Coherence - Big Pic & Day to Day

We often talk about coherence in teaching for several reasons.  One is to ensure that kids are taught the same content within the same grade level and school to school.  I think one could argue, one of the reasons for state standards would be for coherence district to district.  Now with Common Core State Standards (CCSS) coming (link to the right), one of these goals would be coherence state to state.

I do not think that I posted previously -- that during one of my weeks in March visiting three different schools in three different cities (Kirkkonummi, Helsinki, & Vantaa), three different mathematics teachers were all teaching proportional reasoning.  Coincidental?  I doubt it.  There are less instructional hours for mathematics weekly and overall in Finland than in Chicago; thus, I think the teachers need to strategically prioritize their lessons.  The National Curriculum for Mathematics in Finland (link to the right) is more general than our national standards, but I also think it has less "requirements" at each grade level.  (I need to do more analysis and comparison of both USA and Finland's national standards, but I doubt that will get done before I leave Finland.)

There are very consistent, coherent approaches to unit assessments which I suggest have several educational benefits.   Typically mathematics teachers administer unit tests with 5-7 problems.  Here is the interesting dynamic, it is very common (almost standard) that each problem is worth 6 points.  Teachers consistently develop the rubric that the answer of each problem is worth 1 point and the process to get to the answer is worth 5 points.  (Many Finnish teachers, when I asked, would say that maybe it is too traditional because it has been done for so long, but it seems to be working.)  Now, I am not suggesting we should just do this in Chicago, but at least think about the implications.   Would you agree?  What could be some other benefits to both teaching and learning from this consistent practice?

There are many Chicago mathematics teachers who also expect and allocate more credit to the process than the answer, but I am sorry to say as an instructional coach I believe there are even more CPS teachers that do not.  There is still too much emphasis on the answer and not on the process.  We have been emphasizing the process to solve the mathematics for years (decades?) if you think about it.  NCTM standards (link to the right) and now CCSS mathematics standards both expect it, but why don't many teachers build it into their year long instructional program?   It is unfortunate that it is often taught to students that showing your work is "needed to get credit for the ISAT extended response" mathematics problems instead of just modeling and expecting it as best practices of problem solving all year long.

Something else to ponder with you -- teachers here give so, so many less mathematics quizzes and tests (not talking about standardized assessments here) during the course of the school year than I or most of my CPS colleagues do.  Any thoughts?  I need to talk about this idea further in a subsequent post.