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I am an experienced high school physics and mathematics teacher, retired, with current Massachusetts certification in both areas. I have taught various levels of mathematics--through calculus--as standalone courses and as part of the content of physics courses, so I have a range of pedagogical strategies to employ in these areas. I am very much aware of the challenges many students face in their early encounters with these subjects, and work to build confidence as well as proficiency.
Prior to my teaching career a lifelong interest in--and deep affection for--mathematics and physics led me to wonderful adventures as an aerospace engineer. While a NASA employee on the Apollo Project, I made extensive use of algebra and calculus in the development of orbital rendezvous techniques. Later on I participated in the design of the space shuttle and the development of the first GPS operating software, so I have an informed perspective regarding both teaching and application of the relevant disciplines.
On-line tutoring seems to work well for properly prepared students. "Properly prepared" in this context means that the student is able to use the Google Chrome browser, has downloaded and enabled the latest version of Java, and has audio and visual capability on their computer.
Algebra 1 introduces the concept of symbolic representation of numbers whose value is unspecified, and also the basic notion of relations between sets of numbers specified by a recipe called a "function." Operations upon and between functions provide a basis for discovering important properties of relations, properties of number sets, and methods of representation. The axioms and common understandings of Algebra 1 are common to all other algebras, such as vector algebra, and are therefore the essential foundation for all further study in mathematics.
Algebra 2 skills, including factoring, finding roots, solving sets of equations and classifying functions by their properties, are a necessary foundation for trigonometry, pre-calculus, calculus and linear algebra. Particularly important are operations with exponents and an understanding of the definition and properties of logarithms.
While growing up I was an active amateur astronomer, and I have taught this subject at the introductory level. I have the good fortune to be married to a professional astronomer who occasionally involves me in her work on symbiotic star systems.
Calculus is one of the three legs on which most mathematically-based disciplines rest. The other two are linear algebra and the stochastic systems (statistics), which come together in advanced courses. Everyone intending to pursue studies in basic science (including life sciences), engineering or economics should have a good foundation in introductory calculus.
I did not really begin to appreciate the genius of Isaac Newton until I was asked, as a young NASA employee, to code a computer program to solve orbital rendezvous problems. To this day I am overwhelmed whenever I think of his gifts to us.
Mechanics is the basis of physics, physics is the basis of most fields of application, particularly in engineering. In addition to fundamental concepts, the study of physics develops the ability to think mathematically, and apply mathematical methods to many problems of interest, including outside of physics.
Pre-calculus is the gate-keeper course for transition to calculus, and is therefore as important as calculus itself for those intending or needing to study higher mathematics. Typically it includes a review of basic algebra topics; various types of functions--including trigonometric and polynomial; series; limits; and an introduction to vectors. Most troubles with introductory calculus are traceable to an inadequate mastery of algebra and trigonometry.
As noted above, trigonometry is usually encountered as a part of a pre-calculus course. In my view, much of the traditional material associated with trigonometry should be replaced by an introduction to the linear algebra of vectors, which provides alternative methods of solving many of the problems encountered in trigonometry, and is much more generally useful.
Great tutor! — Clark has really been a fabulous tutor. He inculcates a love of learning and definitely makes the subject very interesting! He is very helpful, patient, and explains concepts in a way that is easy to understand. My son definitely enjoyed Physics and Calculus because of Clark. ...
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