was surprised to discover that most had already taken calculus in high school. I studied really hard. My instructor urged me along, because obviously I was in way over my head. I would like to say I excelled but the fact is I got a “C+”. Honestly though if felt like an “A” because that class was hard. That was the end of my university math career as I had to refocus myself on my major (which was history).

After graduation, I worked for a bank and spent a lot of time balancing general ledger accounts, teller draws and cash vaults. I loved the mathematical aspects of the job. But banking really has no soul (absolutely proven in the autumn of 2008) so I decided to become a teacher. I went back to school and got my credential. I have been teaching first grade, kindergarten or a combination of both for the last 15 years.

Primary math seems easy but it really isn’t for kids who have no math background. Really how hard is it to count? For some students it is very hard. Sometimes you do “suggested activities” over and over again. Students always come along who just don’t get it and I am always trying to find a new way. It makes me stop and think all the time. Experience has taught me that no math is easy if you don’t have a good math background or a good teacher. I hope to become a better math teacher through this class. I also hope to one day study a full year of calculus just so I can say I did!

Mathography VII

Another in series from my students. This one in particular fascinated me because this person is an immigrant from the ex-Soviet Union, good but not perfect English, who blew our class away the other night by her proofs for the formula to find area of a triangle. A failure she is not.

I THINK, THEREFORE, I AM ( In Latin, "COGITO, ERGO SUM.") by Rene Descartes.

But what then am I? A thing that thinks. What is that? A thing that doubts, understands, affirms, denies...(Descartes)

Evoking my memories of the early elementary school years, I clearly see myself as a failure. Intimidated to ask questions, ashamed not to understand the material, and being scoffed for getting bad grades are all what I recall in elementary school, until I met one teacher who made a difference in my life. It was a math teacher in the after-school program, who believed in me. I stayed after school as late as possible to get all my questions answered and all material understood. Coming home, I was helped by my father and my neighbor to do some extra work. Later, math became a favorite subject for me. In a high school, I became more confident in expressing myself as an independent thinker: I utilized the deductive and inductive methods of reasoning in solving more complex math problems, logic, and competed with the students in math olympiads.

When I came in the USA, my first goal was learning English. Then I got enrolled in a junior college. I completed all algebra courses. I liked all my teachers, especially Prof. Moss who had an unusual method of teaching: the problems and answers were given to students to solve and learn and the exams were long and challenging. In the San Francisco State University, I completed only geometry in the middle school course,

Working for the elementary school district gives me a lot of experience and ideas of how to teach various subjects. I am planning on volunteering in one of the middle schools to earn 40 hours of experience to get into the single subject credential program. I see myself as a teacher who will accept the idea that there is no student is a failure: all students have potential. I will create group of math scientists who will research on famous mathematicians and their theories. So they will be motivated and inspired to learn, explore,and develop more ideas and theories.

My students will compete with each other to get ready for the challenges awaiting for them. I will promote self-confidence in students, honor their desire and motivation to attain knowledge, and initiate student tutoring program. Learning math will significantly determine their future career and impact their lives.

Mathography V

Another in a series from my university math class.

In my life, childhood memories meld with stories told and retold by my family. Fact and fiction blend together to create the story of my math life. Following are some slices of historical fiction from my memories.

I am six or seven. My father is drilling my older brother with multiplication flashcards at the kitchen table. While my brother is clearly frustrated, unhappy, and slow to recall his facts. I quickly and happily call out the answers from over his shoulder. As an adult I would add “demoralized” to how he must have been feeling. As an adult I also know my brother has a learning disability. As an adult I recognize the differences between how my brother and I learn but the commonality between us that we are each intelligent problem solvers, with different perspectives, strengths, and strategies. P.S. He outscored me on the math SATs.

More slices:

It is my first year at a new school. I am in fourth grade. A parent takes a small group of GATE students into a separate room for challenging math lessons. There are beans on the table and we are learning about powers. One girl just doesn’t get it. She keeps multiplying the base times the exponent. At the time I think she’s not that smart. As an adult I don’t recall if or how we used the beans to better understand the concept. It seems to me we learned a rule and vocabulary for “quick” or “fancy” multiplying. The beans were incidental.

At the end of fifth grade I have a distinct memory of thinking to myself, “I don’t think we learned anything in math this year.” Sixth and seventh grade math didn’t make the memoirs. No memories at all. In Eighth grade my dad attempted to support my learning in several ways. He challenged my teacher because he felt the instruction was not organized. And when I didn’t know how to solve a problem my dad showed me a formal algebra strategy for solving the problem. I had no idea what he was doing and our relationship hurt because of this communication chasm. Amidst my discomfort now with two adult males in my math life, I scored in the top three of my class on a high school math competition.

