Type: Interactive Paper Session

Title:  Mathematics Instructional Quality, Class Size, and Achievement for Low-SES Students

Description (50 words or 350 characters):

We explored relations between observed mathematics instructional quality (MIQ) and achievement in students from families with low income. Participants were 36 third grade teachers and their 205 students. Higher MIQ and smaller class size related to improved student test performance. Discussion considers inequity and access to high quality instruction.

1000-word proposal:

Introduction

The proposed interactive paper session describes relations between mathematics instructional quality (MIQ), class size, classroom ability level and achievement in a population of third-grade students from low-income families. Two research questions were addressed. First, what are typical levels of MIQ in a sample of third grade teachers in socioeconomically mixed schools?  Second, what is the relationship between MIQ and achievement, while also considering mathematical knowledge for teaching (MKT; Hill, Schilling & Ball, 2004), teacher experience, class size, and classroom ability level?  

Theoretical Framework

            Two critical goals for K-12 education are to provide access to high quality instruction for all students and eliminate achievement gaps between demographically distinct groups of children (National Academy of Education, 2010; United States Department of Education, 2010). The National Council of Teachers of Mathematics (NCTM) outlined critical aspects of mathematics instruction for K-12 students (NCTM, 2000, 1989). However, many elementary classrooms fall short of these goals despite efforts to reform mathematics education. Children from families with low incomes are disproportionately likely to receive low quality instruction (e.g. Pianta, Belsky, Houts & Morrison, 2007), and show less success on achievement tests (NCES, 2009) compared with higher income peers. Importantly, the achievement gap between children from families with high and low income has grown over the past 50 years (Rockoff, in press).

Improving the quality of teaching has been raised as a promising focal point to improve mathematics achievement, particularly for children from low-income families (Jordan, Kaplan, Ola'h, and Locuniak, 2006; Nye, Konstapoulos & Hedges, 2004). However, studies of classroom quality often use global measures of classroom quality rather than domain-specific practices most relevant to mathematics classrooms (Pianta et al., 2008; Seidel & Shavelson, 2007). We use a new measure of mathematics instructional quality, Mathematics Scan (M-Scan), that captures eight dimensions of teaching aligned with NCTM standards and outlined by Borko and others in prior work (Borko, Stecher, Alonzo & McClam, 2005). Dimensions include: structure of the lesson; use of multiple representations; use of mathematical tools; cognitive depth; problem solving; mathematical discourse community; explanation/ justification; and connections/ applications.

Data Collection and Analyses

Participants
            Data were collected from control schools participating in a three-year longitudinal cluster randomized control trial of a socio-emotional learning intervention. Students and teachers from eleven schools in a large mid-Atlantic school district were studied. All third grade children (n = 205) who received free or reduced price lunch participated. They included 105 males; 108 Hispanic, 19 Caucasian, 43 African American, and 27 Asian American; 170 English Language Learners; and 30 students who received special education services.

Teacher participants were thirty-six third grade teachers who had a mean of 11 years experience (range 1-35 years).

Methods

Research assistants conducted videotaped observations during three different mathematics lessons, one corresponding to each of the fall, winter and spring observation windows.  RAs were trained in the M-Scan following rigorous reliability protocols and achieved high reliability (80% within one score match) prior to MIQ coding. Teachers completed the MKT measure and reported on their demographic characteristics and class size. Student demographic and achievement data were collected through school records.  See Table 1.

            Data were analyzed using a two-level hierarchical linear model in MPlus. Models were built incrementally, adding level 1 control variables (Stanford 10 second grade mathematics score, level of English Language proficiency), level 2 variables (teaching experience, mathematics knowledge for teaching, classroom ability level, and class size), and the key level 2 predictor (mathematics instructional quality). Level 1 and 2 variables were centered at the grand mean.

Results

RQ 1: Teachers offered low to moderate levels of MIQ across eight dimensions, with classroom means ranging from 2.24 for explanation/justification to 4.41 for structure of the lesson. Table 2 presents descriptive statistics. Findings demonstrate the prevalence of low to moderate levels of MIQ in classrooms where students from low-income families learn mathematics.

