Undergraduate students majoring in mathematics often face difficulties in comprehending mathematical proofs. Inspired by a number of studies related to students' proof comprehension, and Mejia-Ramos et al.'s study in particular, a test was designed in relation to the proof comprehension of the Cauchy Generalized Mean Value Theorem (CGMVT). The…

In this paper, a number of STEM educational proposals are systematically analyzed from the lens of mathematics education. An extensive innovation project was implemented during the 2019/2020 academic year in a pilot study carried out in Schools and Teacher Training Programs in Navarre (Spain), comprising a bibliographical and source analysis as a…

In this paper, we introduce and discuss a construct called "graphical forms," an extension of Sherin's symbolic forms. In its original conceptualization, symbolic forms characterize the ideas students associate with patterns in a mathematical expression. To expand symbolic forms beyond only characterizing mathematical equations, we use…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

This paper discusses the place of precision in mathematics education by exploring its role in curricular guidelines and in classroom life. By means of a joke on precision delivered by a school student in South Sweden, our study focuses on student participation in mathematical tasks that require precision in processes of measuring and reasoning.…

We describe the effects of a change in the mathematics placement policy at a large 4-year public university. The change resulted in a sharp reduction of the number of students placed in remedial courses, while the levels of academic preparedness of the students, the course content, and the instruction methods remained the same. This allows us to…

In this article, the author describes a task given to pre-service secondary school mathematics teachers. By exposing them to a relatively simple mathematics process, it was hoped that their ability to plan and implement lessons for their own students would be enhanced.

The article discusses the role of body movement, perception and kinaesthesia in mathematical thinking and accounts for the virtuality of mathematical concepts. A first person experience with a graphing motion software (WiiGraph), which involves ample body movements and is used to draw a circle, is presented. To study the unfolding of the…

Can a school or district improve student achievement simply by switching to a higher-quality textbook or curriculum? We conducted the first multi-textbook, multi-state effort to estimate textbook efficacy following widespread adoption of the Common Core State Standards (CCSS) and associated changes in the textbook market. Pooling textbook adoption…

This paper considers the kind of pedagogical knowledge and principles involved in the operationalisation of knowledge of children's mathematical thinking as a process of dynamic assessment. Using a case study of a particular child, this paper explores planning and instruction for a child determined by a detailed and informed interpretation of the…

According to Sinclair, Pimm, and Skelin (2012), the four big ideas of high school geometry are (1) diagrams; (2) variance and invariance; (3) definitions; and (4) proofs as the culmination of the proving process. On the first day of geometry class, Wayne Nirode began a multiday activity in which students were actively involved in working with…

The socioeconomic attainment gap in mathematics starts early and increases over time. This study aimed to examine why this gap exists. Four-year-olds from diverse backgrounds were randomly allocated to a brief intervention designed to improve executive functions (N = 87) or to an active control group (N = 88). The study was preregistered and…

The aim of this study is to analyse undergraduate students' understanding of polar coordinates based on two theories, Action, Process, Object and Schema (APOS) and Onto-Semiotic Approach (OSA). These two theories complement each other and each of them separately has been used in many research to explore students' performance of mathematical…

Serious games or educational games have attracted the interest of instructors and researchers for several years. In the field of education, serious games are being used for motivating students, attracting their interest in cognitively demanding fields and making the teaching and learning process more fun. Moreover, learning through implementing…

The flipped classroom (FC) inverts the traditional classroom by having students participate in passive aspects of learning at home and active aspects of learning in class with the guide of an instructor. The introductory statistics course for nonmath majors may be especially suited to the FC model given its unique challenges as a required course…