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During my 31 years of teaching high school mathematics, I can honestly say that I can count on one hand the number of times that I sat down with Middle School teachers and talked curriculum. They did “their own thing” and we did “our own thing.” Consequently there were gaps in learning even before the advent of the Common Core State Standards. The lack of a well defined and coherent curriculum left little incentive for teachers from different grade levels to communicate with each other.
One of the biggest problems that I had at the High School level was students that were taking Algebra 1 without having a firm grasp of fractions. This was not the fault of teachers at any level, but rather, the result of a curriculum that was not well defined and did not emphasize the need for coherence.
With the advent of the Common Core State Standards, common threads are interwoven throughout the curriculum. These common themes can be seen in the Mathematics Progression documents.
One of the six shifts identified as crucial to the implementation of the Common Core Learning Standards in Mathematics is Coherence. Coherence is evident throughout the curriculum, as can be seen in the Mathematics Progression documents mentioned above, as well as the appearance of the same standard in more than one Cluster or Grade Level.
Now, with an emphasis on fractions in grades 3-5, ratio, unit rate, and constant of proportionality in grades 6-7, there is coherence in the curriculum that leads nicely to the graph of a straight line in grade 8 and continues into the Algebra 1 course.
But perhaps the most striking example of coherence in the mathematics curriculum is the intuitive and “hands on” work done in Grade 8 with Congruence & Similarity that form the basis for a more formal treatment of those same concepts in Grade 10 Geometry.
Congruence is no longer defined as geometric figures with the same size and same shape, but rather as a composition of rigid transformations (translations, reflections, and rotations). In Grade 8, students get “hands on” experience with these transformations using transparency paper, among other tools, to physically rotate, move, and reflect different geometric objects both on and off the coordinate plane. This then forms the foundation for more formal work with these concepts in Grade 10 a students use constructions as a basis for these transformations.
For example, in Grade 8, students learn that when a point is reflected across a line, that line is the perpendicular bisector of the segment joining the original point and the reflected point. They use transparency paper to reflect points across this line. Then, in Grade 10, students learn to not only construct this perpendicular bisector, but they also use construction techniques to physically reflect points across this line. This work in Grade 10 is obviously dependent on the work done in Grade 8. Grade 10 teachers need to be aware of what was taught in Grade 8, as well as communicate with Grade 8 teachers about what worked and what didn’t work.
As a member of the OCMBOCES Network Team, one of the most consistent messages that I see coming out of Albany in regard to the new Common Core curriculum is the necessity for teachers to communicate with each other both within grade levels and across grade levels. I myself see this as vital to the success of the curriculum and a welcome change from the isolation some teachers felt in the past. Coherence in the curriculum means that I have to be aware of the curriculum that both precedes and follows my own curriculum. Also, I have to talk to other teachers and discuss common strategies that can help students as they move from one grade to the other. This is not easy! It takes effort on the part of everyone involved. Smaller districts might have to make use of their BOCES to provide opportunities for discussion. But as difficult as this task might be, the rewards, for both teacher and student, far outweigh the effort. Teachers become more aware of the vital part each one plays in the “big picture”, no matter what the grade level. Students are delivered a more coherent curriculum where concepts are introduced and then constantly built upon.
As a former teacher, I welcome this collaboration between teachers! Any time teachers get together and talk curriculum, good things happen.
OCMBOCES Network Team