Teaching Mathematics For Understanding

       There has been a lot of debate in the U.S. about our student's ability in mathematics for the past decades--certainly for my entire career (which started in the 1980's). How do we compare with students in other countries? (see PISA results - 36th out of 70 for mathematics in 2012)  How do we compare with each other state-by-state?  (see NAEP results from 2013)

       What are the causes for these discrepancies?  What do other countries do differently compared to what we do in the U.S.?

       Ask a hundred people and (it seems) you would get a hundred answers.  Everything from "nothing's wrong" to "the system is broken".  Everyone has their point of view; there are experts on both sides of the every argument.

       Recently, I've read two sources on this issue that make a lot of sense to me.  The first is from Phil Daro.  He makes the point that many mathematics teachers in America have the goal of teaching students how to get the right answer.  In other countries the mathematics teachers have the goal of teaching students how to understand particular mathematical concepts.

       This makes sense to me because I've been that mathematics teacher and I've seen that mathematics teacher among my colleagues.  While I believe that our teachers want their students to understand and to gain a conceptual understanding, they are often fighting a battle against an accountability system that seems to reward "correct answers" more than awarding "correct understanding".  (Although the new PARCC and Smarter Balance assessments may have found a balance between these two competing forces.)  We are also fighting a culture of students who avoid the struggles needed understand these concepts and (instead) seek shortcuts for getting the right answer.

       The second source is an article by the education writer Amanda Ripley.  She took the PISA math test in an effort to understand the sort of thinking that it requires of students.  She also interviewed exchange students who spent time in schools in other countries.  From these interviews, she repeatedly heard these students remark about the following three differences between schools in the United States and schools in higher achieving countries.  These are:

  1. School is harder. There's less homework but the material is more rigorous. People take education more seriously, from selecting the content to selecting the teachers.
  2. Sports are just a hobby. In the U.S., sports are a huge distraction from the business of school, but that's not the case in other countries.
  3. Kids believe there's something in it for them. The students in other countries deeply believe that what they are doing in school affects how interesting their lives were going to be. Even if they don't like a class, they see their education as a stepping stone to their future.

       I believe that we have to take a honest look at ourselves here in the U.S. and be open to these differences if we are ever to see a significant rise in the achievement of our students.  Our current climate of new standards and new assessments provide to us an opportunity to make this huge adjustment in our teaching and in our understanding of the true purpose of our mathematics class rooms.

       We can do this.  We must do this.  We must do better.



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