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

Vilma Mesa

Overview of the Grant

Year 1: Sensitizing Studies

The main goal of the work is to understand the context in which mathematics
teaching occurs at this college. The guiding questions are:
• What are the shared visions about mathematics teaching?
• What happens during mathematics instruction?
• What is the quality of the textbooks and tasks?
• What are students’ attributions about their ability to learn mathematics?

Our data sources and outcomes are outlined below. In the next pages we present
some preliminary findings about these aspects of the grant.

Data Sources


Characterizing elements of environment for teaching

Interviews with various stakeholders: faculty, president, vice-presidents, deans, faculty development group, union representatives

Document analysis

Explicit and de facto vision regarding students' success; other stories about students' success; differences between full- and part-time instructors. To what extent are these contexts effective environments?

Characterizing instruction

Classroom observation and audiotaping; lesson plans, lecture notes, handouts, instructor post interview

Three lessons from a stratified sample of 11 teachers (college algebra, trigonometry, pre-calculus)

Descriptions of uses of elements of high-quality teaching during instructions; specifications of what are the different modes of teaching in community college math. To what extent are these instructors effective?

Characterizing the nature of tasks and classroom interactions

Lesson plans, classroom observation data, videotaping, post instructor interviews

Analysis of content of textbooks and handouts used.

Level of cognitive demand of the tasks; public discourse; Opportunities to learn afforded to the students. How are these descriptions different from our current descriptions of enactment of tasks in K-12 education? What is the quality of the textbooks used in the courses?

Characterizing students' attributions about their ability to learn mathematics

Adapted PALS5 survey for students and instructors

To all students of these teachers, including non-study classes.

Realistic descriptions about who are the students who take pre-college mathematics classes in community colleges and the implications this knowledge has for practice. To what extent are these students different from our typical undergraduate mathematics student?

Years 2 to 4:

The purpose of the work these years is to understand what does it take to efficiently
and effectively

• Use student feedback for lesson planning?
• Handle student productions in tasks during instruction?
• Make evident verification strategies while solving problems?

Planned data sources and outcomes are outlined below.

Data Sources


Student feedback

Journaling on the design of the probing activities that use classroom assessment techniques; Interviews with instructors prior and after using the activity; Classroom observation and videotaping; Students' responses to the assessment; Lesson plans and lecture notes.

Six instructors testing different conditions for feedback use

Descriptions of the process by which instructors use student feedback as an instrument for planning; records of students' misconceptions: What does it mean in practical terms to alter plans for instruction? In which cases is it justified? How do instructors process students' learning feedback? How do instructors justify the modifications? How do students perceive the process?

Students' public discourse

Classroom observations and audiotaping; Field notes of students' in-class work and questions; Stimulated recall interviews with instructors and 4 to 6 students.

Descriptions of the process by which instructors use students' solutions and questions to change the interaction in the classroom: what does it mean to change the responsibilities for providing correct answers? How do instructors and students perceive those moves?

Verifying solutions

Classroom observations and audiotaping; Field notes of students' in-class work; Students' worked solutions

Descriptions of the process by which instructors make explicit reasons why answers to tasks are correct: when is it productive? How do students assimilate the process?