Main Themes for the Summer 2009 Semester
As you can see from the panel of courses at the far left, I am teaching 2 classes this Summer Semester — Differential Equations and Trig.
Summer Semester C is ten weeks long. By way of comparison, Fall and Spring Semesters are about 14 weeks long, each. And it is difficult to cover the material in either Trig or in Diff EQs within the 14 week span. So, I hope you can appreciate the fact that we are really going to have to work quickly, efficiently and with concentrated effort to meet the requirements of this class in the Summer.
I see that several of you in Trig are students that I've had in Precalc, and I am glad to see you. I also welcome all Trig students who are new to me.
Many of you in Diff EQs are "transient students," and I welcome you wholeheartedly to TCC. Many others of you are "native" TCC students, and I am happy to see you in my class. Some from each of these categories are students who have been in previous classes of mine, e.g. Calc 3, and you, for sure, know that we are going to (a) have a great time, (b) work, work, work, and (c) learn a lot.
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? Because 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.
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"
- 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
- Consider the paradigm of the "Big T, Little l" transitioning into the "Little t, big L" — where
- 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."
Class Times and Places Where to Find Me.
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