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…

Teachers spend a lot of time talking about students: They talk about how students learn, how to best plan lessons for them, and how to understand their written work using different protocols. Instead of hypothesizing about what a student might do on a task or why a student made a certain mistake, why aren't teachers just asking the student?…

The focus of this paper is on the problem of appropriate teaching in the open/distance education and the need to practically employ effective evaluative tools for improving the academic achievement of learners involved in these modes of education. This paper introduced KPS method that was formulated on the basis of well stated assumptions as a…

Increasing availability of digital devices in elementary school classrooms presents exciting new opportunities for teachers to support the teaching and learning of mathematics. Although many of the math applications available for these devices focus on drill and practice of mathematical procedures, screencasting apps can help support effective…

The traditional method of teaching math--showing students how to do a procedure, then assigning problems that require them to use that exact procedure--leads to adults who don't know how to approach problems that don't look like those in their math book. Seeley describes an alternative teaching method (upside-down teaching) in which teachers give…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

The following report describes an assessment instrument called the Mathematics Performance and Cognition (MPAC) interview. The MPAC interview was designed to measure two outcomes of interest. It was designed to measure first and second graders' mathematics achievement in number, operations, and equality, and it was also designed to gather…

This report provides an overview of the development, implementation, and psychometric properties of a student mathematics interview designed to assess first- and second-grade student achievement and thinking processes. The student interview was conducted with 622 first- or second-grade students in 22 schools located in two public school districts…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

This study aims to examine how five-year-old children demonstrate their learning through mathematical games in preschool settings in Palestine. It also explored the perspectives of children and teachers of different stages of play. The sample consisted of 90 children and 6 teachers. Children were guided to a wide range of mathematical games.…

This archival data study examined the relations between cognitive abilities and math reasoning for Hispanic English learner (EL) students in grades 1 through 5 with an identified learning disability. The 295 student participants were referred for an initial psycho-educational Spanish or English evaluation due to academic concerns by their school…

The application of mathematics to real-world problems is moving more and more in the focus of attention of mathematics education; however, many learners experience huge difficulties in relating "pure" mathematics to everyday contents. In order to solve "modeling problems", it is first necessary to find a transition from a…

This research is an action research which aims to implement contextual teaching and learning (CTL) approach to learn mathematics, focus on the integration subjects. The approach utilizes the use of mathematics manipulative so that students can understand a mathematical concept to construct their own. The method which used in this research are…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…