The first two classes of
Junior/Intermediate Mathematics have come and gone and a common theme that has
resonated with me is the importance of being open-minded and flexible. I find
that often it is easy to stick to what you know or to what you believe has worked
for you in the past. It is easy to
become complacent or set in your ways. It is critical, however, that teachers be
open-minded to new ideas and strategies even if these new approaches push them
outside of their comfort zone. Today, math is moving away from the rigid,
one-way and one-answer approach that I experienced in elementary school and high
school to a much more flexible and engaging approach that encourages inquiry,
discovery, and creativity. While this new approach may seem intimidating at first as it is not what many of us are used to, it is also
incredibly exciting to see such a positive change!
I found Daniel Meyer’s TED
Talk entitled "Math Class Needs a Makeover" (see embedded video below) that we watched during the first class quite powerful and inspiring. Meyer
discussed how “What matters?” is the most underrated question in math. He
emphasized the fact that rather than work with questions that simply feed
them the exact information that they need, students need to work with math problems
that cause them to ask questions and become truly engaged with the material. I
wholeheartedly agree with this sentiment. As a math student, I do not remember
ever feeling particularly engaged with math problems. I would read over the question, pick out the
key pieces of information, plug them into the formula to get the answer, and
then move on to the next question. Looking back, it was almost a robotic
process. I rarely asked the questions why
or how. Open-ended problems,
which typically have several correct answers and several ways to develop an
answer, offer students a fantastic opportunity to more actively engage with
math as they question, reason, and discover. Students are forced to ask themselves
questions about what matters. For example, the open-ended question that we
looked at in class was to provide students with an image of a room and ask them
how many people can fit in the room. Students would need to ask questions such
as: Are all the people the same size? Can people stand on one another’s
shoulders? Can the furniture in the room be removed or re-arranged? Thus,
students are no longer robotically plugging in numbers, but they are actively
problem-solving. This use of logic and critical thinking is imperative for
students to truly understand math and to understand why math matters.
Meyers, Daniel. [TED-Ed]. 2013, August 1. "Math Class Needs a Makover."
Retrieved from https://www.youtube.com/watch?v=qocAoN4jNwc
As a teacher, I need to be
open-minded not only to incorporating new types of math problems into my
classroom, but also to adopting new methods of doing basic math functions. I
was reminded of this when we looked at subtraction in class. When I learned subtraction in elementary school, I was taught that when a digit from the top
number was not big enough, it would borrow from the column to its left.
However, this concept of borrowing, and never giving the number back, is
illogical, unnatural, and confusing for children. It is an algorithm that is
meant for computers, not human beings. A far better method is to choose a number and add it to both the top and bottom number in order to make the top number a more
friendly number for subtracting. Here is an example of this method:
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| Olij, B. ©2016 |
As we learned this
alternative method, I thought of the article “Toward a Practice-Based Theory of
Mathematical Knowledge” by Ball and Bass. The articles talks about how math
teachers need to have pedagogical content knowledge. In other words, they need to
consider what mathematical representations and explanations children find
logical, useful, and helpful. The algorithm of borrowing in subtraction is not very logical or child-friendly,
and thus teachers must be willing to look at how a child understands and
interacts with numbers in order to find new approaches that will help the child
to truly understand math. Thus, this new subtraction method was an
eye-opening moment for me. When Pat first introduced this method, my natural
reaction was to say: “What’s wrong with the way I learned it? Why do we have to
change?” Yet after seeing how unnatural and illogical the old method of
subtraction was, I left the class asking myself: “When I was a student, why did
I just accept that algorithm that didn’t really make any sense? Why didn’t I
ask why we were borrowing digits that we never gave back?” I now look forward
to using the new methods and approaches in my future classroom!
Thus,
the past two classes have been a much-needed eye-opening experience for me. I
have been challenged to let go of the old ways of learning math and to embrace
with an open mind the engaging, creative, and more logical methods of teaching
and learning math. I have been truly inspired to help my future students joyfully
discover why math matters as they actively engage with math in meaningful ways.
