All Roads Lead to Rome

     I don’t know about you, but when I was growing up in the school
system, math class was the one place in which I could depend on there being
a degree of certitude. Whereas many of my other courses were highly
subjective, mathematics was the class in which there was a definite correct
answer and, typically, one correct method used to find that answer. In a
sense, this was a great relief: it was black or white, right or wrong, yes or no.

     However, as a classroom teacher and mathematics specialist, I have
come to celebrate the trend in mathematics towards open-ended questions
that may or may not have one correct answer. Have I gone soft? Have I lost
my edge? It’s possible, but I don’t think so. Hear me out…

     The inherent issue in mathematics problems in which there is only one
right answer and only one “correct” approach in finding that answer is that
there is little room for creative, higher-level cognition. Isaacs and Carroll
(1999) put it best: “The rote approach encourages students to believe that
mathematics is more memorizing than thinking.”

     This is also a question of equity and access to curriculum. We
understand instinctually that there are myriad different types of thinkers, and
we are helped along in this process by folks like Dr. Howard Gardner of
Harvard University, who introduced us to the Theory of Multiple Intelligences.
We understand as educators that it is both our right and our responsibility to
reach all learners, and this calls for creative instruction on our parts. Perhaps
one of the best ways to creatively teach and reach is to differentiate our
instruction to the needs of all students in our classrooms, keeping in mind
how differently their brains operate. We approach teaching today with
multiple intelligences and multiple modalities in mind and, in doing so, even
out the playing field. We recognize that some students are better able to
demonstrate their learning and understanding using concrete materials,
others are more comfortable drawing pictorial representations of their
mathematics, while others prefer to use an algorithm to solve problems. The
research is very clear that none of these approaches trumps the other.

     So, what can you do as the parent of a math student when working
with your children at home? I highly recommend sharing with them what you
learned in your own education, but keeping an open mind to the new and
creative ways your children are approaching the same problem. You will both
learn something! For example, you are probably most familiar with the
standard algorithm for vertical multiplication. Rest assured your students willbe
exposed to this, but they will also see Base 10 multiplication using physical
 manipulatives, array models, linear models, set models, lattice multiplication,
partial products, etc. Exposing your children to these varied techniques assures
us that they will be able to access the information on their own terms, thereby
taking ownership of, and pride in, their learning.

     All roads lead to Rome, and all approaches being taught to your children lead
them to feeling successful and fulfilled in mathematics.