[Today's post is from Steven Fuchs, with whom I recently corresponded and whose enthusiasm was sufficiently infectious that I pressed him to share it here. --Scott]
One day late last spring, while teaching at St. Thomas High School in Houston, I noticed in a book a figure demonstrating Monge’s Theorem. (Don't look this up … Continue Reading ››All posts by Scott Steketee
What Does Rowing Have to Do with Teaching Mathematics?
Polar Graphing
Using Sketchpad, it is very easy to start from scratch and create a polar graph. Here are the steps to create the graph shown on the right below.
- Choose Graph | Plot New Function.
- Use the Equation menu to choose r = f(θ).
- Type "c" (for "cos"), "2", and "th" (for "theta").
- Click OK.
- If your … Continue Reading ››
Cartesian and Polar Graphs
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Exponential Harmony with Sketchpad
Last week was the fourth session of my spring Advanced Secondary Math Methods class at the University of Pennsylvania. Each year I assign a semester project in which groups of three students use lesson-study techniques—on a small scale—to create, test, refine, teach, evaluate, and document specific shared instructional products, composed of a (possibly multi-day) lesson … Continue Reading ››
ICME: The Nature of Students’ Mathematical Thinking
Like other enthusiasts of mathematics, I’m captivated by the way that mathematical ideas can explain things in the physical world around me, and by the way that I can carry out mathematical thought experiments in my mind and then apply the results to control my external physical environment.
Continue Reading ››ICME: A Sensory-Motor Experience of Korea
I had the immense good fortune this year to attend ICME, the International Congress on Mathematical Education. The Congress is held every year divisible by 4, and this iteration (the twelfth) was held in Seoul, Korea. It is quite something to be at a meeting of nearly 4000 … Continue Reading ››
Sketchpad Activities, Cognitive Demand, and Differentiation
Not long ago, I conducted a Saturday morning PD session for some Texas teachers participating in an NSF research project.
(The research is a controlled study of the relationship between students’ use of Sketchpad and their conjecturing and proving behavior. I hope we’ll have a blog post about this study itself before too long.)
Because of the … Continue Reading ››
Parents, Children, and Functions in Sketchpad
Functions are hard for students.
Students seem to master various families of functions – linear, polynomial, exponential, trigonometric, and so forth. They can graph them, evaluate them, transform them, and answer a variety of questions about them. But ask even our better students a question that’s out of the ordinary and we’re likely to be taken … Continue Reading ››
Writing Mathematics with Sketchpad
In a recent blog post, Karen Coe referred to Conrad Wolfram’s opinion that programming is to mathematics what composition is to English. I’ve taught programming and written a lot of Sketchpad code, and I appreciate Wolfram’s analogy. In English class, students read books, poems, short stories, essays, and articles—but to gain a deep appreciation for … Continue Reading ››