Infants and toddlers experience the world in interaction with others. Likewise, social interactions are important in learning about math--concepts of number ("one," "two," "three"), space ("on top," "upside-down," "round"), and magnitude ("more," "big,"…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

In this dissertation, I address two outstanding questions regarding how linguistic and extra-linguistic information are brought together in the interpretation of language situated within a discourse. The first part of this dissertation experimentally addresses how alternatives invoked by sentences containing the focus-sensitive operator 'only' are…

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks…

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…

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…

This qualitative study examined the everyday mathematical experiences and understandings of three, 4-year-old, African-American children from working-class backgrounds. The study drew on Street, Baker, and Tomlin's (2005) broad, ideological model of mathematics as "social" and their analytic concepts of mathematical events (units of…

Number Concepts; Measurement; Geometry; Probability; Statistics; and Patterns, Functions and Algebra. Procedural Errors were further categorized into the following content categories: Computation; Measurement; Statistics; and Patterns, Functions, and Algebra. The results of the analysis showed the main sources of error for 6th, 7th, and 8th…