More than 20 years ago Shulman (1987) wrote a seminal paper about the kinds of knowledge and behaviors that teachers needed to possess and use in order to be effective practitioners who approached teaching with “educational reform” values that emphasized comprehension, reasoning, and reflection. He called for research that was based on actual observations in the context of specific teaching and learning situations of novice and expert teachers.

This call was heeded by researchers in the field of mathematics education. However, the majority of studies on what makes mathematics teachers effective tended to focus on documenting the occurrence of commonly agreed upon but pre-determined best practices of teachers rather than on direct observation of effective teachers to determine what these processes were (e.g., Bewwick, Swabey, & Andrew 2008; D’Agostino & Powers 2009; Graeber 2005; Hill, et al. 2008; Jamar & Pitts 2005; Morris, Hiebert, & Spitzer 2009). While this approach is valid for collecting evidence to support existing assumptions about effective teaching, it does not lead to new knowledge about what actually makes teachers effective. As Deborah Ball (2008) points out, we still do not know exactly what distinguishes effective teachers from less effective teachers based on classroom-based investigations of teachers themselves. If we are to really understand and prepare teachers to be consistently effective practitioners with all students in these times of teacher accountability and evidenced-based practices (NCLB 2002; NCTM 2008; CCSS 2010), then we need to study the teachers who are most effective and study these effective teachers in a variety of schools and communities.

 This presentation will share a description and analysis of case studies of four elementary teachers who were identified by their principals or supervisors as particularly effective in teaching mathematics. The teachers were part of a larger study investigating the behavioral and cognitive decision-making processes used by 15 effective elementary mathematics teachers working in a variety of cultural, language, and socio-economic settings in northern New Jersey and in Israel.

Research Questions and Design

My two general research questions were:

1)What do effective elementary mathematics teachers do and think about in planning and reflecting upon their teaching and students’ learning?

2)To what extent do culture and context impact on what these teachers do and think?

For a larger study, I conducted observations and interviews with 15 effective elementary school mathematics teachers in urban and suburban communities in New Jersey public schools and in four public schools in Israel. The teachers were identified as effective by either their supervisors, principals, or their mathematics coaches based on their perceptions of the teachers as being able to promote successful student learning. All teachers were female with 3 or more years of teaching experience in grades 2 – 6. The study involved visiting schools where each teacher was individually interviewed in response to 12 specific “trigger” questions regarding her planning processes before her lesson was observed. After the interview each teacher was observed doing the lesson discussed. Following the observation, each teacher was interviewed again in response to 10 other specific “trigger” questions regarding their perceptions and reflections on how the lesson went in terms of the plan and the children’s learning.

Israeli teachers were asked questions in English and could answer in English or Hebrew. A Hebrew translator was present at all interviews in Israel. The interviews were audio-recorded and the classroom observations were videotaped. The lessons lasted anywhere from 45 minutes to 1 ½ hours. Subsequently, annotated transcripts of the interviews and observations were made, including translations of the Israeli teachers as needed.

Data Collection Techniques and Analyses

This presentation highlights case studies of 4 of the 15 participating teachers based on their pre-lesson and post-lesson interviews. Two of the teachers were from northern New Jersey school districts and taught mathematics in Grades 1 and 2. Two of the teachers were from schools in Israel and taught mathematics in Grades 2 and 3. In each location, one of the teachers worked in a lower SES community and the other in a more affluent community. The interview transcripts of these participating teachers were examined for similarities and differences in their reported planning processes and reflective post-lesson reactions.

The transcripts were coded into pre-lesson and post-lesson categories using the interview questions as the source of categories. The codes were developed based on what the teachers actually said in response to those questions. The occurrence of these observational codes within categories were then matched and compared for all four teachers across and between geographical location and SES conditions.

Results and Conclusions

            The main finding was that there were 8 common practices reported on by all 4 teachers in both regions and 10 additional practices that were reported by 3 of 4 participants, although not the same 3 teachers for each of these practices. Among the common practices were: these teachers did not just work from the curriculum, but adapted lessons based on their past experiences in teaching the topics and used the Internet to obtain ideas for building their lessons. All indicated that they regularly used formative assessment for adapting lessons as they went along by observing, questioning, and listening to students’ oral comments during both whole group and small group or individual activities. All also indicated that they differentiated instruction by using different instructional materials and/or providing different levels of learning goals for their students, and then worked with individuals and small groups to review and relearn material after the whole group instruction took place. Finally, they all said that although they thought the observed lesson went fairly well (i.e., that most students had achieved the desired learning outcomes and remained on task), there were areas of the lesson that did not go well and that they would change the lesson accordingly in the future. The main areas of differences in responding were that the Israeli teachers indicated that they relied more on tests and quizzes than the New Jersey teachers and only the New Jersey teachers said they differentiated instruction to challenge the more advanced students. There did not seem to be any outstanding differences between SES settings across countries.

Summary of Findings

Interestingly, the most common practices could all be considered constructivist in orientation and indicated that regardless of region or school community, effective elementary mathematics teachers are student-centered, differentiate instruction, engage all students in active learning processes, and expect students to take responsibility for their own learning. Details and the implications of these and other findings will be discussed at the presentation.