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Mastery Approach, etc.



Mike,
        Thanks for such an enlightening post.  I teach 50 Alg 3/Trig
students in a suburban high school in Pittsburgh, Pa.  They are learning
math like you did...No one until myself made them accountable for knowing
why and how it all works.  They want me to continue to teach them what I
phrase "cookbook math".  Give them a set of steps to follow, practice to
death in class, and then ask them to do the same thing on a test.  After
the test, forget it all because it's over and done with.
        But that's not the way it works...Especially in an upper level math
class.  You need to be able to draw upon the broad knowledge base you
presumably have from taking AlgI, Geom, and AlgII.  But they can't!  They
learned for the test moved on to some other technique or topic and never
came back to the one just tested on.  And then through time, forgot it
all....because they never really used it again until they got to my class.
        In all of this, I am the bad guy because all of a sudden an A/B
student is getting C's or D's.  Something they nor their parents are used
to seeing.  I currently have a student who has a "3.5" GPA and never got
less than a afinal grade of an A in a math course struggling to get a C.  I
have another student who confided in me that until my class, she NEVER had
to study math and she got by with A's and B's....but in my class she
finally realized she had to put time and effort into learning the material
if she wanted get a good grade.  She went from a C/D to an A in one nine
week period!

        You can't learn math piece meal.  You can't forget the material
after the test is over.  Saxon has a basically good idea in his books, but
I feel it needs more work.  Likewise the Integrated Math series by Houghton
Mifflin has a good idea but I feel it too needs more work.  A book that is
a combination between the two would be ideal!  But I haven't seen any on
the market yet...

        Thanks again for your insight...I can't wait to read "How I would
change mathematics education if the school systems were foolish enough to
listen to me".

Pat Dzambo