Thinking aloud together: A teacher’s semiotic mediation of a whole-class conversation about percents

How does classroom interaction support students’ apprenticeship into the ways of speaking, writing, and diagramming that constitute the practice of mathematics? We address this problem through an interpretative analysis of a whole-group conversation about alternative ways of solving a problem involving percent discounts that occurred in a sixth grade classroom. This research study draws upon Dewey’s theory of inquiry, Vygotsky’s cultural–historical psychology, Freudenthal’s realistic mathematics education, and Halliday’s systemic functional linguistics (SFL). From Freudenthal, we borrow the notions of mathematizing and guided reinvention—the former notion offers a view of mathematics as an activity of structuring subject matter and the latter one provides insights into the processes whereby mathematizing is learned and taught in the classroom. We glean from Dewey his view of reflective thinking as inquiry and the role that conversations may serve therein. We rely upon Vygotsky’s notions of a verbal thinking plane and a social phase of learning in order to reconsider the function of whole-class interaction in apprenticing students into mathematizing. Finally, SFL provides us with tools for explaining the choices of grammar and vocabulary students and teachers make as they realize meanings in whole-group conversations. Treating the selected whole-class conversation as a text, we focus our analysis on how this text came to mean what it did. Our central questions are as follows: What meanings were realized in the whole-class conversation by teacher and students and how were these meanings realized? How did the teacher’s lexico-grammatical choices guide the students’ choices? In addressing these questions, we advance an interpretation of the conversation as paradigmatic of students and teacher thinking aloud together about percents.     

To see or not to see: analyzing difficulties in geometry from the perspective of visual perception

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual organization: Gestalt principles, (2) recognition: bottom-up and top-down processing; and (3) representation of perception-based knowledge: verbal vs. pictorial representation, mental images and hierarchical structure of images. Examples given in the paper were mostly taken from Gal's study (2005) which aimed at identifying and analyzing Problematic Learning Situations (after Gal & Linchevski, 2000) in junior high school geometry classes. Gal's study (2005) suggests that while this theoretical perspective became part of teachers' pedagogic content knowledge, the teachers were aware of their students' thinking processes and their ability to analyze and cope with their students’ difficulties in geometry was improved.     

The transitional stages in the PhD degree in mathematics in terms of students’ motivation

This paper presents results of a longitudinal study in the transition to independent graduate studies in mathematics. The analysis of the data collected from 24 students doing a PhD in mathematics revealed the existence of three transitional stages within the PhD degree, namely Adjustment, Expertise and Articulation. The focus is on the first two transitional stages, since the data collection focused mainly on these. Based on the first two transitional stages and the students’ ways of dealing with them, which were called ‘survival strategies’, three types of students were identified. The importance of motivation for each transitional stage and the successful transition overall are considered as well.     

Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework

This study was designed to investigate preservice elementary school teachers’ (PSTs’) responses to written standard place-value-operation tasks (addition and subtraction). Previous research established that PSTs can often perform but not explain algorithms and provided a four-category framework for PSTs’ conceptions, two correct and two incorrect. Previous findings are replicated for PSTs toward the end of their college careers, and two conceptions are further analyzed to yield three categories of incorrect views of regrouped digits: (a) consistently as 1 value (all as 1 or all as 10), (b) consistently within but not across contexts (i.e., all as 10 in addition but all as 1 in subtraction), and (c) inconsistently (depending on the task).     

The World Bank,support for universities,and asymmetrical power relations in international development

This article examines the role of the World Bank in advancing higher education sectors in the developing world, considering in particular the increasing power and strength of a global knowledge-based economy. Given the powerful role that intergovernmental organizations such as the World Bank play in shaping global economic policies, the authors are concerned about how the Bank’s policies and actions may limit knowledge generation and capacity building of universities in the developing world. Relatedly, the authors use case studies of the Bank’s involvement in Thailand and Uganda to better understand the role it plays in producing and reproducing forms of global hegemony. The authors discuss hegemony in terms of neocolonialism and neoliberalism. Neocolonialism is described as forms of domination advanced by powerful nations and their institutions, while neoliberalism is understood as an economic ideology by which weaker nations may be brought into greater alignment with global trade initiatives.     

Cognitive load theory,educational research,and instructional design: some food for thought

Cognitive load is a theoretical notion with an increasingly central role in the educational research literature. The basic idea of cognitive load theory is that cognitive capacity in working memory is limited, so that if a learning task requires too much capacity, learning will be hampered. The recommended remedy is to design instructional systems that optimize the use of working memory capacity and avoid cognitive overload. Cognitive load theory has advanced educational research considerably and has been used to explain a large set of experimental findings. This article sets out to explore the open questions and the boundaries of cognitive load theory by identifying a number of problematic conceptual, methodological and application-related issues. It concludes by presenting a research agenda for future studies of cognitive load.