Many students persistently misinterpret histograms. This calls for closer inspection of students' strategies when interpreting histograms and case-value plots (which look similar but are different). Using students' gaze data, we ask: "How and how well do upper secondary pre-university school students estimate and compare arithmetic means of…

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

In this article, I present and build on the ideas of John Threlfall ("Educational Studies in Mathematics" 50:29-47, 2002) about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition,…

This paper describes five growth points in linking representations of function developed from a study of secondary school learners. Framed within the cognitivist perspective and process-object conception of function, the growth points were identified and described based on linear and quadratic function tasks learners can do and their strategies…

This conceptual research framework addresses the problem of rote learning by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of…

Investigates whether the reasons for deaf children's poor achievement lie in their strategy development. Reports that structural aspects of sign language counting may influence deaf children's thinking in a way that does not lead to a developed conceptual knowledge base, but rather to refined procedural competence. (Contains 31 references.)…

Examines the computational strategies of 10 young street vendors in Beirut by describing, comparing, and analyzing computational strategies used in solving three types of problems: (1) transactions in the workplace; (2) word problems; and (3) computation exercises in a school-like setting. Indicates that vendors' use of semantically-based mental…

Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

Analyzes video recordings of three undergraduate students' textbook-based homework. Focuses on the ways in which their exercise reasoning is mathematically well-founded or superficial. Indicates that most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in…

Defines visualization as the product and the process of creation, interpretation, and reflection upon pictures and images. Analyzes, exemplifies, and reflects upon the many different and rich roles that it can and should play in the learning and doing of mathematics. Discusses limitations and possible sources of difficulties visualization may pose…

Focuses on the role of tools, provided by a computer microworld (C.AR.ME), on the strategies developed by 14-year-old students regarding the concept of conservation of area of a non-convex polygon. Indicates that the nature of the tools used affected the nature of solution strategies that students constructed. (Author/KHR)

Describes a study to determine middle school children's representational strategies to form part-whole or part-part relationships for relational numbers such as proportions, ratios, or fractions. Quantitative and qualitative analysis revealed that children prefer a part-part representation to solve relational quantity problems. (15 references)…

This case study uses a sociocultural perspective and the concept of appropriation (Newman, Griffin and Cole, 1989; Rogoff, 1990) to describe how a student learned to work with linear functions. The analysis describes in detail the impact that interaction with a tutor had on a learner, how the learner appropriated goals, actions, perspectives, and…

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…

Mathematics educators have found sociocultural models of teaching and learning to be powerful in their ability to describe and support the pursuit of instruction based on recent standards documents (e.g., National Council of Teachers of Mathematics [NCTM], 1989, 2000). These models of instruction, however, have been criticized for their lack of…