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.
