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- Physics
- Chemistry
Experienced tutor in Physics in Flint, Aaron offers private lessons tailored to your needs.
- Physics
- Chemistry
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About Aaron
As an engineer, my methods focus on the methods and ways of thinking that got me through my classes at Purdue University.
1) HOW to get to the correct answer. Unlike scientists, when engineers make mistakes, people can be injured (physically or financially) or even die. When a scientist makes a mistake, a paper might be retracted, and he or she doesn't get to go to quite as many out-of-town parties.
2) wholistic understanding of the material -- when possible, viewing the same concept from different angles often increases understanding and eliminates many conceptual errors.
3) problem simplification techniques.
4) Use of analogies for concepts that aren't immediately apparent. During my junior and senior years at Purdue, I was a "consultant" in the computer rooms of the Engineering Computer Network ( ecn.purdue.edu) -- a general resource for undergraduates learning how to program computers in various programming languages and for faculty and graduate students who were unfamiliar with Unix, because they had learned computing on other systems. I learned early on that when a student who grew up on a farm in Indiana and (as this was the 1980s) who had only seen computers (very unrealistically) portrayed in movies, that showing the parallel between parts of the computer program that he has to write, and the diesel engine and/or attachments to a tractor were vastly more effective than whatever it was the professor told his class during lecture hours.
4) self-checking -- how can the student figure out if a solution is actually the correct solution or is there a mistake and it needs to be redone (very useful BEFORE turning in your homework or test). A technique called "dimensional analysis" is useful and usable even for 4th-grade story problems.
5) Solving problems: balancing efficiency with mistake prevention -- some things that seem like just more work are well worth the effort. Taking 10 seconds more to due a test problem, on a 20-question test, is well worth it if that extra 10 seconds keeps you from losing 5 points on your test.
6) These techniques are often applicable outside of STEM subjects (Example: Economics. Most undergrad econ problems can be solved with algebra, calculus, and analytic geometry. Solve each problem using algebra, then go back and solve each problem using calculus. If you get different solutions to the same problem, figure out which one has a mistake in it. Or solve again using analytic geometry as a "tie-breaker." This method catches small mistakes, such as arithmetic errors, because the different methods use different steps to come to the same final answer. Unfortunately, this method is more difficult to use, in say, designing transistors and other semiconductor devices).
7) A motto often used in army training after a lecture period for a new task or skill: Crawl - Walk - Run. CRAWL -- work the the task on a problem "lane" slowly, discussing each step before and as it's performed, to get a solid grasp on what's being done at that time. WALK -- proceed through a similar, but different lane, getting verbal cues from the intructor(s). RUN -- proceed through another lane, doing the same task at "full speed." This method identifies misunderstandings, and corrects them early on in the process -- this saves time by reducing or even eliminating time needed to "unlearn" mistaken ways of working the problem.
My academic experience at Purdue was trying to say the least -- because at no time in my life since then have I faced such difficult problems, nor in such tight time constraints. (Example: Write a multi-user, multi-tasking operating system with interprocess communication and simultaneous use by multiple users in 4 weeks -- within the constraints of an 8-bit microprocessor and only 0.06 MB of memory. This was only 4 weeks out of a 13-week, 1-credit-hour course.).
By comparison with Purdue, when I later enlisted in the army, basic training was like a vacation (other than drill sergeants yelling, it was a lot of fun, and I got MUCH more sleep!), and even my multiple tours in war zones were never as difficult as the academic load that Purdue's engineering schools put on students.
P.S. If you're a chemistry student at OCC, my professor, Dr. George Bodner, wrote your textbook.
Science and Engineering are tools to solve real-life problems.
Mathematics is a tool used to solve Science, Engineering and Technology problems.
Everything I work on involves solving somebody's problems. Teaching people how to solve problems is like sharing an important secret.
To
Purdue University, School of Interdisciplinary Engineering.
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1: LISTEN to the student. What brings the student to me?
2: If possible and applicable, determine instructor's emphasis, usually by reviewing such things as class notes, assigned homework, etc.
3: Generally, what class of problems, terminology, or procedures is the student having difficulty with?
4: Backtrack to where the students level of understanding is solid, and work from that point as a foundation to build up the student's knowledge and understanding to meet current class requirements.
5: Use simple, easy to comprehend, cases to show next level concepts. Then show how the same technique/concept works with more complicated cases.
6: Eliminate needlessly complicated or hard-to-remember "special cases" which are merely peculiar forms of a more general rule. (Example, the error-prone "division rule" in derivative calculus can safely be ignored by using a much simpler algebraic manipulation of the equation and then using the easier-to-remember "multiplication rule" and "exponent rule")
7: Use of rote memory drills when appropriate. It's boring, but vastly improves speed in test-taking situations. [Example: Knowing the "addition table" is much faster than counting on your fingers.]
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