Illustrations of deepening knowledge of student-level disciplinary content

An illustration of deepening knowledge of student-level mathematics disciplinary content

Over the course of several months, six, two-hour professional development sessions on probability were delivered over interactive video. About 15 middle grades teachers (mostly grade 6) from several sites participated in all six sessions. The sessions were scheduled in response to substantial expansion of the probability objectives for grade 6 in the state's Standard Course of Study. Sessions were organized around Navigating through Probability in Grades 6-8 (National Council of Teachers of Mathematics, 2003); each teacher had a copy of the book. Major ideas in the four chapters of this book were highlighted.

Most of the teachers had limited experience with the ideas of probability. Many of the teachers were elementary-licensed and had not taught probability much in previous years. Even organizing outcomes of rolls of two dice in a chart seemed unfamiliar to some of the teachers. As problems were presented, participants worked together within their local sites. Debriefing was begun by calling on one of the sites to share the work at that site. Much of the focus of the debriefing centered on the ways that information was organized to create a solution. Highlighting examples of ways to organize information seemed to help teachers become more articulate about their work.

The most influential tasks involved "off center spinners" and geometric representation of probabilities.

As with most teachers, participant understanding of what makes a spinner fair was cast in terms of the area of regions rather than the measure of the central angle around the spinner's center. Asking them to work with off-center spinners seemed to challenge their thinking in constructive ways, forcing them to reorganize their understanding of critical attributes of spinners. Many of the teachers predicted that the spinner shown to the right would generate almost no blue outcomes; their explanation was that the "blue area" was relatively small. When their data did not match this prediction, they began to think differently to make sense of why blue occurred more than they initially expected.

An illustration of deepening knowledge of student-level science disciplinary content

A four day-workshop for high school teachers focused on learning biotechnology, a topic often taught in high school. The participants had a range of teaching experience with biotechnology; some teachers had taught it for several years, and others were teaching it for the first time. The goals of the workshop were to deepen teachers' knowledge of the fundamentals of biotechnology and develop their understanding of how to teach these ideas. The workshop strategy was immersion in the content that teachers are expected to teach.

During the workshop, teachers had opportunities to engage in inquiry-based explorations that were intended to address the molecular basis of heredity and the relationship between biology and technology, both included in the National Science Education Standards for Grades 9-12. Teachers experienced three different stages of learning during the workshop. First, teachers worked through several activities from a Biological Sciences Curriculum Study high school biology program. This experience allowed teachers to review the basics of DNA science and to consider how they might be taught to students. Next, teachers learned the technique of restriction enzyme analysis using gel electrophoresis. This activity was first conducted as a "dry lab" or simulation of the technique, and then a "wet lab" to practice the actual technique. The third phase of the workshop involved applying the technique of gel electrophoresis to learn about DNA sequencing. As one of the facilitators shared, "The content of the workshop got progressively more challenging with each day. In all three parts, teachers were given real-life problems to solve in teams of 2-3 [to] produce a product that could be peer reviewed." For example:

Imagine that you are a scientist helping police to investigate a violent crime. The police have reason to believe that a blood sample collected at the scene of the crime comes from one of two suspects. The police provide you with the blood sample from the scene and with blood samples from the two suspects. Brainstorm your ideas about how you would use biotechnology to provide evidence linking either of the suspects to the crime.