An electronic newsletter for the science education
community
May/June
2005
Goals-Based Mathematics
Study Produces Unique Data Set
Videotaped lessons
aid analysis of changes in teacher practice
At the end of three years of data collection for Project
2061’s study Improving Mathematics Teacher Practice
and Student Learning through Professional Development,
researchers have collected hundreds of hours of carefully
selected videotaped lessons taught in middle school mathematics
classrooms. Project 2061 researchers have recorded the
lessons to explore how the interactions of curriculum
materials, teaching practices, and professional development
can lead to improved student learning in mathematics.
The five-year
study—being conducted in partnership with the University
of Delaware and Texas A&M University—is funded
by the Interagency Education Research Initiative (IERI),
a joint program of the National Science Foundation, the
Department of Education, and the National Institute of
Child Health and Human Development.
(Read
an overview of the study.) Preliminary analysis of the classroom videotapes
provides insight into possible answers to one of the study’s questions:
How does professional development and ongoing support that is focused on specific
mathematics learning goals build teacher knowledge and lead to more effective
teaching practices?
To detect any changes in teacher behavior as a result
of the study’s professional development interventions,
researchers videotaped teachers over the course of two
or three years teaching the same set of 3–5 lessons.
The lessons were selected because they address important
concepts and skills related to Number, Algebra, and Data.
These same mathematics learning goals were also the focus
of the study’s professional development and its student
assessments. While there are other collections of videotaped
mathematics lessons, this one is unique in documenting
how teachers’ approach to the same set of lessons,
which targets specific learning goals, changes over time
and in response to specific kinds of feedback and support.
The videotaped lessons are also being correlated with test
data showing the extent to which each teacher’s students
have achieved the targeted learning goals. When complete,
the study results will provide an unmatched resource
for mathematics educators and researchers.
About the Professional Development
Prior
to the videotaping, teachers participated in a two-day
workshop that included an introduction to and clarification
of the Number, Algebra, and Data learning goals being targeted
by the study. Videotaped lessons from the first two years
were then used in the design and delivery of ongoing
professional development. Videotapes from Year 1 revealed
trends in teacher practice across teachers and curriculum
materials. Based on those first year trends, researchers
chose to concentrate professional development for the
subsequent years on three areas where research has shown
that teachers’ practices
can make a significant difference in students’ mathematical
understanding: (1) teachers’ use of mathematical representations,
(2) teachers’ ability to probe their students’ understanding,
and (3) teachers’ ability to guide their students’ interpretation
and reasoning.
Professional development following the second year of
videotaping built on the three areas studied the previous
year, and was expanded to help teachers examine evidence
of student understanding. Teachers viewed the videotaped
lessons to analyze their own and others’ practices,
focusing particularly on the extent to which students were
encouraged to express their ideas in the classroom and to
demonstrate their reasoning. They also looked at student
responses to specially-designed assessments to see how well
students were learning the mathematics in the target learning
goals.
As we wrap up three years of data collection, we are
in the early stages of data analysis. We now have the
video data from two or three years in a classroom that we
can examine for change in a given teacher’s practice.
Researchers have begun to take a qualitative look at
some of the teachers’ videos, while a quantitative
analysis will be undertaken with the assistance of a Web-based
computer program designed by Project 2061 for this study.
The program allows analysts to document what is happening
in lesson segments, to rate the teaching on very specific
indicators related to criteria for evaluating teacher practice,
and to produce numeric ratings and detailed summaries and
justifications. The preliminary results from one case study
illustrate the kinds of changes in teacher practice we hope
to find in the videos, which we hope will correlate with
the student assessment results.
Mr. Smith* Makes a Leap: A Case Study
Mr. Smith is a veteran mathematics teacher in a
rural-suburban school in the middle Atlantic region of the
U.S. He is experienced using a mathematics curriculum material
that was highly rated in Project 2061’s middle
grades mathematics textbook analysis. Mr. Smith has
participated in professional development for three years
and provided researchers with a three-year video record
of him teaching the same lessons in his sixth grade mathematics
classroom. The lessons focus on the learning goal stating
that students should be able to “use...numbers in
several equivalent forms such as integers, fractions, decimals,
and percents” (AAAS, 1993, p. 291; see
benchmark 12B6-8#2). While the design of the lessons
intends that most of the class period be used by students
to explore the mathematics through activities in the curriculum
material, researchers found a very different climate in
Mr. Smith’s classroom in the first two years of videotaping.
