The ability to properly evaluate one's own academic progress has long been considered a predictor of academic success. However, its distinctive role in the context of computational mathematics remains underexplored. Grounded in social cognitive theory, this study investigates the critical role of self-regulated learning (SRL) strategies in…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

By taking the role as a mentor and a facilitator, a teacher in the 4th grade of elementary school needs to look at the condition of the students in the concrete thinking stage. Learning process needs to be adjusted such that the abstract objects in mathematics can be represented through concrete objects as a bridge to enter the knowledge that the…

This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

The limit concept plays a foundational role in calculus, appearing in the definitions of the two main ideas of introductory calculus, derivatives and integrals. Previous research has focused on three stages of students' development of limit ideas: the premathematical stage, the introductory calculus stage, and the transition from introductory…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

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…

This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. Ways of reasoning deductively are highlighted, using examples drawn from observations of young students. One-step deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple…

Presents young children's concepts related to probability grouped by definite, possible, and definitely not. Discusses the teaching methods of the probability concepts. (YP)

This paper asserts that any intellectually responsible program to instruct young children in math, science, and technology must overcome at least three seemingly insurmountable obstacles: (1) adults' inability to discover, either by reflection or analysis, the means by which children acquire science and technology concepts; (2) the fact that young…

A powerful way of understanding something new is by analogy with something already known. An analogy is defined as a mapping from one structure, which is already known (the base or source), to another structure that is to be inferred or discovered (the target). The research community has given considerable attention to analogical reasoning in the…

This manual was developed to provide guidance to individuals working in Project SOAR (Stress on Analytical Reasoning), a pre-freshman summer program for science majors anticipating matriculation at Xavier University of Louisiana. Following an overview of Xavier University and Project SOAR and an outline of general instructions, specific…

This document is the second of three related volumes. They present the rationale, background, and framework for a comprehensive monitoring system being developed for the National Science Foundation. The system is being designed to gather information about the effects of national, state, and local policy actions designed to change the teaching and…