Identifies factors affecting problem solving strategies in the case of a multiplicative comparative situation involving three unknown quantities whose sum is known, and in which comparison relations between two pairs of the quantities are given. Proposes a model of the complexity of a word problem about such situation to analyze solution…

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)

Summarizes Tarski's semantic truth theory to clarify different aspects of implication. Extends the classical definition of implication as a relationship between propositions to a relationship between open sentences with at least one free variable. Analyzes two problematic situations and the presentation of some experimental results from research…

Presents a preliminary analysis from a study designed to investigate the participation of students learning English as an additional language in primary school mathematics. Concerns how students make sense of mathematics classroom interaction. Describes and uses the findings of three patterns of attention in the process of two students'…

Explores the teaching of four elementary teachers as they incorporated a model of culturally relevant teaching into their mathematics instruction. Examines how teachers sought to: (1) foster critical mathematical thinking and critical consciousness; (2) build on informal mathematical and cultural knowledge; and (3) utilize empowerment orientations…

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…

Examines changes in the problem posing strategies of a group of elementary preservice teachers as they posed problems to pupils. Indicates that the teachers' problem posing practices were changed from posing traditional single steps and computational problems to multiple approaches and solutions with open-ended and exploratory problems.…

Presents a semiotic analysis of the potential of computer algebra systems (CAS) for enabling mathematical activity on a conceptual level higher than usual. Illustrates examples of theoretical points from a development project in the context of a first year university course in calculus. Discusses how CAS may be used in a didactical analysis and in…

Investigates the benefits and limitations of using pre-constructed, web-based, dynamic geometry sketches in activities related to deductive proof at the secondary school level. Focuses on the relationship between the design of materials and the exploration process. Draws attention to the idea that pre-constructed dynamic geometric sketches and…

Examines the views of proof held by university-level mathematics students and teachers. Develops a framework for characterizing people's views of proof based on a distinction between public and private aspects of proof and the key ideas that link these two domains. (Author/KHR)

Suggests that debate on cultural issues in mathematics provided by the critique of ethnomathematics must be based on contemporary writing in the field and should not focus on extreme views within the political justification for ethnomathematics. Addresses philosophical questions raised by Rowlands and Carson and comments on preliminary results…

Presents a teaching approach related to the concept of function that lead students working within a graphic milieu to producing, discussing, and testing the validity of mathematical statements and theorems. Indicates that students experimenting with the approach became able to think of functions as objects and engage in questions of the validity…

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…

Presents an exploration of conversation in a single episode of a 12th grade girls' calculus class. Analyzes Habermasian communicative competence which requires students to show critical thinking and the ability to express their views. Explains learning outcomes by teachers' mode of questioning, cooperative endeavor by students, instructional…

Reviews the Lakoff and Nunez's book, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000)," which provided many mathematics education researchers with a novel and startling perspective on mathematical thinking. Suggests that several of the book's flaws can be addressed through a more rigorous establishment of…