Range of Mathematics Achievement Within Fourth- and Eighth-Grade American Classrooms

• In Event: Who Gets to Learn? Student Achievement and Academic Growth

Abstract

Age is the principal unit by which a majority of American K-12 schools determine the academic needs of students. This organizational scheme was implemented not for the benefit of the students but administrative ease (Pinar et al., 1995). The age-based grouping is rationalized under the assumption that students of similar age require similar instruction. This assumption drives grade-level expectations, high-stakes assessments, and classroom instruction. However, there is a host of evidence that suggests age is an inappropriate proxy of academic need (Engel et al., 2013; Firmender et al., 2013; Peters et al., 2017) and that divergence in academic abilities manifest in early childhood and grow over time (von Hippel & Hamrock, 2019). As a result, age-based grouping has produced classrooms in which the academic diversity of the students is large, and many students’ academic needs are unaddressed, especially gifted-learners.

This study is a part of a larger study that seeks to quantify the range of academic abilities within American classrooms and add to the arguments against age-based partitioning of academic service. To date, the literature has only provided preliminary evidence of the true range of academic abilities within a typical classroom (Firmender et al., 2013) and it is generally recognized that academic diversity within classrooms is large and increasing (Tomlinson et al., 2003, Gottfried, 2016). The current study focuses on the range of mathematics achievement within a typical fourth and eighth-grade classroom.

Data for this paper come from the Trends in International Mathematics and Science Study (TIMSS) 2015 collected in the United States. The TIMSS uses a rigorous two-stage random sampling procedure to select schools and intact classrooms within participating countries. This will provide us with a sample of nationally representative data from which we can characterize the range of mathematics achievement present in a typical American classroom.

The average portion of students within classrooms at the low, intermediate, high, and advanced international achievement benchmarks in the fourth and eighth grades will be described. We expect to find that at least 70% of all classrooms in each grade level will have students scoring within at least three of the four benchmarks. Measures of within classroom dispersion in academic ability will also be reported. Additionally, the proportion of variance within classrooms will be estimated by examining unconditional three-level hierarchical linear models (students nested within classrooms, nested within schools) for fourth and eighth-grade math achievement. Within classroom variance in mathematics achievement is expected to be greater than 35% of the total variability within both grade levels. As of the submission in July 2020, this paper is currently being prepped for a stage 1 registered report.

If the hypotheses above are supported, an educational system that assumes a student’s age is the primary determinant of academic need is likely to underserve many of its students, and in particular, the highest achieving learners. This is especially true given that an overwhelming majority of learners who have been identified as gifted receive no instructional differentiation in a regular classroom (Westberg et al., 1993).

Authors

• Blaine Pedersen, Texas A&M University - College Station

• Cristina Worley, Texas A&M University - College Station