After viewing the following video, I felt that I connected
to the thoughts presented by M.J. McDermott. As a fifth grade teacher, it is
frustrating to see that students cannot multiply or divide fluently. We have
recently worked in multiplication and division in my classroom with very scattered
results. Many of my students did not know how to set up a traditional
multiplication algorithm. Some knew how to use the ‘cluster math’ depicted in
the video, others were familiar with the lattice method (although a precious
few actually used it successfully on more than one or two problems at a time),
and several were familiar with partial products. By not using the traditional
algorithm, my students are not able to master any particular form of
multiplying. In addition to this, when student are asked if their answer is
reasonable, they cannot seem to grasp the concept of determining reasonability
because they are more focused on which method they can use to determine
reasonability. When we moved into long division, I saw that students looked for
an alternative way to do it. One even attempted to create his own ‘division
lattice’. It seems all of these ‘tricks’ have made students less willing to
persist in traditional mathematics for mastery of skills.
Based on Chapter 9 from the Handbook of Research in
Mathematics Education, there is a web of curricula that leads to student
understanding. A few of the points in this web are the Teachers’ orientations
toward curriculum, Teacher beliefs and knowledge, and Teachers’ professional
identity. After reading this, I wondered how a state could have a set list of standards;
yet have teachers teaching a completely different form of mathematics. I have a
recent personal connection to this. My daughter is in 3rd grade in
NC. Her math homework recently included subtraction problems called “Expanded
Subtraction”. Below is an illustration of the method she was instructed to use.
Where you see a (c) is the place she was instructed to use a calculator.
My question for this, is exactly what part of NC or Common
Core Math standards does this fall under? Additionally, if my daughter was
encouraged to use a calculator for two separate parts of this problem, why
would she not logically use a calculator to simply solve 284-95 to begin with?
Finally, the interpretation of this subtraction skill was different between two
teachers in the same building. While my daughter’s teacher did it this way,
another teacher taught it the way you see below. This exemplifies the sections
we see in Explanations for Transformations from the Handbook of Research in
Mathematics.
As a home-educated student, I used Saxon Mathematics during
the course of my education. Saxon Math was very straightforward, teaching the
use and mechanics of all mathematics skills I use today. I cannot say that I
particularly enjoyed math as a student, due in part to the literary nature of
my childhood, but I did not hate it or feel inadequate using the skills
acquired through traditional problem solving.
As a teacher for four years, only one of those years have I had an
actual math textbook to utilize in teaching. The experience with it was
strenuous at best due to a heavy focus on games, investigating math concepts
and unrelated content mixed in throughout the book. Students utilized a very
large workbook version of the textbook that included 1-2 problems per page. The
problems always seemed either very easy or rather convoluted, neither of which
was beneficial to my students.
Stein, Mary Kay, Janine Remillard, and Margaret
S. Smith. "Chapter 8: How Curriculum Influences Student Learning." Handbook
of Research in Mathematics Education. New York, NY: MacMillan Co, 1992.
319-23. Print.
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