Algebra is more than solving equations, of which there are multiple ways – a fact that is also part of Algebra. Yes, a bunch of topics are thrown together into a course called Algebra. But they are not as unrelated as they might seem to be. Developing problem solving strategies and mathematical ways of thinking are important abilities to acquire, no matter what the course is called. Should Pascal's triangle and Fibonacci numbers be in a course called Algebra? If not, where? Maybe there should be a whole bunch of math mini-courses. But for the time being at least we have these year-long courses – so all the various math topics have to be put in somewhere.
Algebra 2/Trig - I've developed lots of my own material, from a student-centered perspective, to make all of it more meaningful.
Equations, inequalities, functions, quadratic formula, imaginary numbers, logs, and laws of sines and cosines - there are patterns and connections among them, not always shown that can make the material more meaningful, and enhance learning and retention. My own way of representing the quadratic formula can help you get the picture better. And you may be surprised to see how complex numbers relate to what you already know, and pictorial proofs of the Pythagorean Theorem that might even seem fun.
I have taught high school chemistry, through which I stress unifying principles and patterns that apply across the whole study of chemistry – often not brought out in textbooks (which can make chemistry seem like a myriad of isolated facts to be memorized). And with my math background I make easy work of problems involving math, including molarity problems, with my own table setup that guaranties doing correct procedures. And my library science background has helped me locate excellent resources, both in-print and online.
I became a FORTRAN programmer (learned on the job) as a Seismologist, the only programmer in my department. I learned and taught BASIC programming in high school. I took college courses in Assembly Language Programming, Terrapin Logo (with a teaching practicum), and PASCAL. I took a technology course in library school in which I was the only one to develop an efficient alphabetical search algorithm. I investigated object oriented programming OOP like Eiffel on my own, and know quite a bit about how computers developed historically. I am familiar with Windows XP and have recently started using Windows 8. I have used Microsoft Office for years, and have recently started using the 2013 version. I never liked C++, a bad attempt at OOP. I would like to look into OOP further, but it's not my top priority.
After obtaining an MLS degree in library science, I have had several jobs as a school library media specialist in K-6 schools, working with students on research assignments, finding information both in the LMC and online, helping students pursue areas of interests, etc.
I have also been involved with homeschooling groups, attended homeschooling conferences, and written about homeschooling, as well as developing curriculum theory in my writings and speaking at educational conferences.
Geometry, as typically presented in textbooks, has so much to memorize about lines and angles, triangles and other polygons, along with circles and all kinds of angles involved with them.
I can show you how seemingly unrelated concepts are actually connected (getting the big picture) results in more meaningful understanding of what is involved, with a lot less to memorize.
Through working with students, I have developed lots of my own methods and materials, some of which I have written about and spoken about at educational conferences.
My family’s getting a phonograph in my youth started me on an unquenchable journey of discovering a world of music I had never known, that involved weekly trips to the library for recordings - a self-induced crash learning adventure like nothing I have ever experienced. I read a few books during this period, but my main guide was the Schwann catalog - any music that had more than a few recordings had to be discovered. I know the major works of every notable composer. In college I took courses in music appreciation and theory, including Bach chord progressions and sight reading, and have sung in choirs. I have pocket notebooks in which I occasionally write down musical ideas that occur to me. I have also done a study of film music and composers, and have a small library of musical reference works. I am currently writing a literary work to be called "A Musical Journey."
My experiences teaching and tutoring middle school math have given me insights into the difficulties students typically face, and the teaching methods that typically lead to these difficulties. They learn one procedure for one type of problem, that procedure for that type of problem, and on and on. I’ve seen students cross multiply when they’re not sure what to do because it seems to work on some problems. I like to ask students “Do you get the picture of what’s going on?” Math developed as a language because it’s useful, but students sometimes don’t get that sense, the way things like order of operations and scientific notation are taught and tested. I have developed my own material and techniques for dealing with difficulties students typically have, along with using problem solving techniques and a simple concept from science that should be part of all math problem solving.
Pre-Calculus (Post Algebra?)
Looking for an easier more meaningful way to learn this stuff?
The usual stuff in greater depth, plus matrices and more on e, and analytic geometry. Another motley collection of topics gathered into “a course,” where connections and patterns nonetheless abound, waiting to be discovered - and thus more meaningful than memorizing a mass of unrelated facts. Be prepared for some surprises - beyond the standard textbook/teaching way.
I have developed lots of my own material to help students see all this and ease their concerns - some of which I have shared with other teachers.
Logs are often seen as abstract and abstruse, but what are they, really – just exponents. There are connections to past math you may have not been taught.
The “abstract” number e is brought forth “naturally” as the base of the quite abstract “natural” logarithms. But if, in an adventurous spirit, you had gotten into exploring certain patterns with your pocket calculator, you may have stumbled across (or at least started zeroing in on) the number e, and thought of it as quite intriguing, even as early as middle school.
There are intimate connections between complex numbers and trigonometry, not often well brought out in textbooks and teaching, including how doing simple calculations with complex numbers generates trig-function formulas, how you can use complex numbers to generate Pythagorean triples and how to estimate products and quotients of complex numbers, to see if your answers are reasonable (not seen in any textbook I’ve checked).
I have tutored all Regents math, at the Lancaster Youth Center and The Learning Experience in Elma, plus a student at home for Lancaster Schools in Algebra 2 from October to June. I have review books in all Regents math.
I taught Regents Chemistry and have also tutored and subbed in Regents Earth Science. My index to the Regents Earth Science Reference Tables was published in the Science Teachers Bulletin, which, after enhancements and revisions, I have given to dozens of Earth Science teachers. I have also developed lots of my own Earth Science materials, on earthquakes, temperature extremes etc. including online sources. And I have my own reference library on the earth sciences.
I also did Home Instruction with an Alden High School sophomore 2 hours a day 5 days a week from Feb. to June, in all his subjects, which included Regents Biology and Global (Social Studies). I have also done actual teaching as a sub in Chemistry and Physics and the other Regents subject.
I have also studied and spoken on the new Common Core Standards, which is going to affect many of these Regents subjects.
I have an MLS degree in Library and Information Science, specializing in education and doing research, along with several years of teaching. I have also developed curriculum theory and written about self-directed learning and life-long learning, and I have been involved with homeschoolers, attended homeschooling conferences, and had several pieces published in Growing Without Schooling.