For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they have examined how mathematicians assess and get to know a proof not just by reading it, but through active engagement with the proof. For example,…

The aim of this study is to examine prospective mathematics teachers' skills of interpreting algebraic formulae at the student level. In this context, 84 prospective teachers studying in the senior class of the elementary mathematics teaching program of a university in Turkey constituted the participants of the study. In this study, the…

Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…

The purpose of this study is to draw attention to the concepts of "formula" and "rule" in mathematics, thereby revealing the views of pre-service teachers relating to these concepts by exploring their knowledge in, and their capacity to exemplify these concepts. The study is important in that it would reveal how pre-service…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…

The aim of this study is to explore mathematics teaching department students' perceptions on the concepts of proposition, theorem, and proof which are very important for daily life, mathematical literacy and studying mathematics; the common mathematical content used in constructing these concepts; and whether these constructions and content…

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

The purpose of this study was to explore and compare the proficiency of Grade 11 Mathematics and Mathematical Literacy (ML) learners in solving two problems based on the temperature conversion formula. The first was a result-unknown problem that asks for the result of a formula for a given input. The second was a start-unknown problem in which the…

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the…

We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

The necessity of using inquiry-based learning (IBL) was recently recommended by studies and reports made for the European Commission. Several European projects are devoted to the widespread use of IBL methods. The effects of using IBL are studied worldwide. In the framework of the Seventh Framework Program (FP7) project PRIMAS, a series of…

This study investigated students' activating positive affective experiences in mathematics lessons, their antecedents, their cognitive and motivational consequences, as well as their effect on achievement. The participants were 682 Grade 8 and 9 students from 37 classes from Germany and Switzerland who participated in a video study of lessons on…

This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…

An important message teachers convey to their students is that mathematics is founded on reasoning and is not just a collection of rules to apply. Many mathematical rules such as area formulas can be derived in ways that are age-appropriate to students, and it is an important part of mathematics education that students engage in these derivations…