Tuesday, March 20, 2012

Royal Bridges To Mathematics

At the Hillsboro school district’s March curriculum committee meeting, we were introduced to the new “Bridges” math program recently introduced for the elementary grades.   The teachers were very enthusiastic, reporting that for the first time, students in elementary grades actually looked forward to math lessons, and there has been an explosion in students claiming math as their favorite subject!   It sounds pretty impressive.  The district is now working on choosing a successor program for middle grades, to be discussed more in upcoming meetings.
Asking for concrete examples of lessons, I was pleasantly surprised.   The one they showed me involved challenging students to make as many different rectangular arrangements of a fixed number of paper squares as possible, using the variety of possible shapes to illustrate the different ways of factoring numbers, and leading to the concept of prime factors.   Through active manipulation of physical objects, they were learning real concepts.  If most of the lessons are like this, there could be some real potential here.
There are a few notes of caution, however.   Bridges advocates do claim anecdotally that the students are learning real math, but “it will be a few years” before the results show up in test scores.   I’m a little nervous that, while not very exciting, the repetitive nature of traditional math worksheets and similar exercises plays a critical role in building an inherent “number sense”.   The cumulative nature of math education, where each level builds on what was learned before, means that if the foundations are shaky, students are potentially put at a huge disadvantage later on.  
Looking online, it’s not too hard to find strident Bridges skeptics, such as “Mathematically Sound Foundations”  and the What Works Clearinghouse, which includes a critique of the various pro-Bridges studies.   Mathematics education also has a poor history of latching on to various fads, such as the New Math of the 60s (see my podcast on the topic) and the New New Math of the 90s.   It seems like every few years, someone wants to find a new miracle in math teaching that will eliminate the need for focused, disciplined study—and these new methods repeatedly fall short.   We seem to be constantly relearning the lesson Euclid taught Ptolemy, that “there is no royal road to geometry”.   Traditional methods of teaching math may not seem cutting-edge or romantic, but might truly be the most effective methods long-term.
Of course, this is not to disparage Bridges—if this new approach turns out to really work, and to really teach the core concepts as well as being fun, it may very well represent real progress in early math education.  But we need to closely watch the progress of test scores and other measures of math achievement in our district, and be prepared to do an about-face if it turns out that Bridges is not coupling its fun methods with truly solid foundations.