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.…

This study examined how word-problem characteristics influenced students' learning and retention of word-problem knowledge during and after an intervention. The participants were 221 fourth-grade students (average age at pretest = 8.8 years) who experienced word-problem difficulties (WPD) and had received a word-problem intervention in third…

The statistical properties of data are not present in any individual value, but rather, emerge only by perceiving the set as a whole. Summarizing the statistical properties of sets (e.g., creating ensembles) is ubiquitous in cognition, yet one unanswered question is how this process changes over development. The properties of number sets (e.g.,…

In 2017, the mathematics assessments that are part of the National Assessment of Educational Progress (NAEP) program underwent a transformation shifting the administration from paper-and-pencil formats to digitally-based assessments (DBA). This shift introduced new interactive item types that bring rich process data and tremendous opportunities to…

Elementary students' difficulties with angles in geometry are well documented, but we know little about how they conceptualize angles while solving problems and how their thinking changes over time. In this study, we examined 26 third and fourth grade students completing a body-based angle task supported by the Kinect for Windows. We used…

This study reports on the statistical content of five U.S. textbook series written for elementary students in grades 1-5. The researchers examined 17,688 pages and coded 7445 statistical tasks to determine (1) the distribution of statistical topics within textbooks, and (2) the relative emphasis on the phases of the statistical problem solving…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

The field of EDM has focused more on modeling student knowledge than on investigating what sequences of different activity types achieve good learning outcomes. In this paper we consider three activity types, targeting sense-making, induction and refinement, and fluency building. We investigate what mix of the three types might be most effective…

The Functional Behavioural Assessment (FBA) is an investigative process that examines the context of challenging behaviours in the classroom. Information gleaned from the FBA process is used to develop a behaviour intervention plan to address the challenging behaviour and teach a socially acceptable replacement behaviour. However, the FBA has…

In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…

The purpose of this study is to evaluate, using a randomized experimental design, the efficacy of TERC's "Using Data" program to change teacher behavior and improve student learning outcomes. The "Using Data" intervention provides professional development and technical assistance to teachers to help them use data…

Action Potential Science Experience (APSE) is a five-day summer camp offering science opportunities for K-8 students. The focus of the APSE curriculum is to teach science concepts and methods while challenging the participants to solve an overarching problem from the popular-culture context. The participants in the APSE entitled Burger 'N Fries…

This study describes a procedure one school district used to increase students' reading abilities through reviewing data and adjusting the instruction to give students intensive services, as needed. This school worked in a problem-solving team approach to develop a comprehensive team that followed the progression of student achievement.…