Well, the end of my transition year with this new curriculum for my colleagues is almost done.  We have realized that we wrote way more problems than we needed in order to get through our old geometry curriculum content-wise.  It is an interesting thing, though, to have to go through and cut problems that you really loved when they were written.

 Anyway, something else that comes to mind at this point in the year is how far the students may or may not have come in their work with problem solving.  Clearly, the stronger mathematics students basically just eat up these problems.  They are confident in their skills and ideas, so being part of the conversation is not difficult.  However, the students who might have come into this course with the preconceived or realistic notions that they are pretty weak mathematics students are much more of a concern.  The concerns range from how attentive they can be during a problem discussion to how they can possibly be metacognitive enough to write a journal entry.  All of these issues surfaced throughout the year with different students and I thought I’d share a few with you.

One student, I’ll call John, came into this course with a barely passing grade in Algebra I.  In fact, there was serious rethinking of him moving on at all into this course.  The year began for him as a studet who was barely engaged in the problems, but because of his positive attitude, persevered.  John had severe retention and learning issues, which a few months into the year were diagnosed by a professional.  Clearly, there was no way this student could remember to solve a linear equation from Algebra I, if he couldn’t recall the properties of parallelograms from the previous problem, two days ago.  This was clearly an extreme case, but worth noting.

John never stopped working and half-way through the year finally was linked with a tutor who specialized in his special needs.  John started meeting with his english teacher to help in writing his journal entries, and finally something clicked.  The entries became much more connected to class problems and ideas.  The work in class kept him engaged and sometimes even volunteering to share a solution that he knew was wrong.  The growth in this student since September has been tremendous, even if grade-wise he’s still in the C- range.

Another success story is a girl I’ll call Sheila.  This is a student who came into the course with very little confidence in her ability to speak her mind(with respect to math) or have good ideas.  She was a B-/C+ student in Algebra I and definitely retained some of her skills from that course.  She started the year mainly complaining blatantly in class about how much she did not enjoy the pedagogical framework of the course (my summarizing of course), and frequently stopped class to comment about how a problem could’ve been more easily stated or how unfair it was that we would expect her to draw her own diagram.  I allowed this to happen a number of times since I wanted to create a sense of freedom of expression in the classroom.  However, at mid-year, I made it clear to her that this type of sharing with the class will no longer be tolerated.  Interestingly, once that happened there was a change in her work and attitude.

Now, I’m no psychologist, so I can’t claim to understand what made Sheila change the way she worked, but all of a sudden so much of this course mattered to her.  It came across in her contributions to class, which were often surface in her understanding, but sometimes showed great insight.  She once described the reasoning behind the Triangle Inequality brilliantly with a piece of her hair.  At the end of the fall semester, she had a C-, and most recently earned an A- on a problem set.  Again, I can’t exactly put my finger on what has changed for this girl, but I can hypothesize.

It might be that Sheila finally stopped complaining enough to see that she did have important things to say in class besides her complaining.  It might also be that once she did that, she actually enjoyed being a productive part of a solution process with her peers.  I sometimes catch her explaining something to another student and think that her confidence in her abilities has grown tremendously.

The more important question that follows is twofold 1) are these changes because of the coursework or are they just the normal intellectual maturity that happens to teen-agers and 2)what will happen next year when they move on to a more traditional course in Algebra II/Trig.  It is the second question that has my colleagues most troubled, and for now we will have to just wait and see.  Although our head of school, would be happy to have us writing another year’s worth of curriculum this summer, we really feel that we need to edit and really solidify the year we have right now.  Hopefully, in the future, we’ll be able to bring this experience to other courses as well.