Proportional reasoning, the ability to use ratios in situations involving comparison of quantities, is essential for mathematical competence, especially in the middle school years, and is an important determinant of success beyond school. Research shows students find proportional reasoning and its foundational concepts difficult. Proportional…

Math fact fluency is critical for understanding complex mathematics. Explicit timing interventions have shown promise for improving math fluency, and they may benefit from being paired with group-oriented contingencies. Further, investigations of independent and dependent group-oriented contingencies would help to identify their relative…

In a course emphasizing interactive technology, 19 students, including 18 mathematics education majors, mostly in their first year, reinvented the definition of limit of a sequence while working in small cooperative groups. The class spent four sessions of 75 minutes each on a cyclical process of guided reinvention of the definition of limit of a…

In this present study, it was aimed to investigate whether the hierarchical structure of mathematics emerged in university students' minds or not, considering the concepts of limit, continuity derivative and integral from the perspective of students in the department of secondary school mathematics teacher training and the department of…

The fact that there is no much study on reversibility is one of reason this study was conducted. Others, the importance of reversibility is also being researcher's motivation for focusing pupils' reversibility. On the other hand, the concern on pupils' reversibility is a major concern. The objective of this research is to identify errors done by…

It is common for freshmen students to enter Calculus I with a wide range of levels of preparation and mastery of background material. In addition, many of the students struggle with the adjustment from high school to college. In an effort to help the students to solidify their understanding of concepts as they progress through the course, as well…

Formative assessment involves the gathering of information that can guide the teaching of individual or groups of children. This approach requires a sound understanding of children's thinking and learning, as well as an effective method for gaining the information. We propose that formative assessment should employ a version of clinical…

This article emerged from an analysis of learners' responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by…

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

Increased attention to reasoning and justification in mathematics classrooms requires the use of more authentic assessment methods. Particularly important are tools that allow teachers and students opportunities to engage in formative assessment practices such as gathering data, interpreting understanding, and revising thinking or instruction.…

The paper presents the use of spreadsheets integrated with digital tools capable of symbolic computations and graphic constructions in a master's level capstone course for secondary mathematics teachers. Such use of spreadsheets is congruent with the Type II technology applications framework aimed at the development of conceptual knowledge in the…

Studies related to school mathematics have shown that students who scored well on standardized tests often are unable to successfully use memorized facts and formulae in real-life application outside the classroom. The outcome of TIMSS and PISA studies further emphasizes the importance of mathematics teaching and learning in the Malaysian…

The aim of this study is to reveal pre-service science teachers' cognitive structures regarding Science, Technology, Engineering, Mathematics (STEM) and science education. The study group of the study consisted of 192 pre-service science teachers. A Free Word Association Test (WAT) consisting of science, technology, engineering, mathematics and…

Previous studies have shown that people start traveling sales problem tours significantly more often from boundary than from interior nodes. There are a number of possible reasons for such a tendency: first, it may arise as a direct result of the processes involved in tour construction; second, boundary points may be perceptually more salient than…

This paper deals with ideas about dynamic presentation of photo-pictures by means of dynamic software GeoGebra in order to motivate art students to get acquainted with some specific mathematical functions. The results of the experiment include deeper understanding of the functions' nature, search of new functions for dealing with a practical…