A quantitative literacy course titled "Computational Geology" has been taught at the University of South Florida for over 20 years at the undergraduate level, largely by the same professor. Due to the extended course tenure, a unique opportunity presented itself to qualitatively study what the perceived broader impacts of the course were…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

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…

The positive correlation between spatial ability and mathematical ability has been well-documented, but not well-understood. Examining student work in spatial situations that require numerical operations provides us with insight into this elusive connection. Drawing on student work with angle, length, volume, and area, we examine the ways in which…

Contextualization is a method used for mathematics curriculum design within lesson plans and as a pedagogical practice in face-to-face classes. Many researchers are studying the effects of using contextualization in the teaching and the learning process for mathematics (Bottge & Cho, 2013; Perin, 2011; Young, Hodge, Edwards, & Leising,…

The purpose of this research was to determine strategies used by 8th grade students in Number Sense problems. This was a case study of 28 8th grade students at three similar secondary schools in a city centre south of Turkey. A Number Sense test consisting of 25 items designed according to five main Number Sense components was used as a data…

This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which…

This report presents dual analyses of an undergraduate student, Cassie, whose work provides nice contrasts between Grounded Theory (GT) analysis and Knowledge Analysis (KA). The analyses highlight particular methodological differences, such as grain size of findings, positioning of novices and more general implications about expert-novice studies.…

This design research type development study aims at producing a set of PISA-like mathematics task which is valid and practical as well as has the potential effects. Then, activation of fundamental mathematical capabilities underlying mathematical process related to the mathematical literacy as the main potential effect of the developed PISA-like…

The aim of this study was to examine the mistakes made by freshman students of science teaching during the process of proving and the reasons for these mistakes. To this aim, the study, which was conducted via the case study method, was performed with 52 freshman students who were studying at the department of science teaching in a state…

This study aims to identify errors made by primary school students when modelling word problems and to eliminate those errors through scaffolding. A 10-question problem-solving achievement test was used in the research. The qualitative and quantitative designs were utilized together. The study group of the quantitative design comprises 248…

This inquiry presents two fine-grained case studies of students demonstrating different levels of cognitive functioning in relation to bilateral symmetry and reflection. The two students were asked to solve four sets of tasks and articulate their reasoning in task-based interviews. The first participant, Brittany, focused essentially on three…

This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…

Manipulatives support students with and without disabilities in mathematics. However, as students age, concrete manipulatives can be limiting and potentially not age appropriate (Satsangi, 2015). An alternative is virtual manipulatives, including app-based manipulatives. This study compared the use of app-based manipulatives to concrete…