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).
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
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