**An electronic newsletter for the science education
community**

** 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.

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** **

**References**

American Association
for the Advancement of Science. (1993). *Benchmarks
for science literacy*.
New York: Oxford University Press.