Lisa Usher
Mathematics Resource Teacher
Los Angeles Systemic Initiative, LAUSD
Monlux Math, Science, Technology Center
We often share the sometimes surprising results of classroom lessons around the microwave in the faculty lounge, but more as "black humor" than as a way to deepen our own understanding of mathematics and teaching.
To a trusted colleague, we might confide our own professional "failures" - the activity from the last NCTM Conference that bombed in period two or the disappointing student results following a month of focus on fractions - but it's a challenge to move these conversations beyond a gripe session.
Yet a process known as "Case Methods Discussion" could give teachers a new tool for self reflection. It has the potential to turn these discussions into provocative analyses of topics that are both "hard to teach" and "hard to learn."
A "case" is a vignette from an anonymous classroom, a teacher's record of instructional decisions (including samples of student work and/or teacher/student dialogue), quandaries, and questions. With the aid of a trained facilitator, teacher-participants read the case, identify its facts, and define for themselves the content and instructional issues at stake. The ensuing discussion will be as varied as the participants' personal questions and teaching experiences.
Developed by WestEd Laboratories' Carne Barnett, this process has been successfully tested in Los Angeles. The Professional Links with Urban Schools (+PLUS+) teacher network conducted the first local case discussions over two years ago among small groups of secondary school mathematics teachers.
Since then, case discussions have been introduced to K-12 mathematics and science teachers, including +PLUS+ workshops participants; LEARN change consultants, practitioners, parents, and students; and the lead teachers in Phase I of the Los Angeles Systemic Initiative (LA-SI).
Using cases concerning rational numbers that have been published in the collection Hard to Teach, Hard to Learn, teachers found their own mathematical knowledge strengthened as a result of raising complex issues. Imagine a three hour discussion prompted by one student's dilemma: "How can 100% of something be just one thing?"
A group of high school mathematics teachers is currently investigating, with the support of LA-SI, +PLUS+, and LAEP, the possibility of drafting mathematics cases based on real events in LAUSD classrooms. A possible theme might build upon the work of Leadership for Urban Mathematics Reform (LUMR) teachers and address the question "What is Algebraic Thinking?"
As we continue to search for more effective teaching tools, curricula, and ways to engage and motivate students in mathematics and science across LAUSD, this "first real professional development" may deepen the discussion.
A parent who participated in a discussion of "Bounce, Bounce" (which involved predicting the height of a ball on the eighth bounce and revealed student misconceptions about remainders, the perception and description of "patterns," and the relationship between subtraction and division), exclaimed, "I can't believe that teachers don't do this every work day!"
