The Mathematics students who perform truth-seeking process upon solving mathematical problems were unique. Therefore, the study deems it necessary to know students' mental structure and mechanism so that they can make the right decision by performing truth-seeking. However, no research has delved into the mental structures and mechanisms of…

The number sequences describe a hierarchy of students' concepts of number. This research uses two defining cognitive structures of the number sequences--units coordination and the splitting operation--to model middle-grades students' abilities to write linear equations representing the multiplicative relationship between two unknowns. Results…

This research questions were "how do the characteristics of learning model of logic & algorithm according to APOS theory" and "whether or not these learning model can improve students learning outcomes". This research was conducted by exploration, and quantitative approach. Exploration used in constructing theory about the…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)

Reports a study which identified different problem-solving strategies among Hong Kong high school chemistry students. Finds that student experts employed a recognition plus a working forwards strategy, whereas student novices attempted a means-end analysis to create a solution procedure. Comparisons were made with problem-solving in physics. (GG)

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus).…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

This paper examines the novel problem solving actions of a pair of college students. The analysis highlights the role of the solvers' inferential processes including abductions, deductions, and inductions as structuring resources that contribute to both their understanding of the problems they face and the emerging novelty that constitutes their…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Argues that the dichotomy between domain-specific and general theories of cognitive development addressed in the "Merrill-Palmer Quarterly" special issue is unproductive. Suggests that polarities of generality and specificity exist in creative tension as seen through developmental processes. (Author/BB)

Presents two teaching ideas for mathematics instruction. The first employs "mind maps" as a method to help students learn, record, and recall mathematical information. Provides examples for solving quadratic equations and complex numbers. The second discusses two ways to find the average speed during a trip employing differing constant…

The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

The ideas of the nature, purpose, and scope of mathematics held by students is an issue of interest to the mathematics education community. Movement from a mathematics as discrete operations perspective to a mathematics as problem-solving perspective is a desired change in mathematics education reform. A pretest/posttest experimental design study…