This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

In this article we explore the theoretical and experimental field of sharing and of partitive and quotitive division problems, as illustrated by recent studies in this field. The purpose was to explain and justify the utility of presenting quotitive division problems, accompanied by graphical representations, to young children. The current study…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

The purpose of this research was to investigate high school students' computer self-efficacy (CSE) and learning behavior in a self-regulated learning (SRL) framework while utilizing an interactive learning module. The researcher hypothesizes that CSE is reflected on cognitive actions and metacognitive strategies while the students are engaged with…

Research on the graphical facilitation of probabilistic reasoning has been characterised by the effort expended to identify valid assessment tools. The authors developed an assessment instrument to compare reasoning performances when problems were presented in verbal-numerical and graphical-pictorial formats. A sample of undergraduate psychology…

Students who otherwise seem unreachable through traditional approaches to algebra require some alternative teaching methods. So do teachers who seek to add elements of freshness and innovation to their classrooms or who simply appreciate variety. This article offers some unconventional techniques for teaching a few conventional algebra topics.…

The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…

This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

The purpose of this study was to investigate the effect of technology on one student's solution methods when solving mathematical tasks that included algebra word problems. The student was presented with context tasks in both paper-pencil and computer environments. The results of this study revealed that the student's solution methods differed in…

This study aims to investigate about the existence of a graphical facilitation effect on probabilistic reasoning. Measures of undergraduates' performances on problems presented in both verbal-numerical and graphical-pictorial formats have been related to visuo-spatial and numerical prerequisites, to statistical anxiety, to attitudes towards…

Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which…

Problem Statement: Kinematics is one of the topics in physics where graphs are used broadly. Kinematics includes many abstract formulas, and students usually try to solve problems with those formulas. However, using a kinematics graph instead of formulas might be a better option for problem solving in kinematics. Graphs are abstract…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Problem-­solving assessment is an essential component of multi-­tiered systems of support such as response to intervention (RTI) and positive behavioral interventions and supports (PBIS). This authoritative work provides a complete guide to implementing a wide range of problem­-solving assessment methods, including: (1) functional behavioral…