This research focuses on the inductive teaching with group process and students' behavior as working in a group. There were four instruments under this study. The descriptive statistics were employed. The findings revealed that, firstly, the effectiveness of LPIDTGP [Learning Package by means of the Inductive Teaching with Group Process] is higher…

We analysed multivariable calculus students' meanings for domain and range and their generalisation of that meaning as they reasoned about the domain and range of multivariable functions. We found that students' thinking about domain and range fell into three broad categories: input/output, independence/dependence, and/or as attached to specific…

Ill-structured tasks presented in an inquiry learning environment have the potential to affect students' beliefs and attitudes towards mathematics. This empirical research followed a Design Experiment approach to explore how aspects of using ill-structured tasks may have affected students' beliefs and attitudes. Results showed this task type and…

We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

This study was to design, develop, and investigate instructional units for freshmen with low academic achievement to learn before they study calculus. Because the concepts, skills, and theories of function are fundamental for the calculus course but the below average students were not familiar with the basic knowledge and ability in function when…

The statistics about community college developmental math level and completion rates can seem disheartening, especially for those who work with these students day-to-day and know their life stories. When it comes to teaching her students, the author chooses not to focus on the statistics. Instead, she pays attention to their varied career goals…

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

Albrecht Dürer is well known as a Renaissance artist, but his 1525 work, the "Underweysung der Messung," or "Manual on Measurement," also contains a significant amount of mathematics. This article outlines four projects inspired by parts of this work, with additional material coming from Staigmüller's 1891 "Dürer als…

"The Language of Mathematics in Science" is an ASE/Nuffield project aimed at supporting teachers of 11-16 science in the use of mathematical ideas in the science curriculum. Two publications have been produced. This article focuses on the first of these, "The Language of Mathematics in Science: A Guide for Teachers of 11-16…

Community colleges are facing increased pressure to accelerate students through their developmental mathematics sequence. However, many individuals feel that some state legislatures and college leaders are frequently bypassing developmental math faculty expertise when implementing acceleration and compression initiatives. This qualitative study…

In this study, we surveyed 570 Calculus I and Calculus II students at two large public universities in the Northeastern region of the United States. We explored the relationship between these students' career goals in mathematics and other STEM fields, with their mathematics identity and self-identified personality attributes. Our findings suggest…

Mathematics anxiety affects primary pre-service teachers' engagement with and future teaching of mathematics. The study aimed to assess the level and range of mathematics anxiety in first year pre-service teachers entering their teacher education course, and to investigate the sources of this anxiety as perceived and identified by them. Data…

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…

Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task…