The interpretation of numerals has been traditionally debated across disciplines including, but not limited to, Linguistics, Developmental Psychology, and Philosophy. A big portion of the debate concentrates on the ontology of numerals, i.e., their basic meaning, and the mechanisms by which (non) exact interpretations (e.g., at least) are derived.…

Number sense is a key indicator of students' future academic success. Students from low socio-economic backgrounds often come to kindergarten lacking number sense skills that other students acquire before they begin formal schooling. Small-group intervention that is focused on number sense skills is an effective way to address this foundational…

Students in developmental math classes have been documented to struggle with arithmetic. This dissertation research was a response to the calls in the literature to qualitatively understand what students are learning in a classroom. Number sequences have been well researched to document the connection of student understanding of math in elementary…

Recent studies show that English learning students are a growing population within the United States school system. Language barriers have been shown to negatively influence reading scores as well as math scores, and math scores are a predictor of future academic success in many subject areas. This qualitative action research study demonstrates…

Despite the importance of mathematical understanding for academic and occupational success, students in the United States are not meeting necessary levels of mathematics achievement. Multi-tiered systems of support (MTSS) provide a framework for schools to allocate resources to best support students. Universal screening, a key element of MTSS,…

This mixed methods action research study examined the implementation process and impact of a 9-week Number Talk intervention to build number sense in kindergarten students. Fifty-eight kindergarten students engaged in daily Number Talk lessons for 9 weeks. Qualitative data were collected to evaluate the strengths and challenges of the…

Without providing effective, evidenced-based instruction during the early elementary years, children who come to school with low initial levels of mathematics and reading skills often continue to fall further behind their peers (Anderson & Nagy, 1992; Hart & Risley, 1995). However, educational interventions show promise for helping…

This study examines the effect of an intervention called Native Numbers on the development of number sense and quantitative skills in low-SES preschool children (ages 5 to 6) in Mexico City, using a randomized control trial (RCT). Native Numbers (NN) is a math curriculum built as an application for "iPads" that includes activities on…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

Understanding the linear relationship of numbers is essential for doing practical and abstract mathematics throughout education and everyday life. There is evidence that number line activities increase learners' number sense, improving the linearity of mental number line representations (Siegler & Ramani, 2009). Mental representations of…

The purpose of this study was to determine whether multiple-choice and constructed-response items assessed prospective secondary mathematics teachers' understanding of the concept of function. The conceptual framework for the study was the Dreyfus and Eisenberg (1982) Function Block. The theoretical framework was Sierpinska's (1992, 1994)…

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…

The National Council of Teachers of Mathematics (NCTM) Curriculum Focal Points (2006) suggested heavy emphasis on instruction in whole numbers for young elementary students. Any intervention curriculum for students who are at-risk for mathematic difficulties should not be oversimplified. Number sense was defined by Berch (1998) as a developing…

Calculation fluency weaknesses are a key characteristic of children with mathematics difficulties. The major aim of this dissertation was to uncover early predictors of calculation fluency weaknesses in second graders. Children's performance on number sense tasks in kindergarten along with general cognitive abilities, early literacy skills, and…