Community Learning Exchange

Although I enjoyed math in high school, as a teacher and a writer about education I was always much more concerned about literacy education than about math teaching: it seemed to me that if kids learned to read in first or second grade and if they enjoyed reading and read when they had the chance they would be okay in school and beyond.  Understanding math was good, but not nearly as important as reading and writing.  


When I came to Michigan State University, however, my office was next to Deborah Ball’s and Deborah, in addition to her professorial duties, taught math to third graders in a local public school every day.  When I visited her class, I was totally enchanted by what I saw: the children were discussing  the math and their ideas were fascinating.  I had never before been in a third grade classroom where children’s thinking was so visible, all of the time.  Their thinking was so exciting that I wanted to go back the next day.  I wanted to know more about this kind of teaching.


Before too long I launched a study group for elementary teachers who had been inspired by videos of Deborah’s third grade math class to think about changing the way they taught math.  And soon after that I began to teach a math methods course for prospective elementary school teachers; my aim was to get the prospective teachers as excited about children’s mathematical thinking as I was and to help them to learn how to build their math teaching around their students’ mathematical ideas.  I really enjoyed the chance to work with prospective teachers on this and the chance to hang out in elementary classrooms, listening to kids talk about math problems. I did manage to get many of my students’ excited about kids’ thinking and I saw many of them make important strides towards teaching math well.   But there was one challenge I did not feel I was meeting very well: when the teachers and prospective teachers I worked with worried about the children who just did not seem to be learning the math the class was studying – the youngsters that many referred to as “my low kids” -  I did not feel as though I was providing them with the help that they needed.   I talked to the best teachers I knew, and to my colleagues. We all pooled ideas.  But still I did not feel I was giving my students the help they needed in order to engage all  their students in mathematical reasoning and to empower all of them to do math with power and pleasure.


Then, in 2006, I learned from Lisa Jilk, then a doctoral student in our education program, about Complex Instruction a pedagogical approach that developed out of the research of Elizabeth Cohen of Stanford University. When Cohen observed in elementary classrooms where children were working in small groups on academic assignments, she noted that in many groups some children did almost no work while others took over all the thinking, writing, and talking (many teachers abandon groupwork because they see this happening so often when they assign groupwork).  Others who have observed this phenomenon have mostly attributed the differences they observed to differences in ability and motivation: the “low kids” held back because they did not have the skills to contribute, or because they just did not care much about academics.  Cohen, a sociologist, interpreted what she saw differently: she saw differences in status shaping who talked and who remained silent, whose ideas got listened to and whose were ignored.  But Cohen did not want teachers to give up on groupwork.  She believed that, if obstacles to equitable participation could be reduced or eliminated, groups could provide a venue for powerful learning of complex and challenging subject matter: children learn by explaining their own ideas and by trying to understand the ideas of others; joint work can challenge them intellectually while providing support for intellectual risk-taking.  


Over the ensuing decades Cohen studied the impact of status on children’s participation, the effect of participation on learning, and the steps teachers took to equalize status and participation.  Through this work, Cohen and the teachers and colleagues with whom she worked developed powerful strategies for reducing the impact of status on  participation and on learning.  These strategies and the ideas on which they rest comprise Complex Instruction,  an approach to teaching using groupwork that acknowledges that although working with others in groups can offer a child multiple opportunities for deep learning, that the children who most need academic help often learn very little when they work with classmates in groups.  Complex instruction offers teachers concrete strategies for addressing this problem and turning groupwork into a venue where all children engage fully with intellectually challenging tasks, contribute to the learning of their groupmates, and develop deep and robust understandings of academic subjects.


Lisa Jilk had taught math in an urban high school for eight years.  She and all of her colleagues in the math department of this school had worked with Elizabeth Cohen and her colleagues at Stanford and had used complex instruction to teach math.  The results of their work were spectacular:  almost half of the students in the school successfully completed AP calculus each year (compared to 27% in a nearby high school that served a more affluent community but taught math traditionally, according to researchers who studied the two schools over a five year period). 

