Raymond Johnson @ downclimb.com

I've always been a fan of Wikipedia, and often I'm happy to see a Wikipedia entry as my top search result. As a math teacher, I never had many opportunities to direct students in the ways of research, including how to choose appropriate sources. Several of my colleagues who do teach research, however, not only discouraged Wikipedia use, but banned it outright. Why? The most common answer: "Because anybody can edit Wikipedia, students won't know if the information is true." It wasn't until tonight that I saw how shortsighted this reasoning really is, and how it gives students wrong ideas about research. Let's assume we not only encourage, but require students to use Wikipedia. If a student only finds factual information, then we've preserved the status quo, and nothing really changes. But what if the student finds a mistake? (Or, more likely, you find it for them.) This isn't a crisis, this is an opportunity! First, students see this as a ...

It's back to school time again, and this year I'll be returning as a student instead of a teacher. While the decision seemed sudden, this has been in the works ever since I left UNI. I was so influenced there by Dr. Bonnie Litwiller, my academic advisor, and Dr. Ed Rathmell, my thesis advisor, that I knew someday I'd want to go to graduate school and pursue higher degrees in math education. But first, for reasons of experience and credibility, I went to Colorado to teach, learn, and explore. Six years later, the time has come to pursue that earlier goal. After evaluating some of the best math education programs in the country, last week I visited CU-Boulder and met with Dr. David Webb. He was extremely generous with his time, working with me for over two hours, and by the time I left we had a plan and any doubts about my decision were gone. Not only is CU-Boulder a great school, it makes sense for me academically, socially, and geographically. So I'm a student aga...

Schools reward their inhabitants in two amazingly different ways: teachers get salaries, and students get grades. Not only are these systems vastly different, but I'm not sure teachers would accept a pay scale that's built like a grading scale, nor would students accept a grading scale that's built like a teacher's pay scale. The vast majority of schools pay teachers according to a "salary schedule," a rigid, two-dimensional matrix of dollar amounts with credits across the top and experience down the left side. The more credit hours you've earned, and the more years you've taught, then the more you'll make. I don't feel it's a fair system, but it's a system that most teachers will agree to use, putting it ahead of most any other pay system available. It's a simple system, perhaps too simple. Its simplicity allows us to easily print and read the salaries on a sheet of paper, and I think that's one reason we continue to rely ...

I've been teaching in Colorado for six years, and there's always been a troubling pattern in our state standardized math scores. As students progress from 3rd to 10th grade, the percentage that score proficient and advanced declines dramatically. Here are the percentages of students scoring proficient and advanced by grade level, averaged over all the years the test has been given (typically 2002-2008): Grade Avg. % P+A 3 69 4 69 5 61 6 55 7 44 8 43 9 34 10 29 The easiest explanation (and the one I've tended to believe) is that students' abilities are, in fact, slipping as they got older. That would be a good assumption if the test at each grade level was equally difficult. But what if the test questions were, on average (and adjusted for grade level), more difficult as students got older? Is it fair to assume a test with increasingly difficult questions would result in lower scores, even with sophisticated score scaling systems that take question difficulty into accou...