Researchers have argued that integrating early algebra into elementary grades will better prepare students for algebra. However, currently little research exists to guide teacher preparation programs on how to prepare prospective elementary teachers to teach early algebra. This study examines the insights and challenges that prospective teachers…

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

Purpose: Early childhood is of critical importance in terms of cognitive, affective and physical development. Undoubtedly, a substantially stimulating environment and opportunities offered to children, as well as appropriate educational materials, have an impact on their development. The object of this study is to investigate the mathematical…

A personal overview about the use of new technologies for teaching and learning mathematics is given in this paper. We analyse the introduction of Computer Algebra Systems with learning purposes, reviewing different frameworks and didactical resources, some of them generated according the philosophy of the European Area of Higher Education.…

In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

When teaching algebra concepts to middle school students, the author often hears questions that echo her own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow…

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing…

Vygotsky's work on the individual/social relation provides theoretical tools for interpreting the origins of thinking and learning. Drawing on Vygotsky's ideas and data from one classroom, categories of practice relating to teaching and learning were developed in order to identify themes for an exploration of mathematical development within the…

Despite research that high-stakes tests do not improve knowledge, Florida requires students to pass an Algebra I End-of-Course exam (EOC) to earn a high school diploma. Test passing scores are determined by a raw score to t-score to scale score analysis. This method ultimately results as a comparative test model where students' passage is…

This study aimed to explore how inquiry-oriented teaching could be implemented in an introductory linear algebra course that, due to various constraints, may not lend itself to inquiry-oriented teaching. In particular, the course in question has a traditionally large class size, limited amount of class time, and is often coordinated with other…

In this study, we investigated students' thinking about the use of letters in algebra. Responses from over 1,400 Australian secondary school students to a set of three algebra items were analysed to determine the prevalence of the "letter as object" misconception. We estimate that 50% to 80% of Year 7 students bring this misconception to…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

The article discusses three empirical examples of Computer Algebra System (CAS) use in a Danish upper secondary school mathematics class that had experienced a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students' mathematical…