For the purpose of illustration, we will focus on one
lesson. The lesson is designed to have students investigate
the concepts of comparison and equivalence of fractions.
Our first analysis of the lesson was qualitative in nature.
Researchers simply watched the videos from the three years
and characterized the nature of the teaching each year.
The videotapes in Years 1 and 2 show the teaching to
be strictly teacher-directed: Mr. Smith does most of the
talking and does not listen to the students. In some instances
when he asks for student input, he re-voices student responses
to articulate his understanding or his agenda. In both years,
he adds in the same “extra activity,” one that
is not in the material. While this activity is not incorrect,
it leads to confusion on the part of students and detracts
from their understanding of the mathematics. The “Launch” or
introduction to the lesson and the mathematics is lengthy,
while the “Explore” part of the lesson is brief,
even though the curriculum intends it to be a significant
part of the class period in which students have the opportunity
to work with and reason through the mathematics. As a consequence,
students have limited opportunities during the lesson to
contribute and express their understanding. The few interactions
that the teacher does allow with students are brief, on
average less than 1 minute in length.
In Year 3, a metamorphosis appears
to take place. Students take the stage with a voice and
a more active role in their learning. Mr. Smith is listening
to them, as a whole class and in small groups, and is using
evidence from what students say to move the lesson forward.
The introduction to the mathematics is brief and clear,
and students’ exploration of the mathematics expands,
as designed in the curriculum. There are many opportunities
for students to express their understanding and the teacher’s
interactions with students expand to an average of 3 minutes
each. Mr. Smith exhibits confidence in his knowledge of
the mathematics and the lesson.
After gaining this qualitative perspective, researchers
moved to a quantitative analysis—a necessary step
in order to examine a teacher’s practice, during a
single class and from one year to the next, with an objective
lens. Researchers wanted to find out (1) if the quantitative
analysis would capture the character of the teaching that
was suggested in the preliminary examination of the videos;
(2) if the quality of the teaching from year to year could
be differentiated by the ratings of the criteria; and, in
the case of the criterion “Encouraging students to
explain their ideas,” (3) if the indicators of meeting
the criterion would capture a change in the quality of student-teacher
interactions. Researchers took this opportunity to determine
if the Web-based program being used for quantitative analysis
would corroborate the characterization of the teaching.
“Encouraging students to explain their ideas” is
one of a subset of five criteria researchers selected
for the quantitative analysis. This criterion requires that
the teaching routinely encourage each student
to express, clarify, justify, interpret, and represent his
or her knowledge/understanding about the mathematics
and provide accurate
and helpful feedback to students. When
Mr. Smith’s lessons over three years were measured
against this criterion using the quantitative analysis,
researchers found that preliminary results do indeed
bear out the initial characterization, as illustrated in
the following graphic.
![[Figure] Results: Encouraging Students to Explain Their Ideas](images/ieri_fig1.gif)
Each bar in this chart represents one class period, for
the same lesson, for each of the three years. The dark dotted
lines denote the beginning and end of the main parts of
the lesson (i.e., the teacher’s introduction of the
lesson and the student exploration of the mathematics) and
the light dotted line denotes the point at which the teacher
moves from the introduction to the exploration. The colors
coordinate with the ratings to illustrate the quality of
student-teacher interactions when students are explaining
their ideas and understanding about the mathematics.
In Years 1 and 2, there is a lot of time during which
there is no student interaction with the teacher, as shown
by the white segments. The teacher is talking; students
are not contributing to the conversation. The shaded segments
show that students had a few opportunities to share their
ideas and understanding, but for the most part the quality
of those comments is fairly low, as represented by the light
shading. These instances may have been times when students
were asked to respond to a question but were not asked to
give further explanation or clarification; when only one
or two students were called on; or when the teacher did
not provide helpful feedback.
In Year 3, the frequency and quality of student talk
is dramatically increased. The lesson introduction is brief,
students move quickly into a lengthy exploration of the
mathematics, and the quality of the student talk is high
throughout most of the lesson, as denoted by the dark shading.
While this is only preliminary and partial data of one
case study, researchers are encouraged by the results,
both in the change in the teacher’s practice and in
the way that the change has been captured using our analysis
tool. As third year assessment results are scored and
analyzed, a clearer picture should emerge about how changes
in teacher practice influence student understanding of the
mathematics.
* Teacher’s name has been changed.
# # #
For more information about this study, please contact:
Senior Program Associate: Dr.
Kathleen Morris
Principal Investigator: Dr.
Jo Ellen Roseman, (202) 326-6666
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