This study explores three aspects of a math emporium (ME), a model for offering introductory level college mathematics courses through the use of software and computer laboratories. Previous research shows that math emporia are generally effective in terms of improving final exam scores and passing rates. However, most research on math emporia…

Students' ability to use appropriate tools strategically is an important skill of mathematically proficient students (SMP 5, CCSSI 2010, p. 7). A parallel practice for teachers is using appropriate tools strategically for mathematics instruction. An important element of this practice is that the use of technology depends on the goals of…

The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

There is substantial evidence that preschooler's performance in early math is highly correlated to math performance throughout school as well as academic skills in general. One way to help children attain early math skills is by using targeted educational software and the paper discusses potential gains of using such software to support early math…

In this paper we analyze and discuss the postgraduate students' performance related to the tracing of tangent lines to the curve of a quadratic function within Dynamic Geometry Software in the context of Mean Value Theorem. The purpose is to show the possibility of using Dynamic Geometry in promoting learning of such Theorem, based on its…

"Limit" is a difficult mathematical concept, even for good students. It is also a key foundational idea for the study of advanced mathematics. It holds a central position as a foundation of the theory of approximation, of continuity, and of differential and integral calculus. However, the difficulty for teachers is how to organise…

Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…

Written communication and computer programming are foundational components of an undergraduate degree in the mathematical sciences. All lower-division mathematics courses at our institution are paired with computer-based writing, coding, and problem-solving activities. In multivariable calculus we utilize MATLAB and LATEX to have students explore…

Sequencing contents is of great importance for instructional design within the teaching planning processes. We believe that it is key for a meaningful learning. Therefore, we propose to formally establish a partial order relation among the contents. We have chosen the binary relation "to be a prerequisite" for that purpose. We have…

The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

The aim of this study was to explore the degree to which a professional development (PD) program designed using GeoGebra influences a group of Turkish middle school teachers' beliefs in relation to mathematics and role of GeoGebra in mathematics education. In order to collect the required data, the PD course was established to provide six teachers…

This paper reports on classroom observations of senior high school mathematics lessons with a focus on the use of digital technology. The observations were of teachers enrolled in an in-service course, Teaching Advanced Mathematics. The paper reports selected results and comments on: software that was observed to have been used; the use (or not)…

An important and interesting area in the study of triangle geometry is the related issue of extrema problems and inequalities. These problems play a significant role in the mathematics study program in high school. In tasks such as these, the difficulty level is high when one does not know in advance what the expected answer is. When one knows…

The 1998 paper by Martin Mühlenbrock, Frank Tewissen, and myself introduced a multi-agent architecture and a component engineering approach for building open distributed learning environments to support group learning in different types of classroom settings. It took up prior work on "multiple student modeling" as a method to configure…

This study investigated the ways in which four middle grades teachers developed mathematical knowledge for teaching (MKT) geometry as they implemented dynamic geometry software in their classrooms with the assistance of a coach. Teachers developed various components of MKT by observing coaches teach, by dynamic discourse with students, which is…