Group items tagged

""What's the sine of π/2?" I asked my first-ever trigonometry class. "One!" they replied in unison. "We learned that last year." So I skipped ahead, later to realize that they didn't really know what "sine" even meant. They'd simply memorized that fact. To them, math wasn't a process of logical discovery and thoughtful exploration. It was a call-and-response game. Trigonometry was just a collection of non-rhyming lyrics to the lamest sing-along ever. Some things are worth memorizing--addresses, PINs, your parents' birthdays. The sine of π/2 is not among them. It's a fact that matters only insofar as it connects to other ideas. To learn it in isolation is like learning the sentence "Hamlet kills Claudius" without the faintest idea of who either gentleman is--or, for what matter, of what "kill" means. Memorization is a frontage road: It runs parallel to the best parts of learning, never intersecting. It's a detour around all the action, a way of knowing without learning, of answering without understanding."

"These maps, published in 1932 in the Atlas of the Historical Geography of the United States and available through the David Rumsey Historical Map Collection, illustrate how arduous travel was in the country's early history. In 1800, a journey from New York to Chicago would have taken an intrepid traveler roughly six weeks; travel times beyond the Mississippi River aren't even charted. Three decades later, the trip dropped to three weeks in length and by the mid-19th century, the New York-Chicago journey via railroad took two days. And the introduction of regional airlines in the 1920s made it possible to travel 1,000 or more miles in a single day." Possible applications for Westward Expansion

Journey beyond the road

""That's why the goal of school has to be automaticity," my dad concluded. The Sunday morning roads were empty, and we'd nearly made it home. "Take learning your times tables. You've got to know them cold so that you can go on to finding common denominators, or reasoning about algebraic functions, or whatever. You need each task to become automatic before you can move onto the next intellectual step."" Humorous, yet enlightening take on math class, which can be applied to school in general. What is more important for us to teach students so that it becomes more automatic? Should we make facts automatic? Or should we instead focus on skills and thought processes that can be quickly applied to many scenarios in a variety of contexts?