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 
Outcomes 
Characterizing
elements of environment for teaching 

Interviews
with various stakeholders: faculty, president, vicepresidents, 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 parttime 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, precalculus) 
Descriptions
of uses of elements of highquality 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 K12 education? What is the
quality of the textbooks used in the courses? 
Characterizing
students' attributions about their ability to learn mathematics 

Adapted
PALS^{5} survey for students and instructors To
all students of these teachers, including nonstudy classes. 
Realistic
descriptions about who are the students who take precollege 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 
Outcomes 
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' inclass 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' inclass 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? 