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Spring 2010 Page — Doug's Courses

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doug w/recorder @ family reunion, sep. 2009

    Main Themes for the Spring 2010 Semester

As you can see from the panel of courses at the far left, I am teaching 2 classes this Spring Semester — Calculus III (MAC 2313-81437) and Trigonometry (MAC 2114-75021).

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Calc III takes the study of motion and area from the realm of two dimensions to the realm of three (and even more) dimensions. It also generalizes the concept of motion to distinguish between rigid motion and the more general concept of flow and it generalizes the concept of plane area to that of surface area.

Calc III also generalizes the concept of number to that of vector, and then proceeds to develop the arithmetic, algebra and Calculus of vectors. These become the tools with which we are able to more successfully investigate the generalizations enumerated above.

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Trig has two aspects or foundations or bases — triangles and functions. All results from trig can be traced back to one or both of these two foundations. From triangles we have the concept of similar triangles and the Pythagorean theorem. From the theory of functions we have the concept of periodic functions and the relationship s = rθ.

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Teaching is a tricky business, because learning is automatic!  Whoa!  What do I mean by that? We (the universal "we" — human beings) are always learning - - - something.  Why do I say this? Because I believe there is a feedback-loop in our senses.

What is this feedback-loop? Example: You put your hand on the hot burner of a stove. You get burned. You don't do that again!

The problem in teaching is that we, the teachers, have no way of knowing the content of that feed-back loop in each individual student. Prime example: I want to teach you "two plus two is four." But I yell it very harshly (perhaps because I'm having a bad day, perhaps because the whole class is chattering and I am trying to talk above them, perhaps because I'm just mean — there are a multitude of different reasons). In one kid the feedback-loop goes "Wow! OK. 2+2=4. Neat!" In another kid the feedback-loop goes "Oh-no, he yelled at me. But what did he say? I'm confused. My feelings are hurt. I hate math, and I'm no good at it!"

I'm not judging either student. The first may well be a hard-headed bozo, like I was as a kid, and the second may be a highly creative, sensitive genius-IQ type. Point is: they react differently, and I have no way of knowing exactly what the reaction will be. And they both learned something, although the second student is not learning what I was trying to teach.

By the way. I promise that I will never yell at you (as an individual). I well may raise my voice to the entire class if and when you all start chattering when I'm trying to teach. But I won't yell at YOU; I won't try to embarass you; I won't try to put you down.

So the teachers' problem is to try to teach in such a way that you learn what we are trying to teach — not something else.

You can actually help me in the process of teaching you. How? You can interact with me. You can ask questions. You can summerize in your own words what I just taught you. Remember, it's not just "you." It's not just "me." It's "we."

But above and beyond the actual subject material of these courses and the teaching thereof, I want to talk to you about a "tent," so to speak, under which this whole thing called education takes place. This tent is held up by a common framework of ideas which, if properly investigated and developed, will help you not only tie together and make sense of the subject material within your particular course, but also provide you with a repertoire of general methods of learning and understanding which will be of life-long benefit to you in all your intellectual pursuits.

So, in addition to the actual subject matter covered in your course, I would like you to keep always in mind the following considerations:

  • Your learning style
    • What IS my LEARNING STYLE?
    • Is this material being presented to me in "my" strongest learning style?
    • After the class is over, after the lecture is over, what do I have to do to really learn the stuff we covered in class? That is, in more highbrow language, in what manner will I need to further study and review this material in order to gain an adequate understanding of it?
    • How do I make the information "stick" in my mind, so that I don't forget it?
  • The intellectual relationship between Teacher and Learner.
    • Consider the paradigm of the "Big T, Little l" transitioning into the "Little t, big L" —   where
      • T and t stand for the teacher's playing either a greater or lesser role in your education (I am the teacher), and
      • L and l stand for the learner's (that's you) playing a greater or lesser role in your education.
    • At any stage of your education, there is always the question to be asked and answered — "Which of us is the lead-agent in your education?"
    • We all start at the   (T,l) level (Big T, little l) with the teacher providing most of the "driving force" in your education,
    • and we should progress to the (t,L) level (Little t, big L) with you, the student-learner, providing most of the "driving force" attendant to your education.
    • The question you must constantly ask is "Where am I now on the road from  (T,l)  to  (t,L)?
  • The notion of critical thinking
    • Who is telling me this?
    • What is she or he trying to "sell" me?
    • Should I simply accept what's being said?
    • Are we examining all the possibilities?
    • What other data or facts are relevant to decision-making with respect to this issue?
    • Is the reasoning involved in this issue sound?
    • Are the supposed "facts" in this discussion true?
    • And, even if I accept the argument, is there a better way to state it?
  • On what level of thought is my current thinking taking place, vis-a-vis Bloom's Taxonomy?
    • Just as there are many levels on the learning path discussed above, there are many levels on the thinking path or understanding path, as it might be called.
    • These levels are described in BLOOM'S TAXONOMY. I invite you to click on this link, visit the site and study the "triangle."
  • Your Academic Success
    • It is a prime mission  of the College that each student reach her or his academic potential.
    • It is also a major concern of mine that each one of you succeed in your college/university experience. I'll work hard to help you achieve the knowledge and judgement necessary for a successful educational experience.
    • But you must work at this goal, too. In fact, it seems reasonable to suggest that you must work harder than me to achieve your goals.
    • To help you devise a plan for success, the College has published the document, My Success. I strongly suggest that you read and study it.


Class Times and Places  —  Where to Find Me.
Ref # Course or Office Time Days Room
81437 CALC III / MAC23139:05-9:55MTWR (F)SM133 (AC112)
 OFFICE 10:00-11:00MWSM 247
75021TRIG / MAC211410:05-11:20TRSM130
 OFFICE 11:30-12:30TRSM 247
 OFFICE Or By Appointment SM 247


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