A group of 30 middle school mathematics teachers participated in an on-going professional development experience that focused on analyzing student work to deepen their pedagogical content knowledge and improve their mathematics classroom instruction. This professional development experience, led by the district's mathematics specialist and teacher leaders, consisted of a two week introductory summer institute and academic year coaching sessions and workshops.
Throughout the year, teachers engaged in solving open-ended mathematics problems as a means to activate and deepen their understanding of the mathematics content addressed. They also participated in debriefing sessions where their mathematical solutions were used to examine multiple problem solving strategies, and to discuss ways in which students typically think about the mathematics problems.
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For example, a problem might ask solvers to come up with three ways to calculate the area of the figure shown to the left. Teachers would work in groups of three to four for about 30 minutes, followed by a full group discussion of the mathematics underlying each group's solution strategies, which ways students might approach the problem, and what those approaches might indicate about their understanding of the mathematics involved. |
Later, teachers used similar problems in their classrooms and partnered with a teacher leader/coach to analyze their own student work examples. First, the paired colleagues discussed and identified the students' levels of conceptual understanding based on the work samples. Then, using that information, they considered instructional strategies that would help to clear up any student misconceptions and/or that would engage students with the mathematics content in greater depth.
The emphasis on having teachers solve the mathematical problems first as learners was deliberately structured into the professional development design. It was found that when the teachers did not engage in solving and debriefing about student thinking of the problems, they were less able to provide students with additional instruction that built on their mathematical understanding and resolved misconceptions.
Elementary/middle school science teachers were engaged in study groups meant to develop their skill in examining student thinking and making instructional decisions based on the knowledge gleaned from their examination. Teachers were given a series of open-ended prompts, like the one below, to elicit their understanding of the flow of matter and energy in living systems.
| Student Prompt: At school you probably have a P.E./gym class, or maybe you play sports. Where do you get the energy you need to participate in those activities? If you are tired, what can you do to get more energy? List everything you can think of and explain what your body does in each of those examples to give you more energy. |
Based on their responses, facilitators engaged teachers in a series of discussions to deepen their understanding of the content. To further teachers' content knowledge in this area and to build teachers' skills in assessing students' thinking, teachers examined student responses, constructed by the group's facilitator.
Using a content framework that specified the targeted science ideas, teachers analyzed students' understanding of the content. They noted what ideas students seemed to understand, as well as which ideas students seemed to be missing or misunderstanding. Teachers were prompted to draw on evidence from the student work samples to support their analyses. This analysis prompted discussions about the targeted science ideas themselves.
Once reaching consensus about the students' understanding of the targeted content, teachers brainstormed what instruction should come next for these students based on the students' understanding. The facilitator led a whole group discussion in which the instructional teachers suggested moves were considered in light of both how well they targeted the content ideas and where students needed additional work.
After teaching a few lessons on the targeted content, teachers in the study group administered the same formative assessment prompt to all of their students. The focus of the next meeting of the study group was on their students' responses to this prompt. Teachers analyzed their students' work in small groups, and then discussed the implications of their students' understanding (or misunderstanding) for their next lesson.
During the course of these experiences, teachers came to an understanding that their ability to analyze student work, and make decisions based on this information, was dependent on the level of their content understanding. In addition, after developing some skill at analyzing student work, they began to identify aspects of their teaching that needed improvement.