In this paper, we present findings from a preliminary analysis of transcript data in the High School Longitudinal Study (HSLS:09), a large-scale longitudinal investigation of academic achievement among U.S. high school students. Using proportional flow diagrams of course-taking patterns, we illustrate differences in calculus completion associated…

Geometrical concepts play a crucial role in developing spatial thinking and reasoning. Further, curricular materials play a key role in shaping student-learning experiences in the classroom. The organisation of the content of textbooks plays a decisive role in how and when students are introduced to concepts, especially given the…

This qualitative case study investigated teachers' Technological Pedagogical Content Knowledge (TPACK) for teaching high school geometry in Turkey. Four TPACK components and their corresponding five TPACK level descriptions were used for examining three geometry teachers' TPACK through their technological instructional plans, microteaching…

The use of digital tools in mathematics lessons has recently gained in significance, especially because of ongoing technical developments. Particularly in the context of mathematical modelling, digital tools have become more and more important. They have been deployed for many years and are currently being intensively discussed from a didactical…

This chapter is a case study examining the symbiotic relationship among an Arts and Sciences mathematics department, a school of education, and a large urban public school district, as a context for the development of pedagogical content knowledge in the curriculum. Specifically, Hunter College, CUNY, has a long-standing master's program in…

The Ghanaian mathematics curriculum expects teachers to adopt technologies as an instructional tool to assist students to learn mathematics relationally. Teachers' dispositions (knowledge, beliefs, and attitudes) towards technology are critical in translating the curriculum intention into practice. This paper presents teachers' initial…

The present study examined the ability of content domain (algebra, geometry, rational number, probability) to classify mathematics misconceptions. The study was conducted with 1,133 students in 53 algebra and geometry classes taught by 17 teachers from three high schools and one middle school across three school districts in a Midwestern state.…

This paper proposes a philosophical approach to the mathematical engagement involving students and a digital tool. This philosophical proposal aligns with other theories of learning that have been implemented in mathematics education but rearticulates some metaphors so as to promote insight and ideas to further support continued investigations…

This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…

Often solved problems are problems of students' motivation in the process of teaching and learning. Some authors see the solution in creation a more space to students' creativity in teaching and learning. It is the aim of modern pedagogic and humanistic education, too. The submitted study aims to present possibility of how to teach geometric…

Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students' learning during graphing functions. However, the display of graphs of functions that students sketched by hand may…

While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the…

This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof--statement, proof, and theory--suggested by…

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning…

The aim of this research was to investigate high achievers' erroneous answers and misconceptions on the angle concept. The participants consisted of 233 grade 6 students drawn from eight classes in two well-established elementary schools of Trabzon, Turkey. All the participants were considered to be current achievers in mathematics, graded 4 or 5…