I have truly mixed feelings about group work. In general, people learn more and get more done when collaborating with colleagues (or fellow students) than when they try to go it alone. And working with others is unquestionably a valuable… Read More ›
Teaching & Learning
The four pillars of high-school mathematics
What do we teach in high-school math? If we look at the big picture —not at specific topics in specific courses — what do we teach? Numbers? Formulas? Algorithms? Taking standardized tests? All of the above? None of the above? There’s… Read More ›
The Last Samurai
What a fascinating story! There are several books by this title, but I’m talking about the first novel by Helen DeWitt, published in the year 2000. If you know me, you won’t wonder which half of the story I liked… Read More ›
The case against Algebra II?
The reason these kids are upset is that they are required to do something they can’t do. They are forced, repeatedly, to stare at hairy, square- rooted, polynomialed horseradish clumps of mute symbology that irritate them, that stop them in… Read More ›
How to pick a tutor…or not
Who needs a tutor? You do! Well, no…you probably don’t. Even if you’re faced with the challenge of Honors Geometry (a rude awakening to many students who are suddenly faced with the demands of their first high-school honors math course),… Read More ›
The soft bigotry of low expectations
I hate to use a phrase that was coined by a senior advisor to President George W. Bush. But use it I must…and even in a similar context. Michael Gerson described the all-too-common educational practice of expecting less from members… Read More ›
Learning goals and common assessments
Yesterday we had our final workshop of the summer, so we must be ready (hah!) to return to school on Tuesday. This workshop was titled “Learning Goals and Common Assessments.” You might be wondering what that means. I’ll tell you…. Read More ›
Using web-based technology in math courses
Yesterday we had a one-day workshop on using web-based technology in math courses. The premise was that the technology used in our math courses has been almost unchanged over the past ten years, despite the big improvements in web-based applications that… Read More ›
BYOT
Just finished participating in a two-day workshop on BYOT, a.k.a. BYOD. If you’re not up on current educational jargon, you might not realize that the T stands for “technology,” the D for “device.” In either case, the idea is that… Read More ›
It’s tough to type math.
Mathematical expressions and equations are normally written on paper with a pencil, or on a blackboard with chalk, or on a whiteboard with markers. There’s a good reason for this: it’s really hard to type math, whether you’re using an… Read More ›
Paul Lockhart
Three and a half years ago I wrote a post about Paul Lockhart’s book, Mathematician’s Lament. Now he has a new book, oddly titled Measurement. Why, you ask, is that title odd? It’s because the book is only peripherally about measurement. Mostly it’s… Read More ›
College admissions, the achievement gap, and throwing money at the problem
Boston College (2), Boston University (2), Brandeis, Clark, Denison, Framingham State, Hamilton, Harvard, Holy Cross, Lafayette, Northeastern (2), Skidmore, Suffolk, Tufts, U. of Maine, UNH, UMass Amherst, UMass Boston, Union, Wheaton, and Williams. That’s the complete list of where the… Read More ›
From strangers to family
Yesterday evening the Crimson Summer Academy held its Tenth Annual Celebration to recognize the conclusion of another summer’s hard work. (Hard to believe that it’s been ten years!) Among the many fine presenters, one in particular stood out: the junior class… Read More ›
How many levels should there be?
“I don’t want to stay in Honors Geometry. It’s too difficult!” “I’m bored in regular Geometry. It’s too easy!” We hear remarks like these from a sprinkling of students — sometimes both of them from the same student — usually… Read More ›
All iPads, all the time?
Can we survive in the classroom if we entirely replace laptop computers with tablets? Last summer we converted from laptops to iPads for the incoming sophomores at the Crimson Summer Academy. This summer we expanded the program to the juniors…. Read More ›
Plagiarism: Pro and con
Pro and con? Perhaps you think this is a deliberately provocative title. Every teacher, after all, is vehemently against plagiarism, right? We are justifiably outraged when a student turns in a paper in which whole paragraphs are cribbed unattributed from… Read More ›
Graphing lines
So here’s the question: should we teach students that the slope-intercept form of the equation of a line is y = mx + b ? Or should we teach it as y = a + bx ? And does it matter? I contend that it does matter, and that there are several good reasons… Read More ›
As you know, college admissions have become more competitive.
Does it matter that the most competitive colleges are harder to get into than they used to be? It certainly matters at Weston, and I’m sure at other top-ranked high schools as well. The question is whether the net effects… Read More ›
AIME revised
Contrary to my post of February 22, it turns out that Weston actually has nine students, not eight, who qualified for the AIME. Pravina Samaratunga (junior) took the qualifying test at a different location and therefore wasn’t included in my original list…. Read More ›
The Joy of x
Steven Strogatz has made a useful contribution to the surprisingly large set of math books written for the general public: The Joy of x: A Guided Tour of Math, from One to Infinity. I have to admit that I started out… Read More ›
Learning Strategies 