This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

Using the capabilities of expert knowledge structures, the researcher prepared test questions on the university calculus topic of "finding the area by integration." The quiz is divided into two types of multiple choice items (one out of four and one out of many). After the calculus course was taught and tested, the results revealed that…

Mathematics is the foundation of all sciences, but most students have problems learning math. Although students' success in life related to their success in learning, many would not take a math course unless it is their university's core requirements. Multiple reasons exist for students' poor performance in mathematics, but one prevalent variable…

Online adaptive tutoring systems are increasingly being used in classrooms as a way to provide guided learning for students. Such tutors have the potential to provide tailored feedback based on specific student needs and misunderstandings. Bayesian knowledge tracing (BKT) is used to model student knowledge when knowledge is assumed to be changing…

This article reports how statistical analyses of PhD thesis records can reveal future research capacities for disciplines beyond their primary fields. The previous research showed that most theses contributed to and/or used methodologies from more than one discipline. In Australia, there was a concern for declining mathematical teaching and…

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…

At the beginning of preschool (M = 46 months of age), 197 (94 boys) children were administered tasks that assessed a suite of nonsymbolic and symbolic quantitative competencies as well as their executive functions, verbal and nonverbal intelligence, preliteracy skills, and their parents' education level. The children's mathematics achievement was…

E-assessments of students profoundly influence their motivation and play a key role in the educational process. Adapting assessment techniques to current technological advancements allows for effective pedagogical practices, learning processes, and student engagement. The "Handbook of Research on E-Assessment in Higher Education"…

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

The Mathematical Resilience Scale measures students' attitudes toward studying mathematics, using three correlated factors: Value, Struggle, and Growth. The Mathematical Resilience Scale was developed and validated using exploratory and confirmatory factor analyses across three samples. Results provide a new approach to gauge the likelihood of…

Researchers who make tutoring systems would like to know which sequences of educational content lead to the most effective learning by their students. The majority of data collected in many ITS systems consist of answers to a group of questions of a given skill often presented in a random sequence. Following work that identifies which items…

Included are probability models for various strategies that contestants on the television game show, "Let's-Make-a-Deal," might use when given the option to stick with their original choice of three unopened doors or switch to the unopened door after one of the other two doors has been opened. (JJK)