Purpose: Traveling Salesman Problem (TSP) that can be extended and modified in various ways, is a practical and realistic type of problem and forms the basis for the visual and spatial solution of many optimization problems. In this study, 15, 25 and 35 nodes Travelling Salesman Problems were solved by secondary school, high school and…

Monte Carlo simulations for uncertainty propagation take as inputs the uncertainty distribution for each variable and an equation for the calculation of a desired quantity. The desired quantity is then calculated by randomly drawing from the specified uncertainty distributions of the input variables. This calculation is then repeated many times…

This paper examines turn-by-turn interactions [Wagner, D., & Herbel-Eisenmann, B. (2014). Mathematics teachers' representations of authority. "Journal of Mathematics Teacher Education," 17(3), 201-225. doi:10.1007/s10857-013-9252-5] in mathematics professional development, looking specifically at facilitators' positioning of…

We propose to assess conceptual knowledge of mathematical notions by having recourse to isomorphic word problems. We assumed that failing to solve isomorphic problems is an indicator of lack of conceptual knowledge. To reach these conclusions, two experiments were conducted among 4th and 5th grade students. In experiment 1, each student had to…

Learners intending to enter some higher education (HE) institutions in South Africa write the National Benchmark Tests (NBTs) that are expected to provide a measure of their readiness for HE. A large gap exists between the quantitative literacy competencies of many of these learners and expectations at HE level. In this article I explore the…

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…

Learning models that can improve critical thinking, skills collaborate, communicate, and creative thinking are needed in the 21st-century education era. Critical and creative thinking are the two essential competencies of the four skills required in the 21st century. However, both are still difficult to achieve well by students due to a lack of…

This study explored how approximating the practice of mathematicians by communally negotiating the standards for proof mediates middle grade students' abilities to collaboratively construct mathematical arguments. Forty-seven eighth-grade students engaged in an instructional sequence wherein they, along with the instructors, negotiated communal…

In this article we examine 4th and 5th grade Portuguese students' performance on problems of structuring 2D rectangular arrays of squares, which was analyzed and categorized into the five levels of sophistication described by Battista, Clements, Arnoff, Battista, and Borrow (1998). In general, the results suggest that students in the higher-grade…

Creating opportunities for students to learn mathematics in authentic ways is key to positioning them as the problem solvers of tomorrow. Outside the classroom, mathematics does not exist in a vacuum but rather as an integrated part of everyday life. This work centers on meaningfully engaging students in grade-level mathematics content and…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

This paper presents results from three teaching experiments intended to guide students to reinvent truth-functional interpretations for mathematical disjunctions. The initial teaching experiments revealed that students' emergent strategies for assessing disjunctions did not entail or facilitate the development of a relevant partitioning of example…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

The current study examined the development of two effects that have been found in single-digit multiplication errors: relatedness and distance. Typically achieving (TA) second, fourth, and sixth graders and adults, and sixth and eighth graders with a mathematics learning disability (MLD) performed a verification task. Relatedness was defined by a…

This research study investigates the ability of students to tackle the solving of unique mathematical problems in the domain of numerical series, verbal and formal, and its influence on the motivation of junior high students with learning disabilities in the Arab sector. Two instruments were used to collect the data: mathematical series were…