Unitizing, a cognitive support for number sense, describes how students conceptualize quantities in terms of units. Given the importance of this skill, a formative assessment tool was developed for array multiplication problems, including arrays that model the distributive property found in typical classroom curricula. Video of 77 fourth grade…

Math facts are foundational for later math skill development but have been identified as a common skill deficit among students in early schooling (Gersten, Jordan, & Flojo, 2005). Drill-based interventions effectively target and improve foundational academic skills (Burns, 2005), however, there is limited research examining drill-based…

This qualitative descriptive study was designed to address the deficiency in early math literacy skills, specifically those related to multiplication fact fluency, in early elementary students. More specifically, this study was designed to gather research and data to provide understanding of the mathematical curriculum instruction used in…

Over half of 4th grade students did not meet proficiency standards in mathematics on the National Assessment of Educational Performance in 2019 and this problem has persisted over time. This underachievement coupled with the numerous barriers to implementing evidence-based practices in schools reveals a need to provide a menu of effective…

The present study evaluated the effects and interaction of item set size and instructional time on students' fluency growth rates with multiplication facts over time when using an Explicit Timing intervention. The first goal was to determine an interaction between set size and instructional time across time that would influence the fluency growth…

This research presents a new, socially adaptive robot tutor, Ms. An ("M"eeting "S"tudents' "A"cademic "N"eeds). The goal of this research was to use a decision tree model to develop a socially adaptive robot tutor that predicted and responded to student emotion and performance to actively engage students in…

This study explored the impact of numbers used in instructional tasks on the construction and generalization of multiplicative reasoning by fourth grade students designated as having learning difficulties or disabilities in mathematics (SLDs). In particular, this study addressed the following research questions: (1) In what ways do SLDs'…

Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…

This study reports findings from a teaching experiment in which 4th grade children engaged in solving multiplication tasks with rectangular arrays in a computer environment. The environment provided flexible task-solving through dynamic virtual manipulatives (VMs) so children could use their existing knowledge of multiplication to complete array…

This research investigation examined the effects of Singapore's Model Method, also known as "model drawing" or "bar modeling" on the word problem-solving performance of American third and fourth grade students. Employing a single-case design, a researcher-designed teaching intervention was delivered to a child in third…

Deficiencies in mathematics standardized test scores prompted school district policymakers to consider implementing a program designed to increase students' basic multiplication fact skills. This study was an evaluation of the Math Factual Operations for Understanding program. The program, marketed with a martial arts theme, was intended to…

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

This study purposed to determine the effect of an endogenously designed instructional game on conceptual understanding of the associative and distributive properties of multiplication. Additional this study sought to investigate if performance on measures of conceptual understanding taken prior to and after game play could serve as predictors of…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…