Complex instruction

Today, as part of helping me get oriented to the complex instruction model being used at my school, my CT gave me a copy of the textbook from which they draw most of their tasks.  The book, Algebra Connections by CMP, is really a big binder full of mathematical “tasks.”  These tasks are used to augment the book officially used by the district: McDougal Littell’s Algebra 2.  Homework is generally assigned from the McDougal book.

In reading through the first section, I came across the following paragraph:

The third key component of an effective CPM class is the teacher’s ability to ask good questions and draw knowledge out of students.  Since one of the major goals of the CPM curriculum is to get students to accept responsibility for their own learning, teachers need to ask good questions in order to get students to use their own resources.  These questions are aimed at getting to the heart of the students’ difficulties and drawing connections with other topics the class has covered.  When answering questions, teachers try to make students be very specific about what they do not understand.  Often when students are forced to articulate their questions clearly, they are then able to answer them on their own. (Emphasis in original.)

This seems to be a core component of complex instruction, as well.  In my experience so far, students make an effort to use one another as resources.  When that doesn’t work, they turn to the teacher (me).  My job, though, is not to act as a resource for knowledge, but to them think about their situation in a new way, by asking questions that may not yet have occurred to them.  These questions might be leading, but the goal seems to be to keep the students thinking.  Once or twice, I have had students answer their own questions in the process of simply trying to explain the situation to me so they can ask a question.  Although I have seen this happen in classes that use direct instruction as well, it does seem like the students in a complex instruction environment spend a lot more time having conversations about mathematics.

Something else I have noticed is that some students struggle with this model, in part because while they understand the mathematics on some levels, they are not able to communicate their understanding very well.  I observed two students working on piece-wise functions.  One was attempting to explain to the other why it was not acceptable to have two sections of the function overlapping across x-values.  The term she used was “intersect,” but in mathematics this word does not describe the problem well.  The second student was very confused by this term, because to her the lines did not intersect (they did not touch, but shared space across the x-values).  Unfortunately, the first student did not try to find new ways of explaining this key feature of piece-wise functions.  Instead, she seemed to conclude the other student was incapable of understanding, and attempted to complete the exercise without her.  (I intervened at this point.)

What was so interesting about this interchange was that the first student seemed to feel that she was somehow “better” that the second student because the second student didn’t understand her.  I don’t know if my intervention made an impact on that opinion, but the second student did at least learn why different sections of a piece-wise function cannot share x-values.  I would not have agreed with the first student’s evaluation of her ability, however.  Her inability to use correct vocabulary and communicate herself with clarity is a serious drawback, especially considered in the context of future employment.

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