There is much to be learned and pondered by reading "Proofs and Refutations," by Imre Lakatos. It highlights the importance of mathematical definitions, and how definitions evolve to capture the essence of the object they are defining. It also provides an exhilarating encounter with the ups and downs of the mathematical reasoning process, where…

This study presents an efficient approach to personalized mispronunciation detection of Taiwanese-accented English. The main goal of this study was to detect frequently occurring mispronunciation patterns of Taiwanese-accented English instead of scoring English pronunciations directly. The proposed approach quickly identifies personalized…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

How can a teacher use the practice of reflection to create rich mathematical learning environments that are engaging to students? In such environments, one can hear and see a seamless integration of Problem Solving, Reasoning and Proof, Communication, making mathematical Connections, and Representation (the NCTM Process Standards) through Number…

"Proceedings of International Conference on Social and Education Sciences" includes full papers presented at the International Conference on Social and Education Sciences (IConSES), which took place on October 21-24, 2021, in Chicago, Illinois. The aim of the conference is to offer opportunities to share ideas, discuss theoretical and…

Many students struggle with fractions and must understand them before learning higher-level math. Veteran educator David B. Spangler provides research-based tools that are aligned with NCTM and Common Core State Standards. He outlines powerful diagnostic methods for analyzing student work and providing timely, specific, and meaningful…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

Although a plethora of research evidence highlights positive and significant outcomes of the incorporation of the Graphing Calculator (GC) in mathematics education, its use in the teaching and learning process appears to be limited. The obvious need to revisit the teaching and learning of Probability has resulted in this study, i.e. to incorporate…

This study was conducted in order to examine how and to what extent the implementation of the performance-based bonus program in South Korean schools has motivated teachers to improve their behavior, as well as to identify any other positive or negative effects of the program. Interviews with teachers indicated that a large percentage of teachers…

This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…

This study examined the role of particular tasks implemented through two instructional methods on college students' "achievement" and understanding of probability. A mixed methods design that utilized a pre-test and post-test was used. This included treatment and control groups, each comprised of students in three sections of an…

The scholarship of teaching and learning increasingly recognizes that active and dynamic instructional models promote better, more holistic, and lasting educational outcomes. This article summarizes an in-class engaged learning activity based on the popular playing card game, "President". This game requires players to exchange cards with each…

Monte Carlo simulations are a classical tool to analyse physical systems. When unlikely events are to be simulated, the importance sampling technique is often used instead of Monte Carlo. Importance sampling has some drawbacks when the problem dimensionality is high or when the optimal importance sampling density is complex to obtain. In this…

Using data from the Education Longitudinal Study of 2002, a nationally representative sample of US high school students, I investigate how features of secondary schools influence the likelihood of Latino students completing high school. To do so, I introduce the concept of school incorporation, which includes school policies, school receptivity…

This paper describes a development and evaluation process used to create teacher education materials that help prepare middle and secondary mathematics teachers to teach data analysis and probability concepts with technology tools. One aspect of statistical reasoning needed for teaching is the ability to coordinate understandings of center and…