Developed from Noddings's (2002) care theory, von Glasersfeld's (1995) constructivism, and Ryan and Frederick's (1997) notion of subjective vitality, a mathematical caring relation (MCR) is a quality of interaction between a student and a mathematics teacher that conjoins affective and cognitive realms in the process of aiming for mathematical…

There now appears to be widespread agreement that early childhood mathematics education (ECME) should be implemented on a wide scale, particularly for disadvantaged children. Yet little is known about the teaching of early mathematics. The goal of this paper is to demystify the process. We analyze one early childhood teacher's work as she attempts…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

This paper provides an instrumental account of precalculus students' graphical process for solving polynomial inequalities. It is carried out in terms of the students' instrumental schemes as mediated by handheld graphing calculators and in cooperation with their classmates in a classroom setting. The ethnographic narrative relays an instrumental…

High schools may still be anchored to 20th century expectations, but what are the critical guideposts for a 21st century high school education? There are many specific skills and competencies that young people will need to succeed, but more than particular skills, they will need the cognitive capacity to educate themselves throughout their entire…

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…

Describes an earlier study on the main characteristics and background of undergraduate students' difficulties when trying to solve mathematical tasks. Focuses on and extends part of an earlier study that concerned task solving strategies. Indicates that focusing on what is familiar and remembered at a superficial level is dominant over reasoning…

Interviews 120 children in kindergarten and grades 2, 4, and 6 with five Piagetian tasks to determine the grade level at which most have constructed transitive reasoning, unit iteration, and conservation of speed. Indicates that construction of the logic necessary to make sense of the measurement of time is generally not complete before sixth…

Articulates and operationalizes a framework for investigating the level of quantitative literacy in the United States. Uses data from the Third International Mathematics and Science Study (TIMSS) to document the level of quantitative literacy in the U.S. Indicates that students fall short in their understanding of the nature of mathematics and the…

Examines the feasibility of including instruction in common schemes of inference in the elementary grades. (CP)

Studies 6- to 8-year olds' responses to sliced task, standard and choices were discontinuous quantities, and non-sliced task, standard was continuous and choices were discontinuous quantities in order to discover whether children use half boundary in ratio comparisons between continuous and discontinuous quantities. Reveals that "dhalf" plays a…