**Year**2017**NSF Noyce Award #**1240003**First Name**Karen**Last Name**Hollebrands**Discipline**Math**Co-PI(s)**Hollylynne Lee, NCSU, hollylynne@ncsu.edu

Molly Fenn, NCSU, molly_fenn@ncsu.edu

Laura Bottomley, NCSU, laura_bottomley@ncsu.edu**Presenters**Michele Cudd, NCSU, mdcudd@ncsu.edu

## Need

High school mathematics classrooms have been slow to change (Rakes et al., 2010). In 1979 Fey described a typical mathematics classroom as following a sequence of instructional activities that include: review of previous day’s assignments, brief explanation of new material, and individual ‘seat work’ (pp. 494-495). He also noted that secondary teachers tend to use whole class organization most often, individual work second, with small group work occurring least often. These activities are similar to the list of expected teaching tasks Haberman (2010) describes in her article on the pedagogy of poverty. For the past six years we have worked with preservice mathematics teachers to prepare them to teach in districts defined as high-needs. Many of our teachers accept jobs in districts with high rates of poverty. We were interested to know whether we would see different instructional methods and ways of organizing students than that reported by Fey (1979) and Haberman (2010).

## Goals

Beginning teachers were observed to document their organization of instructional work (i.e. whole class, small group, or independent work) and methods of instruction (i.e. discussion and sharing, teacher directed, student centered, or assessing student understanding) during five-minute intervals to investigate the following research questions: (1) in what ways do beginning teachers organize their students for learning and how frequently are various organizations utilized? (2) what methods for teaching mathematics do beginning teachers use when organizing their students as whole class, in small groups, and individually? and (3) are there differences in the ways teachers organize students for instruction and the methods teachers use when they are teaching different types of mathematics courses (ie. introductory, core, advanced)?

## Approach

Eight teachers, with six or fewer years of experience, were observed 31 times during the 2016-2017 school year. Teachers’ organization of students (i.e. whole class, small groups, individuals) and the instructional methods used (i.e. discussion and sharing, teacher directed, student centered, or assessing understanding) were documented in 5-minute intervals. Information about the course being taught was also recorded. These data were analyzed to address the stated research questions. Where necessary, randomization was used to determine the statistical significance of differences in results (StatKey).

## Outcomes

Across the sample, nearly half of instructional time was conducted with students organized as a whole class (48%); whereas, small groups were used 31% of instructional time and 21% of time was allocated for individual work. Collectively teacher directed methods occurred during 51% of observed class time, assessment took place 27% of time, student centered methods about 12% of time, and roughly 10% of class time was devoted to discussion and sharing. While teaching advanced courses, teachers organized students as a whole class significantly more often than while teaching core or introductory courses. With respect to teaching methods, beginning teachers designated significantly less time on assessment in advanced courses compared to core and introductory courses. Student centered methods were used significantly more often in advanced courses than in core and introductory courses. Other findings will be shared.

## Broader Impacts

Our findings show that whole class instruction still seems to be the predominant way high school mathematics teacher organize students for learning. What is interesting to note is that small group work appears more often than in the past. This may be a result of an emphasis on the use of small group instruction that has stemmed from reform documents and national organizations (NCTM, 1989, 2000, 2014). While organization and instructional methods are interesting to examine, a more in depth examination of high school mathematics instruction can provide additional insights to mathematics teacher educators about how to prepare future high school mathematics teachers.