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My Philosophy: Math is like baseball - if you master the fundamentals, you can do almost anything. Mastering the fundamentals is not about memorizing rules, but understanding the underlying logic involved. My own memory is terrible and I did very poorly in subjects requiring a good memory - basically all subjects that did not involve math. I did well in math because I was able to remember a core set of postulates, which (thankfully) never changed, and work from there. As a result, in tests I was able to reason out the answers in real time to solve the problems. That skill served me well in 35 years as an electrical engineer in the aerospace industry, because the core skill I needed was not to memorize rules that someone invented to solve textbook problems, but to be able to solve the new problems we encountered in the course of our business. To do that, I had to move beyond the rules of math to the understanding of math. This is what I would endeavor to convey to the students.
My Background: BSEE/MSEE from UCLA with major in electromagnetic theory and minor in numerical analysis. I've spent the past 36 years writing scientific software to calculate antenna radiation patterns, radar scattering patterns and radar images. I've written 4 books on optics and 2 IEEE papers on photonic bandgap structures. I have also passed the CBEST (73 in math), all 3 CSET math tests, and have a current TS/SSBI from DISCO.
I took calculus a little late in life, as a first quarter freshman at UCLA in 1971, and got a B then 2 A's. Later, I took real analysis and also got an A in that, along with many other math classes including linear algebra and matrix inversion techniques, ordinary and partial differential equations, and so on. My entire adult life has been involved in applying calculus concepts to my daily work as a scientific software developer at TRW and Northrop Grumman, in areas ranging from Fourier analysis to orthogonal polynomials to Bloch waves in solids.
I have a BSEE and MSEE from UCLA and my specialty area is in electromagnetic theory and optics. I've written 4 books on EM and optics including, "Introduction to Optics and Optical Imaging," with John Wiley.
I have helped my own child throughout elementary, middle and high school years and I've also helped in the classroom back in the 2nd and 3rd grades. My most memorable experience in this regard was with one little girl who, only in 2nd grade, told me she "was no good in math." I was shocked that at such a young age, this child had already internalized the incredibly limiting belief that she was "no good in math." So I worked with her on one problem, basically just asking very simple questions at every step of the way - questions that were basically impossible to get wrong - and we just took baby steps getting through the problem. At the end of this process, she seemed almost stunned that she got the right answer. I hope that experience helped her to at least question (and maybe even discard) her previous assumption that she was no good in math. I think in the primary grades, if you can do nothing more than just not alienate kids from learning, you've done a good job, and if they're already alienated, to make them at least question their previous beliefs that that they aren't "good" in this or that subject. I think the whole thing is to open up possibilities for them and sometimes just one little success can undermine their limiting belief system and allow them to see that they really can do it and it is not as hard as they had previously believed.
In addition to taking 2 undergrad classes in linear algebra at UCLA, the first being right before the vector calculus sequence and the second being a junior-level class on more advanced topics), I also took a graduate-level seminar on direct and indirect matrix solve/matrix inversion techniques for problems in physics and engineering. Over the past 35 years, I've written numerous inversion routines (solvers) in Fortran, implementing both traditional Gaussian elimination and LU decomposition, as well as utilities to compute the determinant of large matrices.
I've been a VB/VBA programmer since 2000 and have written numerous apps to do: polar plotting, ISAR imaging, near-field imaging as well as to programmatically create, open & fill MS Excel workbooks for data summary & presentation.
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