Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Workshops 6 and 7

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Workshops 6 and 7

Graphing Unit

Barbara's unit on graphing demonstrates an approach to teaching math at Whittier that has developed from consideration of the NCTM standards and the California frameworks. The current curriculum is much more hands-on and includes substantial integration of mathematics and science.
 
In Barbara's classes, students must take more responsibility for their learning and are asked to share their understanding with their peers. Students work in groups, discussing problems, and seeking solutions. The teacher introduces the concepts and then the students continue their exploration through group problem solving.
 
Barbara's students bring to this unit of study some experience in computing the output ("y") when given the input ("x") and the rule (function) that describes the relationship between the input and the output. Also, they have had some practice in placing "xy" pairs within the Cartesian coordinate system.
 
human graph
To begin this study of graphing, the students go outside, into the school courtyard, to construct "human graphs." Groups of students take turns, using the input values on cards they've been given, in finding their places on the long rope that serves as the x-axis. Barbara reads the rule that allows them to compute the corresponding "y" value. They then move forward or backward to align themselves with that value on the rope that is the y-axis. Students not involved in forming a particular graph take notes relating the rule to its corresponding graph (e.g., straight line, parabola). They bring these notes back inside and translate the graphs to poster-size graph paper attached to the chalk board. Included in the class discussion about the graphs are Barbara's questions about how the students worked together (e.g., "How many of you found that while you were out there, forming this line, that someone helped you or you helped someone else?").
 
In continuing their study of graphing, the students examine various families of functions and explore the relationships between the functions and their graphs. Throughout the unit, a primary focus is on the production of high quality work, in the graphing of functions, in group problem-solving, and in presenting their results to their peers.
 
graph 
exhibits
In developing the unit, Barbara conferred with members of her Critical Friends Group. She expressed her desire to encourage students to be self-critical and to assess the quality of their own work and that of their peers. Her colleagues suggested that she engage her students in identifying the standards for excellent work.

Critical Friends Group Meeting

Barbara elicited from her students ideas which were incorporated into a set of standards for a "quality graph" and into a scoring rubric for group presentations. The students' involvement in developing assessment tools led to greater understanding of expectations for their own work and enabled them to more effectively assess their own performances and that of their peers.
 
Graphing Unit Rubric | Expectations and Goals | Evaluating Presentations | Student Ideas List | Poster Criteria | Group Test | Individual Test | Graph Exhibition Assignment

 

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