NSF CAREER — Teaching Mathematics Well in Community Colleges: Understanding the Impact of Reform-Based Instructional Resources

Vilma Mesa

Classroom Participation

We analyzed classroom interaction in order to get a sense of the context in which learning occurs at the community college. We looked at the quantity and quality of student participation, the ways the instructor encourages classroom interaction, and the knowledge and cognitive engagement required of the students.

We created transcripts of audio recordings from three consecutive lessons and classroom maps from each lesson that indicate where each student sits, personal characteristics (e.g., gender, ethnicity) and the number of times each student asks a question or gives an answer. The instructor’s position and the number of questions he or she asks and responds to is also indicated.

We performed three analyses:

• Surface characteristics of classroom interaction: Using the classroom maps we got a visual distribution of classroom participation and information for estimating the average number of student utterances and to contrast them by gender or minority status. These averages allowed us to seek similarities and differences across classes observed. We used the transcripts to estimate the length of students’ and instructors’ utterances and the number of turns taken.
• Types of instructor questions: We sought to classify the questions instructors ask depending on whether students respond to them or not. Four types of questions (Statement-Right?, Rhetorical Question, Question Wait, and Question No-Wait) constituted questions for which no answers were given. Initiation-Response-Evaluation sequences with variations and other questions that were not in the IRE form but were answered constituted the types of questions for which responses were given.
• Knowledge and cognitive engagement of students: We aim to understand how classroom structure and activities aid in student learning and cognitive engagement. We attempted to parse transcripts for activities (using Mesa, 2009) as well as purpose (using the TIMSS video coding, U.S. Department of Education & National Center for Education Statistics, 2003).

Key Findings:

There is variation between the instructors in all the analyses done so far.

Surface Characteristics

• In general student participation is low (compared to data from developmental courses collected last year, Mesa, 2009)
• Participation is concentrated on a few students (in 7 of the 10 classes, 3 students contribute more than 60% of the utterances, with 3 students contributing an average of 62% of the utterances)
• Women and minorities participate less frequently than males or White students
• The main mode of delivery is lecture.

Percent of Students Who Participate

Instructor Questions

• About 26% of the questions instructors ask do not require a response, of those questions that a response is expected, about 57% are answered, and about 43% are not answered.

• Students’ contributions to the class are not very elaborate grammatically: 75% of their contributions are 1 to 5 words.

Average Number of Turns Each Class

Knowledge and Cognitive Engagement

• Activities: Due to the nature of instruction (lecture) in most of the courses we observed, it was difficult to determine what constitutes an “activity” in this setting. We continue to discuss this.
• Purpose: We have looked at transcripts from two instructors, one of whom has a fairly consistent purpose across the lesson (presenting/practicing new material with the instructor leading) and one of whom has divided purpose (including warm-up activities, presenting/practicing new material, and student individual seat-work).
• This is an area in which we are in need of guidance in order to create a systematic and reliable way to characterize the quality of the mathematical demands that are present in these classes.

Next Steps:

• Analyze the contingencies in which patterns of questioning occur and of the follow-up moves in instructors’ discourse
• Determine the level of cognitive engagement that occurs in these classrooms