September 25, 2012
May 6, 2009
Today some homeschoolers had their weekly algebra class. They are coming along well, and getting a good grasp of the subject. After class and after I got home, I sent them their assignments for the week. In today’s email, however, I decided to add some detail as to what we covered in class — sometimes I’ll write up a summary like this, sometimes I won’t. So sometimes parents get a good, detailed, written report of what a class or a student in private tutoring covered.
But this email sketches out what typically happens in my classes and private tutoring sessions, so I decided to post it. (But in this post I added a few things to the email to illustrate more of what we had actually done in class, instead of reporting only some of the highlights.)
Today we started class by looking at one reason why we need to learn to graph linear inequalities (which topic we covered last week): so we can graph, evaluate, and criticize the graphs we use and find in statistics. Graphs of inequalities play an important role in statistics. Then we worked an inequality together: p. 434 #22.
Then instead of doing more inequalities, we started working on graphing linear systems, to make sure we’d have time to cover that topic first. We started out with some motivation: knowing how to find points of intersection is a critical part of understanding how some people navigate, or locate a position on the earth’s surface, using LORAN. LORAN works by finding the intersection of two hyperbolas, as we saw in class. We are not yet ready for working with hyperbolas or systems of hyperbolas, of course; we need to work with lines first. We will build up to hyperbolas one step at a time. (In looking at the LORAN example, we were able to introduce some classic properties of hyperbolas, ellipses, and circles, so we had an idea how a hyperbola was generated and how it was different from other conic sections. And we were able to see how LORAN depends on the basic idea D = RT.)
May 5, 2009
“I have sworn upon the altar of God, eternal hostility against every form of tyranny over the mind of man.” –Thomas Jefferson (From a letter to Dr. Benjamin Rush of September 23, 1800. ME 10:173; see the quotations page of the University of Virginia Library.)
But I’d make the caveat that whether the irrationalists are of the kind he identifies, or are of the kind we find in the Middle Ages (some of which type are still around today), they are enemies of reason and to be opposed. The Scholastics, for example, were “followers” of Aristotle, but they did not even get the essence of Aristotle: follow reason and the evidence of the senses. A Scholastic was anti-Aristotle and anti-reason to the extent that he/she violated the authority and kingship of reality for the sake of subjugating himself or herself to printed word and authority — and was just as anti-reason as the people Dr. Campbell identified in his article. Irrationalism can come disguised as Christianity just as it can come disguised as Marxism. The Salem witch trials, to take a clear example, were not executed by Marxists.
As Jefferson pointed out, it is every form of tyranny over the mind of man (i.e., reason) that must be opposed.
I just wanted to thank Mr. Campbell as a fellow “fighter” for a rational education and against indoctrinating students or numbing or destroying their minds through years of cognitive neglect or abuse. I work really hard in teaching mathematics to get students to think for themselves, to be independent, to know and live first-hand, to develop the methods of mind that will allow them to achieve their own goals and live their own lives — in short, to train students to reason — so I had to tell Mr. Campbell thanks for being another rational teacher out there (going by only the evidence of his article), and I wanted to let him know there there are more teachers facing the challenges and opposition he is facing while striving to develop the conceptual awareness, the “conceptual eyes,” of students.
I enjoyed your essay “The Classroom Without Reason.” I have seen the same thing, and fight the same fights: against irrationality and for reason.
Thanks for your comments on Becoming a Critically Reflective Teacher by Stephen D. Brookfield, and Courage to Teach: Exploring the Inner Landscape of a Teacher’s Life by Parker J. Palmer. I saw exactly that type of thing and those types of books when I was getting my teacher’s credentials from the University of Houston in the 90s. And in reading what is going on in modern education, I have learned about more of the same — for example, William Ayers’ “social justice.” In getting my credentials, I kept quiet mostly, so I could get my credentials and get out. I was “threatened” in writing once (a professor saying he thought I should not be a teacher, and if I contested the low grade he gave me, he’d grill me and speak against me) and in getting my B.S in Math and B.A. in Philosophy at UT, Austin, I had a few professors threaten to fail me for speaking against them (‘do not oppose me, or you will be failed’).
In some back-and-forth correspondence, a parent of a student I tutor and I segued from paleo nutrition and exercise to independence and to tutoring; we ended up coming up with a (hypothetical, in fun) new business name, and the parent came up with a good explanation of the name and a good slogan to go with it, too! The parent said:
I kind of like that….Lone Wolf Tutoring – Setting the Gold Standard in Education
Meant in an entirely positive, Paleo way. Strong in mind and body, individual, not following the pack, wise, self-sufficient, hunter…… you get the idea. Quite fitting for you, I think.
I like it. There’s a Lone Wolf Productions film company…so why not Lone Wolf Tutoring?
Update (5-7-09, 2:10 PM): I am only being rhetorical. I like the name when looked at as above, when looked at as a dignified appelation, but I don’t think the name would go over and be practical in today’s context, where “lone wolf” is a pejorative.