(Page 5 of 7) - Sixth Grade Mathematics Teachers in Transition: A Case Study authored by Bergthold, Trisha. and Roddick, Cheryl.

and deepened as they came to view mathematics, both concepts and processes, as a connected
body of knowledge. For Celia, this growing understanding manifested itself as a desire for her
students to experience mathematics as connected as well. This led her to search for ways to
revise her curriculum and incorporate more algebraic reasoning and problem solving. The
turning point for Dee was that, as her understanding of the connectedness of mathematics
increased, she began to analyze more critically how and whether the textbook was actually
addressing the state standards. She came to realize that she could not just depend on the
textbook and began to rely on her own knowledge of mathematics and the standards to determine
the curriculum that worked best for her.

Perspectives

Pre-Workshop Perspectives

Both Celia and Dee believed that, in order to address the state standards, they needed to teach

from the textbook. They had both tried activities to supplement the book, with mixed opinions
about the effectiveness. Celia did believe, however, that activities were important to include in
her lessons. She commented in a journal entry, “I like to break up the routine and surprise them
with some fun days. I just need more activities that support the text!” One of her goals at the
time of the workshop was to develop an activity for each chapter of her text.

In a pre-workshop interview, Dee conveyed great concern about the standards and the need

to cover everything, but felt she didn't have a lot of time to "stray from the book." In addition,
she felt that routine practice was valuable for her students, and was not convinced of the value of
the regular use of activities in mathematics instruction.
Changes in Perspectives

For Celia, the intensive workshop was a catalyst for complete revision of her perspective on

teaching. She began to rethink how, what, and why she was teaching, and decided to make
major changes, starting with the review material in the first chapter. Instead of reviewing, she
believed that a unit on problem solving would point her students in the direction she wanted to
go for the rest of the year. She also came to view patterns as a central theme throughout the sixth
grade mathematics curriculum. Furthermore, Celia, who was also teaching a seventh grade
mathematics class, realized that the same activities she used for sixth graders could be adapted
and extended for her seventh graders.

Dee, who has always been reflective about her teaching, began to reflect more upon effective

ways of teaching. For example, during the Perfect Party Place activity, students created many
table arrangements that were not rectangular. This unexpected outcome of the lesson led into a
very nice discussion about the definition of a rectangle, whether a rectangle can have "holes,"
and how to find the area of the shapes that were made. This activity was an important one for
Dee. She realized that, although her sixth graders were adept at applying the formulas for area
and perimeter, these concepts had not been previously well developed. In a follow-up discussion
of this activity, Dee commented how valuable this lesson was for her students, and although she
had spent more time on the activity than originally planned, she strongly perceived the time to be
well spent.

Teaching Practices

Pre-Workshop Practices

For Celia, a typical day began with warm-up exercises, followed by “giving notes,

introducing an activity, or reinforcing concepts”, after which homework would be discussed and
students would start their work. Once each week, she gave a basic computation test that all 6

grade students took and once each week, she assigned a single word problem or puzzle