Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

Experimental research on perception and cognition has shown that inherent and manipulated visual features of mathematics problems impact individuals' problem-solving behavior and performance. In a recent study, we manipulated the spacing between symbols in arithmetic expressions to examine its effect on 174 undergraduate students' arithmetic…

The paper examined the relations among problem solving, automaticity, and working memory load (WML) by changing the difficulty level of task characteristics through two applications. In Study 1, involving 68 engineering students, a 2 (automaticity) x 2 (WML) design was utilized for arithmetic problems. In Study 2, involving 76 engineering…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

The authors present mathematics problems related to the packaging of sporting goods which they used to motivate and engage their students in the USA. This article reports on a series of questions/problems that were explored in groups by the students in a college class designed for sophomores, as part of a program to prepare them to be teachers at…

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with…

The paper presents results of two case studies with undergraduate students majoring in applied mathematics and engineering. The first case study deals with students' preferences for and difficulties with application problems and pure mathematics questions in their courses. The students were majoring in applied mathematics and taking a second-year…

In this study, the aim is to evaluate the problem-solving processes in the understanding of problems and to determine and provide strategies, demonstration, expression and problem-writing dimensions in a numerical analysis course for engineering students. The quantitative data and qualitative data were interpreted using exploratory sequential…

Previous research has investigated the representational translation practices of high school students, high school teachers, and college preservice teachers in various mathematical contexts including linear functions. Findings from qualitative research has frequently led to new notions about participant work and understanding. Many quantitative…

Bachelors and graduate students are offered in the course of teaching computational informatics, the ability to solve nonstandard mathematical problems, which, as a rule, are not included in the content of teaching computational informatics. The article aimed to analyze the application effectiveness of non-standard mathematical problems in the…

This research is motivated by the difficulty of students in expressing economic problems in verbal and linear program languages. It is important to develop a linear program teaching material through realistic mathematic education approach with problem solving strategies with national character. This study aims to describe the needs of students and…

This study examined the criteria used by prospective mathematics teachers in determining whether a problem was a mathematical modeling problem. Two data collection tools were used in this case study. The first was a written evaluation form which consists of four problems developed by 27 prospective teachers individually that enrolled in a…

In order to support physics students in their future careers, there is a need to understand the relationship between undergraduate education and professional practice in physics-related fields. This study investigated high-level goal driven mathematical problem-solving activities that are found within two disciplinary cultures: physical science…

The aim of this study is to improve the quality of the mathematics curricula in Saudi universities by investigating the required changes in mathematics curricula in order to satisfy the demands of the Saudi Vision 2030. The researcher used qualitative methods to answer the research questions by randomly selecting a sample composed of some faculty…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.