The purpose of this session is to examine the mathematics instructional quality in two sets of elementary school classrooms.  The first set of classrooms primarily has students of low socioeconomic status (SES), defined by their eligibility for free or reduced lunch.  The second set of classrooms primarily has students of middle or high SES.  Mathematics instructional quality includes two key components, mathematical discourse and tasks (NCTM, 2007).  Three research questions guide our work:  (1) What is the nature of the discourse and the tasks in elementary school classrooms with primarily students of low SES?  (2)  What is the nature of the discourse and tasks in classrooms with primarily students of middle or high SES?  (3)  What are the similarities and differences in discourse and tasks between the two sets of classrooms? 

Theoretical Framework

Comparisons of industrialized countries on international assessments (Cooke et al., 2005) and examinations of achievement gaps between various groups (e.g., Lee, 2002, Caro, 2009) warrant attention to mathematics instruction in the United States.  One group who warrants particular attention is students of low SES.  Extensive research has been conducted that offers conclusive evidence of a positive relationship between SES and academic achievement (Jordan & Levine, 2009; Sirin, 2005).  However, there is a lack of research focused on the experiences of low SES elementary students. 

Researchers in mathematics education (e.g., Lampert & Blunk, 1998) and NCTM (2000, 2007) emphasize that discourse is an important component of school mathematics because it is a central part of what and how students learn.  A teacher’s role is significant in facilitating discourse and can be a primary source of support for student learning of mathematical concepts (Yackel, Cobb, & Wood, 1991).  Typically, teachers are made aware of the importance of discourse patterns other than initiate-respond-evaluate (IRE) (Mehan, 1979).  Communication in classrooms with an IRE discourse structure is often dominated by teacher talk focused on making sure students understand mathematical procedures rather than concepts (Franke, Kazemi, & Battey, 2007).  In contrast, multidimensional discourse moves beyond IRE and focuses on sense-making of mathematical ideas (Franke et al., 2007).  The teacher asks students to explain and justify their strategies, pushing for mathematical meaning behind the tasks.  Ball (1993) and Yackel & Cobb (1996) found elementary school students engaged in explanation and justification when their teachers expected and modeled these processes.  When Lubienski’s (2000) own middle school students of low SES struggled with multidimensional discourse, she suggested they would benefit from explicit modeling of how to communicate mathematical ideas. 

A task is a classroom activity during mathematics instruction designed to focus students’ attention on a mathematical idea (Stein, Grover, & Henningsen, 1996). When selecting a task for a mathematics lesson, one characteristic to consider is its level of cognitive demand, based upon the type of thinking required of students (Stein et al., 2000).  While research has indicated that deeper cognition during a mathematics lesson increases students’ engagement (Boaler & Staples, 2008), lower level tasks are prevalent in mathematics lessons (Hiebert et al., 2005).  Tasks of higher level cognitive demand could perhaps benefit elementary students of low SES, who often become disengaged in school (Condron, 2007). 

Data Collection and Analysis

Through purposeful sampling, participants include teachers and students in 10 fourth-grade classrooms from a large, suburban, mid-Atlantic school district.  Five classrooms have primarily low SES students (receive free or reduced lunch).  The other five classrooms have primarily middle/high SES students.  Three videotaped mathematics lessons from each classroom are analyzed, for a total of 30 lessons (15 for each set of classrooms).  This study uses a case study, qualitative research design with each set of classrooms as a case.  There are two levels of analysis: (a) an individual analysis of each of the two cases, noting themes that arise from the 15 videotaped observations for that case; and (b) a cross case analysis (Yin, 2009) to find similarities and differences between cases.

To guide the analysis of the discourse and tasks in each lesson, we use two existing frameworks from the literature.  First, Hufferd-Ackles, Fuson, and Sherin (2004) provide a framework for classifying discourse through “levels” of math talk.  The four-part framework outlines whether the teacher or the students are: questioning, explaining mathematical thinking, the source of mathematical ideas, and responsible for learning.  Second, in their task analysis framework, Stein and colleagues (2000) outline how higher level tasks require students to connect procedures to mathematical concepts or to engage in complex, non-algorithmic thinking.  On lower level tasks, students perform exercises they have memorized or procedural steps with no conceptual connections.

Preliminary Findings and Discussion

Preliminary findings in this study provide insights into the data.     

• IRE discourse is predominant in both sets of classrooms.  However, in examples of multidimensional discourse, there is a difference.  Teachers in low SES classrooms allow students to question and explain mathematical thinking, but teachers tightly control the mathematical ideas and explicitly model how to share thinking.  In contrast, students in high SES classrooms are more likely to generate their own mathematical ideas and be responsible for their own learning. 
• There are low level and high level tasks in both sets of classrooms, but the type of high level tasks differ.  In the low SES classrooms, the high level tasks involve procedures while making connections to mathematical concepts.  In contrast, the students of high SES are more likely to be given a task of non-algorithmic thinking. 
• The home experiences of low SES students may explain these two differences. Working class child-rearing practices often include the expectation that children obey and follow directions (Lareau, 2003), hence teachers’ reasons for providing more direction in discourse and tasks. 

Significance

The discrepancy in achievement among various levels of SES, the importance of preparing students to communicate their ideas, and the need to engage students in worthwhile tasks makes this research study a relevant one.  An improved understanding of students’ experiences in school mathematics, particularly students of low SES, can inform future foci and directions of professional development and teacher education programs.

References

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