Workshops 6 and 7
 |
| 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. |
 |
| 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. |
 |
| 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. |
 |
| 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 |
|