External praise continued to be a part of my math life. Therefore, as long as I understood what to do and did it correctly, I felt externally satisfied. I had no clue as to what connections we left unexplored and I had no intrinsic desire to seek them out. So as I continued on the Algebra I to Calculus path, my father’s repetitive question in response to my pleas for quick math help, “Do you understand why that works?” only irritated me and widened the chasm. I heard the question as an opportunity for him to explain something to me in his words which I expected not to understand and decided not to care about. Besides, I had no time for understanding.

The irony here is that I now work with teachers and students to embed that same question my dad asked me into everyday teaching and learning. I work to build a learning community where teachers and learners alike ask such as questions as, “Will that always work? How do you know? What’s going on in this problem? Is there another way to solve it?” This is no accident. The artistry of helping seventh grade students to understand integer operations first opened my eyes to the creative world hidden behind the wall of rules and procedures. Ample professional development and learning beside my colleagues continues to challenge my perceptions of understanding mathematics. Though I describe my math life as having fallen into math instruction from a path of environmental education and social justice, I truly believe I landed solidly with a sound purpose. My math life is about the social justice of providing quality, equitable, applicable math education for all students, not just a select few

Mathography IV

Another stellar mathography to consider. This year's crop of math writers seem to tilt towards the positive more.

I have friends who are majoring in the sciences: engineering, astronomy, physics, etc. Soon, their study of math will help them build bridges, predict the next solar eclipse, and show how big of an impact certain cars have in a car crash. As for me, I only care about the San Francisco Giants’ baseball statistics and buying things for the cheapest price. No matter what it takes, I will find the best offer for CDs, even if I have to wait months. My mom always taught me at an early age whenever we went grocery shopping that I can always find a better deal somewhere else. Of course, she’s the type of woman who would probably drive two miles to buy gasoline to save three cents per gallon. I don’t take it that far because that would be counterproductive. I aspire to be a math teacher between grades 5-12. Why do I care about rocket science or building nuclear bombs? All I need to know are the practical things in life: buying cheaper groceries, finding a reasonable place to live, and the on-base percentage (OBP) of my favorite baseball players.

I was always good at math, scary good even. I struggled in reading comprehension, so there would be a huge comparison in my other subjects with math. In my report cards, literature, language arts, social studies, and science would range between a C and a B-minus. Math, however, would usually fall between a 94% and a 98%. Maybe it was my mother who emphasized that a lot of life’s everyday situations involve math. She still wanted me to read better, but she was right. There was more use of math in everyday life, as opposed to explaining the significance of the grayness in The Great Gatsby. Besides, my math teachers seemed more passionate about math than the literature teachers. In fact, I never learned how to fully comprehend literature until 11th grade, and I didn’t start writing stronger essays until I started college. Math just seemed more useful for me at the time.

Sometimes, though, I did struggle, and I let my emotions get the best of me. I had struggled with geometry in seventh grade. To me, it just felt like the rules were being made up on the spot. It didn’t make sense to me that some formula could tell me how many vertices could be on a specific polygon, instead of just counting. Even if it was a 200-sides polygon, I was hell-bent on imagining it in my head and counting the vertices. Also, in eighth grade Algebra 1, I struggled in the later stages of solving for x. In particular, I hated factoring quadratics. My math teacher didn’t offer me any specific ways of how to factor better other than “Practice, practice, practice.” Laziness has always been my forte, so I hated hearing that. It took me until ninth grade to finally understand Algebra 1, and I regained my expertise in math. The differences between my middle school teachers and my high school teachers were very noticeable. My high school teachers taught in a way of my liking. They offered me clear step-by-step instructions on how algebra is in all mathematics. In high school math classes, I still had my struggles, but I pulled through with hard work. Recently, I struggled in Calculus 1 because I could not understand the professor’s accent, but I tried again with another SFSU professor. I passed with an A. Currently, I am taking Calculus 2, and I am pushing through my struggles.

I am interested in teaching math because it’s my best subject, as a student and as a tutor. I have seen the struggles and the victories in my life with math. I can apply the strategies my high school teachers taught me with the grading style of my college professors. My college professors use positive reinforcement in their grading due to the addition online homework assignments. These online homework assignments allow for multiple attempts at a single problem with step-by-step examples on how to do a similar problem. I believe that if students become positively reinforced that it encourages them to study harder in the subject in general. My own personal style also involves the use of different colors to differentiate the original problem, the work to solve the problem, and the answer to the problem. When students are copying notes, they don’t always comprehend what they see. I want to guide students through the steps without and maybe even keep the classroom entertaining and positively reinforcing.

