Linear pattern is the primary material in learning number patterns in junior high schools, but there are still many students who fail to generalize the linear pattern. The students' failure in generalizing the pattern occurred when the students ended to view the problems globally without breaking them into the constructors' components such as the…

We report on the construction, validation, and implementation of an instrument for measuring students' strategic knowledge about drawing for geometry modelling problems, namely, the "strategic knowledge about drawing scale." We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation…

The mathematics education community has long emphasized applying wordproblem tasks in mathematics classrooms to foster understanding of mathematical concepts. As such, teachers of mathematics are eager to expose students to wordproblem mathematical tasks. However, students find such mathematical tasks particularly challenging, leading teachers to…

Background: Developing the questioning skills of Foundation Phase Education students when teaching mathematical problem-solving is often a neglected area of student curricula. Aim: This gap in mathematics programme is the focus of this study. Three main components were identified: presentation of mathematical problem-solving, the role of the…

In this paper, we present a design experiment in a "Teaching Mathematics" course for prospective elementary teachers where we sought to develop a "measurement approach" to fractions. We focus on the conceptualization of the mathematical content of the approach. We attribute our progress in the conceptualization to our efforts…

The sheet resistance of a conducting material of uniform thickness is analogous to the resistivity of a solid material and provides a measure of electrical resistance. In 1958, L. J. van der Pauw found an effective method for computing sheet resistance that requires taking two electrical measurements from four points on the edge of a simply…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

Members of a third-grade class were involved in a heated discussion. They were using a fixed number of links to create fences for toy cows. The children could change the shape of the field produced by the links, but they could not add any links or take any away. Understanding the relationship between perimeter and area is a difficult concept for…

Problems for students with a high mathematical potential can be far more complex and challenging than problems normally used in regular classrooms. The problems we developed for mathematically gifted students offer the possibility of acquiring and using heuristics (so called patterns of actions) which are useful in problem solving processes.…

This research examined the role of the teacher in supporting students to make sense of fraction multiplication when using a problem solving approach. Using a qualitative approach, the teaching of four skillful experienced sixth-grade teachers was examined as they implemented a problem-based unit on fraction multiplication. This paper will present…

The Common Core State Standards for Mathematics highlight the importance of not only content standards for mathematics but also mathematical practices such as communication, representation, and reasoning, skills that are often difficult for students with autism spectrum disorder (ASD). Through a single-case multiple-probe-across-participants…

The purpose of this non-experimental research study was three-fold: (1) to investigate the relationships among the attributes of creative problem solving ability (divergent thinking, convergent thinking, motivation, general knowledge and skills, and environment) and their relationships in the humanities (specifically those that took enrichment…

In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled…

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population…

Mathematics teachers often resist generic literacy strategies because they do not seem relevant to math learning. Discipline-specific literacy practices that emerge directly from the math content and processes under study are more likely to be embraced by math teachers. Furthermore, national and state-level mathematics standards as well as Common…