This qualitative case study aimed to investigate prospective middle school mathematics teachers' instructional responses based on the students' correct and incorrect functional thinking within the context of pattern generalization. The data were collected from thirty-two prospective teachers through a written task and semi-structured interviews…

There exist many studies on modeling competencies and their promotion; however, there is a need to investigate what modeling competencies are and how they vary in lower and higher-achieving groups of students in mathematics within the current modeling literature domain. This study examined how mathematical modeling competencies were displayed in…

Although students' nonstandard strategies have great importance in understanding students' thinking and creating effective mathematics classrooms, much remains unexplored in the literature. This study investigated 22 middle school teachers' reasoning about a student's nonstandard strategy for the division of fractions. The data were collected…

The purpose of the current article is to test and revise the hypothetical learning trajectory designed for teaching quadrilaterals by reporting the classroom mathematical practices emerged in a social learning environment developing preservice middle school mathematics teachers' understanding of quadrilaterals. Ten preservice teachers participated…

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…

Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

The purpose of this study was to detail teachers' proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers'…

The purposes of the study reported herein were to identify the common mistakes in geometry made by junior secondary school students in Hong Kong, and to compare the students' performance in geometry with their results in a logic test. A geometry test and a logic test were developed and administered to a sample of 554 students aged between 13 and…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…