This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…

In classrooms today, teachers continue to strive to enhance student knowledge and application by designing learning environments which create experiences for students to interact collaboratively, solve problems, think critically, and learn by doing. Research has indicated that teacher knowledge of the experiential learning cycle has become…

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…

Mobilizing scientific knowledge for understanding the natural world and for critically appraise socio-scientific situations and make decisions are key competencies for today's' society. Therefore, it is essential to understand how students at the end of compulsory schooling use scientific knowledge for understanding the surrounding world. The…

This study examines Swedish upper secondary school teachers' gendered conceptions about students' mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results…

The main aim of this research is to disclose the essence of students' multi-dimensional thinking, also to reveal the rating of factors which stimulate the raising of effectiveness of self-development of students' multi-dimensional thinking in terms of subject-oriented teaching. Subject-oriented learning is characterized as a type of learning where…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

The paper proposes a theoretical and methodological framework based on a pluralistic, concerted approach to the study of activities that take place in and through speech interactions. The framework has a general scope, applying to any collective activity taking form through language interactions. It contributes to a fuller understanding of the…

This work investigates the formation of particular student profiles based on of their ideas relating to basic characteristics of the atom. Participants were secondary students of 8th, 10th and 12th grades from Northern Greece (n = 421), with specific cohort characteristics e.g. age, grade and class curriculum, and individual differences, e.g.…

This paper explores teachers' perceptions of their learners' proficiency in statistical literacy, reasoning and thinking. Research in Statistics education has prompted a move away from the teaching of statistical skills, towards focusing on the development of statistical literacy, reasoning and thinking. The recent South African Grade 10-12…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

This article explains four kinds of inquiry exercises, different in purpose, for teaching advanced-level high school and college students the hypothetico-deductive (H-D) method. The first uses a picture of a river system to convey the H-D method's logic. The second has teams of students use the H-D method: their teacher poses a hypothesis…

Demands placed on teachers and students continue to increase in order to develop the skills required of the 21st century workforce. There continues to be a need to utilize curriculum and instruction to inspire students to engage in STEM majors and careers. Improving instructional methods and providing opportunities for students to question and…

The purpose of this research study was to learn about students' conceptions concerning the line of best fit just prior to their introduction to the topic. Task-based interviews were conducted with thirty-three students, focused on five tasks that asked them to place the line of best fit on a scatterplot and explain their reasoning throughout the…