| In recent years, examples from mathematics classrooms have been used to engage pre- and in-service teachers in conversations about teaching and learning mathematics. Critical lesson incidents, or "cases," have been presented through a variety of media, including written vignettes, classroom video segments, teacher journal excerpts, and other artifacts and descriptions of mathematics education practice. The "Investigations in Teaching Geometry" CD-ROM is an integrated media case centered around a three-day lesson sequence on geometry. | It features video, text, and graphic information that provides an authentic context in which teachers can explore issues raised in recent mathematics reform documents. The materials were developed at Vanderbilt University for use by elementary and middle school mathematics teachers. Materials of the case include: QuickTime movies from the fifth-grade class and interviews with the teacher, scanned images of students' work, the teacher's lesson plans, information from the NCTM Standards, and related literature references and abstracts. |
| The Overview of Lessons button accesses a video-based description of the lesson sequence. This overview, which is narrated by the teacher, provides background information and planning decisions. | The Investigations button leads to a screen containing a description of each of the four activities: Planning and Teaching the Lessons, The Teacher's Role, Assessment of Student Learning, and Key Mathematical Ideas. | The hypermedia tools (including the Hypertext Notebook and Floating Clipboard) are available throughout the program to enable users to record notes or link video for later analysis. |
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The Planning and Teaching interface pictured to the left contains a table of issues that influenced the teacher's planning and decisions in these lessons. By clicking a bullet to indicate the specific issue and lesson day, the user can view the corresponding classroom video segment, the related teacher commentary, and the lesson plan reference. The purpose of this tool is to help viewers see the links between how the lesson was planned, how it was actually implemented, and how the teacher reflected on the incident. |
| The Teacher's Role | Key Mathematical Ideas |
|---|---|
 This series of questions relates to pedagogical and content issues that arise during the lesson. One example question is shown above. After viewing the classroom video showing the children building boxes, the user can simulate the classroom activity by clicking on squares in the grid in order to see the resulting boxes. This simulation was included to help viewers visualize how the classroom students constructed boxes with uneven sides. |
During the three days of instruction, the children
engaged in a series of investigations designed to provide a context for a number of important mathematical ideas. This section of the program provides background for these concepts and suggests additional investigations, some of which may be appropriate as extensions to the lessons shown in the video. |
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This investigation enables teachers to compare students' growth across time as well as to view how different students approached a given assignment. The data base contains scanned images of each student's written work and video clips of different pairs working on the same assigned tasks. For example, these data enable teachers to note the development of children's computational strategies for determining the number of cubes that would fill the boxes. These notes can be entered into the "strategy" field for later analysis. The fields can be sorted by name, assignment, or strategy in order to derive an overall feel for what strategies the students were using or how they progressed over time. |
| In addition to providing questions to guide investigations, the program contains technological tools that allow users to make notes and highlight various points with video segments. These tools, which are available from all activities, can be used by teachers to develop | HyperCard stacks summarizing their analyses for whole-class presentations. The set of integrated media tools includes a Hypertext notebook with text export options, a video index for quick access to various segments, and a floating clipboard for making notes. |
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The Video Index enables users to access different segments by either clicking on the picture or segment description. This index facilitates the process of identifying various activities and students in the videos for use in the Hypertext notebook. |
| The Floating Clipboard is available for use at any time to make text notes. Viewers may want to use it to make notes about questions for discussion. Text entered in this notebook can be exported to an ASCII file. |  |
Faculty: |
Graduate Students: |
Programmer: |
Teacher: |
| Dr. Linda Barron Box 330, Peabody College Vanderbilt University Nashville, TN 37203 voice: (615) 343-6149 e-mail: Barronlc@ctrvax.Vanderbilt.edu |
Dr. Elizabeth Goldman 221 Kirkland Hall Vanderbilt University Nashville, TN 37240 voice: (615) 343-3224 e-mail: Goldmaes@ctrvax.Vanderbilt.edu |
This work is supported by grants from the National Science Foundation (#TPE-8751472, #TPE-8950310, #TPE-9053826, and #TPE-9154067). Any opinions, findings, or conclusions expressed are those of the developers and do not necessarily reflect those of the National Science Foundation.