SED 535 Contemporary Mathematics Teaching Assignment Due: December 2, 2008

Read: Jacobs, J., Hiebert, J., Givvin, K., Hollingsworth, H., Garnier, H., & Wearne, D. (2006). Does eighth-grade mathematics teaching in the United States align with the NCTM Standards? Results from the TIMSS 1999 video studies. Journal for Research in Mathematics Education, 37(1), 5-32. (I will email)

Write to submit: The study by Jacobs et al. examines video from 1995 and 1999. You have been commissioned to conduct the 2008 follow-up study. Because of limited funds, you can only videotape a small sample of math classrooms: ones in your school and ones taught by people you know.

1) Write the executive summary of your study, describing the alignment between mathematics teaching in 2008 and the NCTM Standards. In 2-3 sentences per each of the five Process Standards, describe the trends in teaching since the 1999 study.

2) In an additional 1-2 paragraphs, provide your expert opinion about why these trends have occurred.

Video Presentations:

Be prepared to present your video analysis next week (there won’t be time for all; some will present on the 9th). You’ll have 15 minutes per person to present in the following format:

(5 minutes) Present to your group:

• Background information—only what’s necessary for the next parts.
• Your analysis and reflection on one important part of your discussion facilitation and your effectiveness in promoting understanding and/or autonomy during this part.
• A question for your group to discuss that would help you interpret your students’ responses during this part and/or plan for better facilitation in the future.

(10 minutes) Facilitate a group discussion to answer your question.

Thought for the week:

The difficulty of studying learning—and teaching—lies, in my view, in the fact that it demands the study of the processes by which children come to know in a short time basic principles…that took humanity thousands of years to construct. H. Sinclair, 1990

Major research findings regarding Complex Instruction or groupwork:

1) Students’ rate of participation in the classroom is strongly linked to learning gains.

· At the classroom level, the proportion of students talking and working together positively predicts the class’s average learning gain.

· At the individual level, a student’s rate of participation in a small group is a significant predictor of her learning gains.

· Gains are documented for both high and low-achieving students.

2) Students in cooperative learning settings experience more discovery learning, use more high-level reasoning, and spend more time on task than students in an individual learning setting.

3) Cooperative learning has been shown especially to benefit English language learners and minority students.

· ELs learn English faster when engaged in meaningful interaction with native English speakers in both academic and personal contexts.

· In a major study of a bilingual Complex Instruction program implemented in working-class, largely Latino schools, students who started with limited or minimal English proficiency gained significantly in English, even though much of their group discussion was in Spanish. At the same time, these students showed greater gains in reading, science, and mathematics than national norms predict for similar students.

· Other studies find that math classrooms using more cooperative learning and less individual seatwork promote higher achievement among girls, African American, and Latino students.

4) Certain features of Complex Instruction are important to achieving student results, and teachers must deliberately build these into the structure.

· One is having mechanisms for both group and individual accountability.

· Another is to assign roles to group members and train them for these.

· One study showed that the use of facilitators boosted the rate of group members’ talking and working together.

Examining Group-Worthy Tasks

Big Idea:

¨ Is the organizing concept or big idea – a big idea indeed? How do you know?

¨ How central is the concept to the discipline?

Multiple abilities:

¨ Do the resources incorporate multiple representations/ ways of understanding/ ways of presenting information?

¨ Is there a tight connection between the resources and the activity?

¨ What are the multiple intellectual abilities called upon to access the task? To complete the task?

¨ How will these multiple abilities enhance students’ access to reading and writing?

Open-endedness:

¨ What is the problem to be solved in the activity?

¨ Is there a right or wrong answer, or an “expected” answer? (Is the answer “It depends?”)

¨ Are there different ways of arriving to a possible solution?

Interdependence:

¨ Is there enough to do for a group? Is the activity rich and complex?

¨ Is there a group product? What is the relationship between the group product and the discussion questions? And the resources? Are there group data collected among members?

¨ How is the group discussion essential for producing a quality product?

Individual accountability:

¨ Are individual reports included in the activity? Are they tightly connected to the activity? To the big idea/ central concept?

¨ How will the group discussion become critical for a student completing the individual report?

Assessment:

¨ Are there clear evaluation criteria for group product and group process? How are they stated?

¨ How will you assess what students are learning as they complete this activity?

(complied by Dr. Rachel Lotan, Stanford University)