Students' difficulties understanding the meaning of logarithms could stem in part from differences between teachers' and students' views of them. The purpose of this article is to unpack some specialized content knowledge for teaching logarithms. The author discusses the history of logarithms to show why they can be understood as repeated…

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

This paper provides a comparative study of mathematics textbooks as the primary construct via the Anthropological Theory of Didactics (ATD), which was founded by Yves Chevallard. The aim is to suggest principles that can be incorporated to improve the designing of mathematics textbooks. Definitions, examples, and tasks dealing with the teaching…

We present a synthesis of the Onto-semiotic Approach (OSA) theoretical system to mathematical knowledge and instruction, while highlighting the problems, principles and research methods that are addressed in this approach and considering the didactics of mathematics as a scientific and technological discipline. We suggest that Didactics should…

The act of explaining can help students to develop new understandings of mathematical ideas, construct rules for solving problems, become aware of misunderstandings or a lack of understanding and develop their mathematical communication. Their explanations can also offer opportunities for a teacher to understand more fully what the students are…

This study investigates 27 preschool teachers' verbalization of various aspects of pattern structure as well as their knowledge of pattern structure while solving patterning activities. Aspects of structure that are investigated include the unit of repeat, its length and the amount of times it is repeated, and whether or not the pattern ends in a…

In the historical process, scientific knowledge is constantly changing and developing. Concepts in curricula and textbooks are also affected by these changes and developments. The function concept is a typical example of this situation. The concept of function gained different meanings in different historical contexts although no clear information…

This chapter focuses on the development of concepts that children draw on as they work toward understanding negative numbers. Framed from a conceptual change lens, I discuss different interpretations children have of minus signs, numerical order, numerical values, and addition and subtraction operations and how children draw on these varied…

The research this report belongs to aims at exploring the functional reasoning of high-school students from a covariation approach and proposing a framework to describe and predict the student's responses to modeling tasks in Dynamic Geometrical Situations. Items were designed for the students to build/construct the corresponding function guided…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

We present a case of one teacher's engagement in project-based learning for algebra I students. This teacher was a member of a cohort of mathematics teachers and career technical educators who participated in a two-week intensive summer institute investigating autonomous vehicles. During the academic year, the follow up support for these educators…

Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…

The use of manipulatives to develop conceptual understanding appears to be a prevalent practice in many mathematical learning experiences, particularly in the early years of schooling. This study evaluates the impact of mathematical manipulatives on young children's attitudes towards mathematics (YCATM). The modified three-dimensional model of…

This study explored students' mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson's 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students…

The purpose of this study was to investigate the understanding of prospective elementary mathematics teachers of the formal definition of the limit of a sequence. The participants were 32 prospective mathematics teachers (8 male and 24 female) who were in their third year of study in a four-year mathematics teacher preparation programme Istanbul…