This study aimed to describe students' ability to arrange proof of abstract algebra problems (Subgroups) after receiving Information Technology (IT)-assisted scaffolding materials. To achieve this objective, we conducted exploratory qualitative research with students of Mathematics Education, Universitas PGRI Ronggolawe Tuban, participating in the…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students' algorithmatizing activity. In both…

Theon's ladder is an ancient method for easily approximating "n"th roots of a real number "k." Previous work in this area has focused on modifying Theon's ladder to approximate roots of quadratic polynomials. We extend this work using techniques from linear algebra. We will show that a ladder associated to the quadratic…

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…

The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

In this paper I describe how I have used the classic buried treasure problem with prospective and practicing mathematics teachers to enhance their problem solving abilities and disposition to integrate interactive geometry software (IGS) into the learning environment. I illustrate how IGS may be used as a strategic tool to gain insight into the…

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…

The use of computer algebra systems such as Maple and Mathematica is becoming increasingly important and widespread in mathematics learning, teaching and research. In this article, we present computerized proof techniques of Gosper, Wilf-Zeilberger and Zeilberger that can be used for enhancing the teaching and learning of topics in discrete…

A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.

Proving and refuting mathematical claims constitute a significant element in the development of deductive thinking. These issues are mainly studied during geometry lessons and very little (if at all) in lessons of other mathematical disciplines. This study deals with high school students' perceptions of proofs in the geometry. The study explores…

Augustus De Morgan (1806-1871) was a significant Victorian Mathematician who made contributions to mathematics history, mathematical recreations, mathematical logic, calculus, and probability and statistics. He was an inspiring mathematics professor who influenced many of his students to join the profession. One of De Morgan's significant books…

In this thesis, our aim is the study the Vanishing of Maps of Tor Conjecture of Hochster and Huneke. We mainly focus on an equivalent characterization called the Strong Direct Summand Conjecture, due to N. Ranganathan. Our results are separated into three chapters. In Chapter 3, we prove special cases of the Strong Direct Summand Conjecture in…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…