Mathography III

Third in a series of mathographies from my students:

I don't remember school nearly as well as most people seem to. I suppose I was too absorbed by my own insecurities and all of the horrors that come with wearing glasses and braces and having frizzy hair. I really didn't place academics near the top of my priority list, and therefore, I don't have many academic memories.

My first memorable math-related experience happened in 9th grade. I was taking Algebra II that year, and I was all set to be in the class of one of the best teachers in the school. Unfortunately, she greeted us only to let us know that she would be taking maternity leave that year, and that we would have a replacement. Our replacement teacher, Mr. Triolo, was dorky, boring, and lacked confidence. This seemed to me, to be an invitation to misbehave and shirk my responsibilities. I did not have enough maturity to realize that I was causing the problem, as my grade slipped further and further. I ended up failing the class and going to summer school to make up the credit.

In 11th grade, Mr. Stackhouse became my favorite teacher of all time. He taught me Algebra III/ Trigonometry and inspired me to teach. I still haven't gone back to tell him what an inspiration he was, but I really should. That summer, I decided to get very serious about academics and getting into college for studies in the hard sciences. Therefore, I went to a summer program for high school students held at a polytechnic college called Renssalear Polytechnic Institute. I took Calculus that summer even though I hadn't taken Pre-Calculus. I struggled, but I believe that it strengthened my transcript. I then took Calculus in my senior year of high school.

I went on to major in Aerospace Engineering at the University of Maryland, where I needed to be able to use my math training in almost all of my classes without prompting. Therefore, my foundation was often tested, and I learned to love to reach into my "tool bag" for the most appropriate problem solving tool.

While I loved pursuing my degree, and found it so interesting, I didn't really think I would love the realities of working as an engineer. Therefore, I turned to teaching, since I had been attracted to this profession since childhood. For the last 6 years, I have been teaching Pre-Calculus and Calculus. I try to continue learning every day and to help my students enjoy grappling with problem solving as much as I do.

Mathography II

2nd in a Series of Mathographies from my students:

As far back as I can remember my family supported my learning and helped me, if they could, with my homework. Since neither of my parents graduated high school, the help that I received stopped at about 6th grade. In my day, high school mathematics consisted of 9th grade algebra I, 10th grade geometry, and 11th grade algebra II, and senior year studying trigonometry. My parents valued the study of math, even when they could not participate in my learning. I remember liking algebra I, and finding algebra II more challenging. As for geometry, I got very lost in the first and second semester, even though I would go for extra help after school, I just was not getting it. Then, a student teacher took over for the 3rd semester, and began by teaching a review of the course. Eureka! I went on to excel and discovered a love of geometry.

My elementary math consisted of rote memorization followed by drill work. I still remember the smell of the blue mimeograph ink and the handwritten teacher driven test problems. I do not remember the use of manipulatives or books about math. In 1960 when I was in 7th grade the new mathematical pedagogy emerged, referred to as “New Math.” I remember learning a new way of looking at numbers. I learned that in different base systems that the actual number of objects did not change, but the numeral describing that number changed depending on the base system. For example, the objects “NNNNNNNNNNNN” is numerically written as 40 in base three, 30 in base four, 22 in base five, and 12 in base ten. I remember adding, subtracting and converting various base systems. I can only imagine the professional development days that preceded this innovative way of teaching math, especially for those elderly, and extremely gifted, teachers at Girl’s Latin School in Boston.

The first time I studied the use of manipulatives and other ways to approach teaching and learning of math was in my math multiple subject credential program. It is here that I first learned the lattice form of multiplication, worked hands on in math, and listen to the story books such as Grandfather Tang’s Story, Anno's Mysterious Multiplying Jar, and How much is a Million? For me, this approach to learning math made good sense and was fun.

We live in a world where advanced math skills are essential for the technological fields, and just to name a few, include biomedical engineering, computer electronics, mechanical engineering, civil and structural engineering, nuclear medicine, petroleum technology and mining technology. I am a 3rd grade teacher and need to know and use the best practices in teaching math, that I may prepare my students for their future. I use hands on learning, class discussion, and journal writing in my classroom. I am hoping to improve my skills so my students may benefit.