The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

Increasing use of intelligent tutoring systems in education calls for analytic methods that can unravel students' learning behaviors. In this study, we explore a latent variable modeling approach for tracking learning flow during computer-interactive artificial tutoring. The study considers three models that give discrete profiles of a latent…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined 1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction and 2)…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction; and…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

This paper demonstrates how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. We examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance prediction; and (2) what types of in-game features were associated with student…

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are…

Learning analysts often consider whether learning processes across time are related (1) to one another or (2) to learning outcomes at higher levels. For example, are a group's temporal sequences of talk (e.g., correct evaluation [right arrow] correct, new idea) during its problem solving related to its group solution? I show how to address these…

This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

Presents an approach to task sequencing that is based on a component-skills view of intelligence and learning. Related research in cognitive psychology and in computer based instruction is reviewed, and a cognitive model of human task sequencing is developed and then applied to an intelligent tutoring system for algebra. (39 references)…

This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the…

Discusses the need to consider the cognitive models of students and their learning processes when designing computer tutorials, and describes a tutorial designed to teach students how to generate algebraic equations for story problems. Testing and revisions of the tutorial, with both college and high school students are described. (14 references)…

This paper presents a critical review of computer assisted instruction (CAI); an overview of recent intelligent tutoring systems (ITSs), including current perceived shortcomings; major activities of the field, i.e., analysis of teaching/learning processes, and extending and developing artificial intelligence techniques for use in intelligent…

The psychological mechanisms that underlie human question asking and answering during comprehension and complex learning were studied. The transcripts of 83 tutoring sessions on research methods for college students and 22 algebra tutoring sessions for seventh graders were collected and analyzed. It was estimated that student questions were about…