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.

Assessment Data - Where does it go?

So... there are some assessments that schools can "choose" to take to see how their students are doing in comparison to other schools in their city and the national average.  These exams are optional at 6th and 9th grades.  Many of the schools I have been visiting chose to give the 9th gr mathematics exam (along with some other exams) last week.

The ninth grade mathematics exam is written and distributed by MAOL (Matemaattisten Aineiden Opettajien Liitto MAOL).  MAOL is the national mathematics, physics, and chemistry teachers organization (kind of like NCTM and NSTA combined).  MAOL also writes a detailed rubric to ensure the tests are graded consistently.

Ready for this?  The mathematics teachers (who choose to give the exam) grade their own students' exams and then enter the scores anonymously into a central database.  Thus, there is a national database without student names so each student, teacher, school, and city knows how they are doing in comparison to the national average.

The benefit of anonymity?  There is no ranking of students or schools or cities' performance - it is just a formative baseline.

Another educational benefit - think of the educational coherence and consistency that is established when all the teachers score and report their own assessments.  In addition, everyone takes the mathematics test the same day; thus, afterwards the test becomes a public document.

At the end of secondary school, students who choose to pursue college take the required national matriculation exam.  I will explain how that whole process works in a subsequent post.

PhD Seminar - Mathematics Teacher Beliefs

I was invited to attend a seminar with a professor and about a dozen current teachers pursuing their 2nd master's degree or PhD in mathematics education. There were teachers in attendance from Finland, U.S., and Ghana.

The PhD research project that was presented and critiqued will research mathematics teacher beliefs -- whether their philosophy of instruction is more constructivist or more traditional. To my surprise, in the last couple of days, I have learned that there is already research here to show that many mathematics teachers here are more traditional than I thought. Hmm... another similarity between our teachers. Teachers realize or at least say that they believe in inquiry-based, constructivist learning, but it seems that many mathematics teachers prefer the textbook of problems. I look forward to learning how this project progresses and possibly being invited to a future PhD seminar...

I am pursuing avenues to share the MARS tasks from the Inside Mathematics website and the Connected Mathematics curriculum with both the mathematics professors with the university Department of Teacher Education and possibly these mathematics teachers pursuing their advanced degrees.