## “Student Learning Can Only Be Described, Not Measured,” by Rog Lucido

Rog Lucido has written an interesting article against standardized testing, and suggesting better alternatives. (Hat-tip to Susan Ohanian.) He argues that the numerical aggregation of final test scores is not valid and therefore not meaningful, and that subjective assessments together with verbal descriptions are meaningful and valid. (This post first appeared at my other (now … Read more

## A Neat Trick For Determining The Integrals Of exp(x) cos x and exp(x) sin x

The standard method (typically found in first-year calculus textbooks) for determining the integrals $\int e^x \cos x \, {\rm d}x$ and $\int e^x \sin x \, {\rm d}x$ is to integrate by parts twice. If you haven’t seen the standard method, I’ll show you how to do the first one; the second one is similar. … Read more

## “No Student Left Untested,” by Diane Ravitch

Measuring teacher effectiveness by the performance of students on standardized tests is insane. New York State has just signed on to a particularly dangerous form of this insanity. Diane Ravitch has clearly explained the insanity and its destructive consequences in No Student Left Untested, in the New York Review of Books (hat-tip to Observational Epidemiology). … Read more

## Both Students And Professors Need Certification, and the Elsevier Boycott

I’ve written before about the evils of grading (for example, see here and here), the main purpose of which is to make certifying students easy. Our current grading system in mathematics is counterproductive to learning (students are inhibited from engaging in essential learning activities out of the fear that is naturally induced by typical high-stakes … Read more

## A Number Riddle, Updated With Solution, And Some Comments On Iterative Playgrounds

Two weeks ago I posted a puzzle sent to me by my nephew Matthew: 1 is 3, 3 is 5, 5 is 4, and 4 is cosmic. Why is 4 cosmic? What happens to the other numbers? As I mentioned in the earlier post, I slept on this before solving it. I initially thought about … Read more