Many research problems in social science involve multilevel phenomena. However, discussions about multilevel research designs are limited in the mixed methods (MM) literature. Building on early writings in the field, this methodological discussion advances a refined definition of a multilevel MM research design. The refinement emerges from a review of qualitative and quantitative conceptions of multilevel research designs and an analysis of a literature-based definition of a multilevel MM research design. To illustrate the application of the refined definition, we present an exemplar of a multilevel MM study aimed at explaining cultural, behavioral, and neurobiological aspects of literacy for mathematics. This comprehensive and versatile definition advances the field by offering guidance for designing and conducting innovative multilevel MM studies.

The written language of mathematics is dense with symbols and with conventions for combining those symbols to express mathematical ideas. For example, reading a factored polynomial function such as f(x) = x²(2x + 15) requires the knowledge that parenthesis can be used to signify function notation in one context and multiplication in another. Mathematical orthography is defined as orthographic knowledge of symbolic mathematics. It entails both knowledge of discrete mathematical symbols and the conventions for combining those symbols into expressions and equations. The ability to read text written in the base-ten system, comprised of digits and conventions for combining digits to express whole and rational quantities, is an important aspect of mathematical orthography. However, success in secondary and post-secondary programs requires more advanced mathematical orthography. The goal of this research was to determine if a simple and novel measure of mathematical orthography captures individual differences in adults’ mathematical skills. Mathematical orthography was measured with a timed dichotomous symbol decision task. Adults (N = 58) discriminated between conventional and non-conventional combinations of mathematical symbols (e.g., x² vs. ²x; |y| vs. ||y). The mathematical symbol decision task uniquely predicted individual differences in whole-number arithmetic, fraction/algebra procedures, and word problem solving. These findings suggest that the symbol decision task is a useful index of symbol associations in mathematical development and, thus, provides a tool for understanding the role of mathematical orthography in individual differences in adults’ mathematical skills.

In her role, Amy works collaboratively with K-12 science and engineering teachers to develop and implement standards-based curricula and assessments. She also provides mentoring and coaching and co-teaching support to K-12 teachers across the entire trajectory of the profession. Her research focuses on teacher education, classroom assessment, and P-16 environmental and engineering education.

No abstract

No abstract