Showing posts with label algebra. Show all posts
Showing posts with label algebra. Show all posts

Wednesday, February 10, 2021

Sub Vision: Mathematics Again




After many months of staying home, enjoying a flexible time and trying to fill this period with different activities, I find myself drawn toward math again. My first project, creating a program for learning and teaching algebra, is done, waiting for me to decide if I want to advertise or publish it, and now I am debating what will be my next project. Remarkably, mathematics still appeals to me...                      

I am looking at my college ‘intermediate algebra’ book, the equivalent of high school algebra II, and thinking I should keep on developing algebra, continue to trigonometry and maybe even get to calculus. Crazy… I know…

Maybe it is just that I am a frustrated math teacher, who was never able to use her full potential as a teacher. I am not as good with math as I am good in explaining math; maybe because I understand what other people don’t understand.

My, relatively, short teaching career is a sequence of unsuccessful experiences with unmotivated, unwilling and undisciplined students. The whole literature of how to become a good teacher, acquired during my teaching credentials program, proved to be completely useless, and rather aggravating. The philosophy that throws all responsibility on teachers, and the system that allows students not to do their work, or pay attention or even just be quiet, system that does not require students to be responsible for their materials, or even bear the consequences of having no skills by 12th grade, make it impossible for teachers to do their job.

My only satisfying school job was teaching a Pre-Calculus class. It was my hardest assignment, as I was not familiar with the material, challenged to the top of my knowledge, but it was also my finest. Students did want to learn. They knew they needed to put an effort to get where they wanted to be; they did their work, came up with good questions, and kept asking until they understood. And when they did, there was a sparkle in their eyes, and they did appreciate it.

Looking back, perhaps I should have invested more effort in becoming an advanced level math teacher, working with motivated students, bringing the light to their eyes. As it is now, I can expand my knowledge and understanding, taking advantage of the time I have, and hope to be able to use it sometime in the future...

                                          

Friday, January 8, 2021

Sub Vision: Graduation 2020

 


It had been a rough year of pandemic and political turmoil... a year that I would have liked to be in a classroom, serving as the educator I wanted to be…

Through the first semester of the 2019-20 school year, before the pandemic had started, I knew that soon I will have to choose my approach to work. It was good to have preferred schools, and be their preferred substitute, yet I wished to be able to select only assignments that I desire and not compromise with schools’ terms.

I realized that while deciding on a new path, retirement seem a reasonable option; quitting and waiting out the cooling period of six months, and then returning to jobs that I prefer to do. But the routine kept me going…

It all came to a halt when we were hit by the pandemic, and with almost no warning schools have closed their doors. As we thought it was temporary and will be over soon, we waited for few weeks, then few months, but as graduation came closer we realized that this is the way 2019-20 school year will be manifested.

It was exciting, yet heart breaking, to see graduation turn into a parade of cars, and diplomas handed through a window. I can imagine seniors’ disappointment staying home instead of becoming kings and queens of the campus, enjoying special activities, festivities, recognition. Exceptional and memorable graduation as it was, never has been like that, never (hopefully) will be, it was an agonizing letdown.  

As summer was drawing to an end and virtual learning seemed to be the only way, I decided the time is right to quit and wait for a better time to be a teacher, or a sub.

I still love teaching math, and still wish one day to be able to show the light to those confused math learners, who say they’ll never understand the subject.

During the long months of staying home I developed a plan for teaching algebra in a logical, commonsense method, with the expectation of using it one day through the right channel, private of established.

I do hope to get back to a school, even only as a volunteer, to do just that …

  

Thursday, January 29, 2015

Ch 16 of 20: Language Deficiency


Another learning inhibitor that is part of classroom reality, and is originated in student’s background, is language deficiency.

In many parts of the state, and the country, (including the school district where I work) deficiency in the language is a key problem. A large group of students who are defined as English Learners is only part of the problem. A source of a bigger crisis is a population who communicates in English but doesn't master the language beyond its everyday conversation’s vocabulary. The trouble is not even mastering the English language to its deeper layers, but rather mastering any language to a level that connects to abstract nouns and terms. This obstacle is not necessarily rooted in immigration status, but rather in socioeconomic status.

The language deficiency has an absolute effect on learners of literature, social studies and humanities in general. It has no less effect on subjects like science and mathematics. If a student had never heard terms that are used in these subjects he/she will have hard time connecting with them. When words like ‘acceleration’ or ‘friction’, for example – are new to a student, in English or in foreign language, he/she will have hard time creating a mental picture of their meaning, and thus will have difficulties understanding, assimilating and applying the concept.

A subject that all math teachers have trouble teaching is geometry. This field requires language connection to the terms, as well as mental ability to picture it. If ‘diameter’ or ‘perimeter’ is not already part of student’s vocabulary, he/she will have hard time grasping the idea. Skills that are expected from middle, or even elementary school students, are not mastered by so many high schoolers; they struggle with basic computation, but, worse, with their concept. Terms that are meaningless for them are memorized the same way an odd cell’s name in biology is stored; for a short time, to be immediately forgotten after the test.

It is possible, then, that in order to address this problem, a new theory that is now widely used, was conceived. The new idea consists on presenting young students with advanced concept, so that later on, at high school, concepts will be familiar and thus easy to recall and ready to build on and expand with new knowledge.

This theory might have justly earned its merit being well researched and well accepted by educators, but in my experience does not serve its purpose. I feel that instead of advancing knowledge, we limit learning by teaching the same material over and over, skipping other important topics. I notice it when I, periodically, cover social studies classes, but I can, for sure, testify for its harm in math classes.

In mathematics, the progress of the curriculum is almost comic. I had my doubts before, teaching high school students and being dismayed by their poor knowledge of arithmetic, and fractions. But it was not until I taught middle school grades 5th   6th  7th and 8th math, that I realized how poor the program really is. I was obligated to teach exactly the same material, though using different, grade appropriate, books, to each of my four different grade levels… No kitting… I didn't even have to change the titles on the board from one grade class to another...

When students start their “official” algebra course, they had already been exposed to algebra concepts for years. They had seen equations and already know how to plug a value instead of a variable. No wonder, then, that they conclude they know it all, and listening is a waste of time… The problems start when equations get more complicated and they need to learn new, correct, methods to deal with them. Now a strong resistance starts to build: “but we already know it!”, “that’s not the way our teacher had taught us”, “you are just complication things”. Not only that I waste time defending my competence, but students’ adjustment is much harder.

Algebraic equations are only one example. The sad fact is that while teachers at elementary and middle schools are forced by the education planers to teach algebra concepts – they don’t have enough time to focus on what middle school learners must know before advancing to algebra. They don’t have time to strengthen basic arithmetic concepts, and fractions and decimals are completely neglected. I can’t even count the times that I had to explain the difference between 1 over 2 and 2 over 1 to algebra, geometry and even algebra 2 students.

The harm in introducing high school material too early is twofold. Lower grade teachers don’t have time to concentrate on basic math skills to create a sound base. But even worse - early introduction of a concept that is beyond students’ mental readiness can be either too confusing thus creating math-phobia, or can form bad habits that will be hard to change later. High school teachers are juggling their limited time between those two challenges; closing gaps and uprooting bad habits.

The solution for the language disconnect is not to introduce complicated concepts before their time, to students who are not yet ready, but to intensify and enforce language skills in the lower grades, presenting the terms in their everyday usage, as well as investing massive resources in reading comprehension; enriching vocabulary and developing reading skills will prepare students for higher math, not premature algebra.