Context personalization is an instructional design principle where tasks are presented to students in the context of their interest areas like sports, music, or video games. Personalization allows for understanding of domain principles to be grounded in concrete and familiar experiences. By making connections to prior knowledge, personalization…

This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin's concept of "professional vision" as a way of bringing analyses of culture and power into studies of…

Drawing on a review of recent work conducted in the area of pattern generalization (PG), this paper makes a case for a distributed view of PG, which basically situates processing ability in terms of convergences among several different factors that influence PG. Consequently, the distributed nature leads to different types of PG that depend on the…

The focus of the current proposal is to examine the effect of two dynamic simulations on the participants' conceptions of rate of change. Conceptions of rate of change were measured according to Carlson et al.'s (2002) Mental Actions framework and how the participants related the physical simulations to the graphical representations (Heid, et al.,…

An important open issue in Functional Measurement is whether the three most important models of cognitive algebra are sufficient to describe the great majority of possible response behaviors. Generally speaking, the individual response "R" is a function of the subjective scale values "s[subscript k]" and can be imagined as a continuous manifold.…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question of communication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching…

This paper explores the algebraic expressions of deaf learners as they explore and construct sequences using the digital microworld Mathsticks. More specifically, it attempts to identify how the deaf students coordinated bodily, discursive and digital resources in order to attribute their own personal senses to the notion of variable. Examples of…

This paper charts the design and application of a system to support 11-14 year old students' learning of algebraic generalisation, presenting students with the means to develop their understanding of the meaning of generality, see its power for mathematics and develop algebraic ways of thinking. We focus squarely on design, while taking account of…

I investigate how and whether a heterogeneous group of first-year university mathematics students in South Africa harness the potential power of a computer algebra system (CAS) when doing a specific mathematics task. In order to do this, I develop a framework for deconstructing a mathematics task requiring the use of CAS, into its primary…

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

This paper presents the results obtained from a study comparing the strategies used by 1,070 Chinese students and 1,002 Singaporean students from primary grade 6 to secondary year 2 in solving three fraction-related problems. It is part of the author's Ph.D. study, which involves more word problems on speed. The Chinese students performed better…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

This paper examines various cognitive strategies applied while CAS (Computer Algebra System) are used in undergraduate-level engineering mathematics teaching and learning. We posed some questions in relation to such CAS use: What kind of tools can CAS offer to enhance different cognitive strategies of students? How can the use of CAS widen the…

Research has suggested that musicians process music in the same cortical regions that adolescents process algebra. An early adolescence synaptogenesis might present a window of opportunity during middle school for music to create and strengthen enduring neural connections in those regions. Six school districts across Maryland provided scores from…