Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha (commonly abbreviated to Bharati Krishna) was a scholar who studied ancient Indian Veda texts and between 1911 and 1918 (vedicmaths.org, n.d.) and wrote a collection of 16 major rules and a number of minor rules which have collectively become known as the "sutras of Vedic…

CATO is a new user interface, written in Java and developed by the author as a response to the significant difficulties faced by students who only sporadically use computer algebra systems (CAS). The usage of CAS in mathematical lectures should be an integral part of mathematical instruction. However, difficulties arise for those students who have…

Mathematics anxiety is known to be detrimental to mathematics learning. This study explored if an embodied agent could be used to help alleviate student anxiety in classrooms. To examine this potential, agent-guided algebra lessons were developed, in which an animated agent was equipped with prescriptive instructional guidance and anxiety treating…

The purpose of this paper is to propose an "operational" idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of…

While the mathematics education community encourages teachers to support students in developing a more meaningful contextual understanding of algebraic symbols, very little is known about teachers' quantitative understandings of algebraic symbols themselves. The goal of this study was to fill this gap and examine secondary teachers' ability to…

Teacher educators have been examining the professional status of teaching, including defining central practices of teaching, comparing teaching to other professions, and understanding teachers' own perspective via interviews, surveys, and observations. The present study intends to contribute to the discussion by examining the meaning of teaching…

Faced with meeting the challenges that school districts have for the pass rates set before them by the state many schools have looked for new ways to engage their students and increase competency in the class. Intrinsically motivated students have always been shown to have a higher success rate compared to the students that do not possess this…

The purpose of this study was to gauge the degree to which selected NWEA MAP Growth assessments are aligned to the Virginia Standards of Learning (SOL) and the extent to which MAP Growth reports can be used by school divisions to gauge student achievement relative to grade level and to identify learning gaps. The study was delimited to four MAP…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

This study examines the language use patterns of students in a math class that is part of a Spanish-English two-way, secondary continuation program. Audio recordings from five class periods were analyzed in order to quantify the opportunities provided for minority language by the teacher, as well as student uptake of those opportunities. This is…

In this paper, we examine the interactions of mathematical abilities when 6 high achieving Swedish upper-secondary students attempt unfamiliar non-routine mathematical problems. Analyses indicated a repeating cycle in which students typically exploited abilities relating to the ways they orientated themselves with respect to a problem, recalled…

This paper provides a set of five indicators of CAS use, which provide a means to analyse a student's written solution to determine whether they used CAS for solving a given problem. These indicators provide a way for researchers and teachers to determine CAS use without requiring classroom observation or the explicit recording of extra…

The use of digital games as an instructional tool has garnered increasing attention in the education community. Empirical work supported by theory on the learning affordances of digital games allowed the game-based learning community to arrive at the consensus that digital games provide an excellent medium for the acquisition of skills and the…

Across community colleges in the United States, most students place into a developmental math course that they never pass. This can leave them without the math skills necessary to make informed decisions in major areas of social life and the college credential required for participation in growing sectors of our economy. One strategy for improving…