The most important ingredient of the pedagogy for teaching non-majors is getting their engagement. This paper proposes to use gamification to engage non-majors. An innovative game termed as Cover the Hungarian's Zeros is designed to tackle the common weakness of non-majors mathematics in solving the assignment problem using the Hungarian Method.…

Every semester, the authors encounter students who are attracted to the visual and spatial aspects of geometry. They have other students who consider geometry to be challenging for the very same reasons. Students are confounded not only by the fact that geometry relies on visual interpretations but also because it has a language of its own and…

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

Reasoning and sense making are at the heart of mathematics teaching and learning throughout the K-12 mathematics curriculum. Focusing on these skills gives students the opportunity to analyze, interpret, and critically think about the mathematics they learn. The terms "reasoning" and "sense making" are frequently used to describe the wide range of…

Word Problems those are also named as "Story Problems" which are well known to the students around the world. In this book there are 26 chapters which encompass diversified problems of four basic mathematical rules--addition, subtraction, multiplication and division. These problems may help students to practice more and more as well as…

Recreational Programming (RecPro) is the discipline that encourages the study of computer programming through ludic problems. Problems that are typically studied within this discipline are similar to those of Recreational Mathematics (RecMat), which sometimes leads to the confusion of these two disciplines. The objective for RecPro is to write…

Collaborative learning has long been proved to be a crucial agent for enhancing students' social skills, problem-solving abilities and individual learning performance. Understanding how students move from one phase to another in their collaboration process can inform educators of how best to facilitate such learning. However, this is still an area…

In this study we document how a mathematical idea, shared by a student, changes the development of the class discussion. Our work characterizes the flexible and open dynamics in mathematics instruction that a teacher adopts to give her students control of their own mathematical ideas. Our work argues that this flexibility is necessary for teachers…

This study designed a learning system to facilitate elementary school students' fraction learning. An experiment was carried out to investigate how the system, which runs on multi-touch tabletop versus tablet PC, affects fraction learning. Two groups, a control and experimental, were assigned. Control students have learned fraction by using tablet…

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

The aim of this research is to examine prospective mathematics teachers' quantitative reasoning, their support for students' quantitative reasoning and the relationship between them, if any. The teaching experiment was used as the research method in this qualitatively designed study. The data of the study were collected through a series of…

In my experiences, students with Developmental Disability (DD) are routinely excluded from Algebra and other high-level mathematics courses. People with DD do not have the opportunity to learn Algebra, which may support the understanding and provide purpose for learning money and budgeting skills that, perhaps, could help them avoid financial…

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

For many years the need to educate and support our teachers to implement science and mathematics education has been ongoing throughout the world (National Academies of Sciences, Engineering, and Medicine, 2019; Mundry et al., 2009). In more recent years, this call has extended to include teaching through integrated science, technology,…

Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…