I was convinced by what Lisa told me, and by what I read, that my students could learn a lot from Lisa, and when she offered to work with them I accepted gratefully. 


After Lisa Jilk  had worked with my students – all of whom were teacher interns in the final semester of their elementary teacher preparation program – over 3 three-hour seminar sessions, the prospective teachers used what they had learned to plan math lessons using the strategies and structures of complex instruction.  And when they returned the following week, after teaching their complex instruction lessons, most of my students were beaming.  They spoke of hearing the voices of children who had barely spoken in math class during the previous five months of school.  They described the important intellectual contributions some of these children had made to the work of their small groups. Moreover, they began to refer to the children who were not doing well in math as “my low status kids” rather than “my low kids.”  Although this change in vocabulary might seem trivial, we felt it was important: calling children “my low kids” locates the problem in the children themselves; calling them “my low status kids” suggests a problem that is situated in –and perhaps created by -  the environment, in this case the elementary classroom.  It suggests a teaching problem, a problem that a determined and imaginative teacher can do something about.


What I saw heard from my students, and what I learned as I dug deeper into the ideas behind complex instruction, made me see that complex instruction could be a powerful tool in my efforts to help teachers and prospective teachers to teach math in a way that gave all of the children in their classrooms opportunities to develop deep understandings of mathematical ideas, to make important intellectual contributions to collective work, to see themselves and their classmates as capable mathematical thinkers.  It was clear that it would take hard work to give prospective teachers the tools they would need in order to teach math this way,  but I was excited about trying.


Probably I would never had gotten beyond this insight if I had been working alone, but fortunately Marcy Wood, a doctoral student and a gifted former elementary school teacher was with me on this journey: Lisa had worked with her students as well as mine. Indeed, Marcy had taken the lead in designing with Lisa what the students would do during Lisa’s 9 hours with them. Marcy was as passionate as I was about empowering prospective teachers to teach all of their students to reason mathematically and  she shared my enthusiasm for what we had seen happening for our students.  Together Marcy, Lisa, and I worked with the other faculty and grad students who were teaching the elementary math methods courses, persuaded them of the potential of this work, and found funding for a weeklong summer workshop on teaching math using complex instruction for teachers and university folk who worked with prospective teachers in the MSU elementary program.  We participated with the teachers in the workshop and built complex instruction into the math methods course for the following year.


The teachers who had participated in the workshop and the prospective teachers in our courses taught some fine lessons that addressed issues of status and got more children engaged with math.  However, I came to realize that there was more to teaching challenging mathematics (and the math must be challenging: if math continues to be about memorizing the multiplication tables and solving straight-forward computation problems,  complex instruction will not help children to learn) to a diverse classroom of young learners than prospective teachers – or most others – could absorb in even a very intense week-long course.  At that point, I asked the rest of the team - Joy Oslund, Lisa Jilk, Marcy Wood, Amy Parks, and Sandra Crespo - if they would be willing to join me in an effort to write a book about teaching math using complex instruction that we could put in the hands of our students and other elementary teachers and prospective teachers (the book is finally done and will be published by the National Council of Teachers of Mathematics this spring).


Although all of us were working together in the teacher preparation program at MSU when we started this work, we are now scattered across six universities in Georgia, Massachusetts, Arizona, Michigan, and Washington state. In our different venues we are all working to help the prospective elementary teachers in our classes to teach math with complex instruction.  We do this work because we believe that teaching math with complex instruction can empower children who have in the past learned math as procedures to memorize (many of whom are poor and/ or of color) to reason and communicate mathematically, to tackle and solve hard problems, and, ultimately, to succeed in advanced theoretical math classes that have in the past been populated mainly by students from affluent suburban schools.


Our society will continue to jail, silence, and  push aside  whole categories of "low status"  Americans.  There are systematic ways in which inequality continues to be reproduced, in and out of schools.   The "macro"  barriers are so  high that schools alone  will not suffice to remove them.         But in the "micro"-realm of math classrooms,  my colleagues and I think we are showing  teachers some small yet  practical steps to take toward a world in which mathematics, too,  can be democratized.   

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