Latent variable models, such as the popular Knowledge Tracing method, are often used to enable adaptive tutoring systems to personalize education. However, finding optimal model parameters is usually a difficult non-convex optimization problem when considering latent variable models. Prior work has reported that latent variable models obtained…

This article presents four inquiry-based learning activities developed for a liberal arts math course. The activities cover four topics: the Pythagorean theorem, interest theory, optimization, and the Monty Hall problem. Each activity consists of a dialogue, with a theme and characters related to the topic, and a manipulative, that allow students…

This study is motivated by the desire to address some of the enormous challenges faced by the students as well as the lecturer in fulfilling their respective expectations and duties demanded by the process of learning--teaching of mathematics and statistics within the framework of the constraining schedules laid down by the academic institutions…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

The National Assessment of Educational Progress (NAEP) is the only continuing and nationally representative measure of trends in academic achievement of U.S. elementary and secondary school students in various subjects. For more than four decades, NAEP assessments have been conducted periodically in reading, mathematics, science, writing, U.S.…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

This classroom note illustrates how dynamic visualization can be used to teach conditional probability and Bayes' theorem. There are two features of the visualization that make it an ideal pedagogical tool in probability instruction. The first feature is the use of area-proportional Venn diagrams that, along with showing qualitative relationships,…

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…

Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…

Preschoolers' experiences with shapes are important because geometry is foundational to aspects of mathematics and it is now part of the Common Core for school-readiness. Exposure to shapes also provides experiences that are key to developing spatial thinking more broadly. Yet achieving a strong conceptual understanding of geometric categories can…

The purpose of this study is to investigate the mathematical literacy of the 15-year-old students in terms of PISA mathematical literacy questions. The research model of this study is the survey model in the quantitative models. The sample of this study was composed of 1.227 students who received formal education in five different types of schools…

Faced with a chronic shortage of single-subject mathematics teachers and a directive from the federal legislation "No Child Left Behind" that all students are taught by highly qualified teachers, California instituted a new subject-matter competency exam, the California Subject Exam for Teachers for Mathematics (CSET), and created a new…

The paper presents inequalities between four descriptive statistics that can be expressed in the form [P-E(P)]/[1-E(P)], where P is the observed proportion of agreement of a "kappa x kappa" table with identical categories, and E(P) is a function of the marginal probabilities. Scott's "pi" is an upper bound of Goodman and Kruskal's "lambda" and a…

Although ITSs are supposed to adapt to differences among learners, so far, little attention has been paid to how they might adapt to differences in how students learn from help. When students study with an Intelligent Tutoring System, they may receive multiple types of help, but may not comprehend and make use of this help in the same way. To…