Bivariate correlations between classroom-level variables lend insight into the prediction of MIQ. For example, classrooms of students with lower achievement receive higher quality instruction than classrooms of students with higher ability students (r = -.15, p < .05). Teachers who performed better on mathematics knowledge for teaching offered higher quality instruction than teachers performing lower on the MKT measure (r = .60, p < .001). Thus, these variables were included in subsequent statistical models.

RQ 2: Results from the Hierarchical Linear Model are presented in Table 3. Mathematical instructional quality related to third grade achievement for students from low-income families. For every one point higher a teacher scored on the M-Scan, students scored approximately 12 points or .19 standard deviations higher on a third grade achievement test. Even when teachers offered moderate levels of MIQ, differences of 1 point on the M-Scan related to achievement. Further, smaller class size predicted higher math achievement. For every 4 fewer students in a classroom, students scored almost 15 points or .23 standard deviations higher on the third grade achievement test. The final model explains 43.9% of the total variance in student achievement, including 91.56% of the classroom level variance.

Discussion

Family socioeconomic status “sets the stage for academic performance” in relation to direct resources at home (e.g., math flashcards, workbooks, or computer software) or indirect provisions (e.g., knowledge of schools and teachers) (Sirin, 2005, p. 438). Results suggest that teaching practices that include the use of high quality discourse, cognitively demanding tasks, and the use of multiple representations are helpful to students from low-income families in learning mathematics. Perhaps high quality classroom instructional resources compensate for fewer resources that are aligned with school mathematics achievement at home. Further, smaller class size appears to be an important predictor of mathematics achievement for children from families with low income, even after controlling for MIQ. 

Findings will be discussed in relation to contemporary efforts to improve access to high quality mathematics instruction for all children, particularly those who have experienced previous disadvantages.  We describe the potential for professional development interventions to improve mathematics instructional quality and consider findings pertaining to class size in relation to trade-offs evident in existing class size research literature.

References

Borko, H., Stecher, B. M., & Alonzo, A. C, & McClam, S.  (2005). Artifact packages for characterizing   classroom practice: A pilot study. Educational Assessment, 10(2), 73-104.

Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing Measures of Teachers' Mathematics Knowledge for Teaching. The Elementary School Journal, 105(1), 11-30.

Jordan, N.C., Kaplan, D., Ola'h, L.N., & Locuniak, M.N. Number sense growth in kindergarten: a longitudinal investigation of children at risk for mathematics difficulties. Child Development 77(1), 153 – 175.

Lubienski, S. T. (2000). Problem solving as a means toward mathematics for all: An exploratory look through a class lens. Journal for Research in Mathematics Education, 31(4), 454-482.

National Academy of Education. (2010). World-Class Science and Mathematics. Retrieved from http://www.naeducation.org/NAEd_White_Papers_Project.html

National Center for Education Statistics (2009). The Nation's Report Card: Mathematics 2009 (NCES 2010–451). Institute of Education Sciences, U.S. Department of Education, Washington, D.C.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics.  Reston VA: National Council of Teachers of Mathematics.

Nye, B., Konstantopoulos, S., & Hedges, L. V. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26(3), 237.

Pianta, R. C., Belsky, J., Houts, R., & Morrison, F. (2007). TEACHING: Opportunities to learn in America's elementary classrooms. Science, 315(5820), 1795.

Pianta, R.C., Belsky, J., Vandergrift, N., Houts, R., & Morrison, F. J. (2008). Classroom Effects on Children's Achievement Trajectories in Elementary School. American Educational Research Journal. 45(2), 365-397.

Reardon, S. F. (in press). The widening academic achievement gap between the rich and the poor: new evidence and possible explanations. In R.M. Murnane & G. Duncan (Eds.), Whither Opportunity? Rising Inequality and the Uncertain Life Chances of Low-Income Children. Washington, D.C.; Brookings Institution.

Seidel, S., & Shavelson, R.J. (2007). Teaching effectiveness research in the past decade: the role of theory and research design in disentangling meta-analysis results. Review of Educational Research, 77(4) 44 – 499.

United States Department of Education. (2010). A Blueprint for Reform: The Reauthorization of the Elementary and Secondary Act. Alexandria, VA: Education Publications Center.