I have been teaching a couple of courses-College Algebra and a math content course for future elementary and special ed teachers-consistently for the past couple of years. In that time, they have become highly polished and elaborate structures. I know the strengths and weaknesses of my incoming students, I know which ideas they’ll struggle with, which they’ll find interesting, etc. To be sure, I learn something new each semester and I never quite meet all my goals as a teacher of theses courses, but I know a tremendous amount about them.
Calculus 2 is a different animal.
NOTE: The following paragraph contains short summaries of brief conversations that have recently taken place. They are offered as examples of student questions that would not have occurred to me, and from which I have learned a great deal. They are NOT offered as complaints about students, nor as wishes that they had never taken place. Identities have been concealed intentionally.
This is the opening of the third week of Calculus 2 and I have had individual conversations with
- A student who swears he never saw a formula for finding an antiderivative of a polynomial in Calc 1,
- A student who asked in all honesty how I knew to use the Pythagorean Theorem in a problem involving volumes of spheres, and
- A student who took umbrage with a quiz question on volume of a cone because I had never worked a problem about cones in class (until after the quiz, when an example involved the work required to empty a conical tank of water).
Each of these conversations was a surprise to me because I am new to the course.
So I have been thinking a lot about relationships between students, content, textbooks and teachers.
And then Apple did what it did recently, inspiring some of the most thoughtful folks I read to discuss. Lots of fussing about Open Educational Resources (OER), iOS, proprietary blah blah blah. All of which I get.
And then Audrey Watters of Hack Education (and many other venues) wrote this lovely summary paragraph of what, exactly, needs disrupting in education:
One of the things that digital content makes obvious is that the current physical manifestation of a print-bound textbook is a strangely awful construct — one designed to remove students one step (at least one step) from the primary sources that inform the field they’re studying. You don’t read Darwin; you read “Introduction to Biology.” You don’t read de Tocqueville; you read “American History I.” Sure, textbooks offer easier-to-digest summaries of the content, geared to the particular grade level of the student. They offer diagrams and illustrations and review questions and a glossary. But textbooks are always an assembly from a variety of sources, geared towards a classroom setting where the teacher leads students through the chapters and the exercises and the examinations. Neither the teacher nor the student is expected to be an expert. You just need to know enough to pass the test.
Yeah. That’s a problem all right. Text materials are not going to solve that problem. Only careful, thoughtful instruction and human relationships will. One student, one teacher and one classroom at a time.