Meaningful learning occurs when individuals connect their existing knowledge with their current understanding. Unfortunately, many teaching practices neglect the learners' subconscious knowledge, also known as their "funds of knowledge." The result is a disconnect between school and home knowledge, social injustice towards students whose…

Feedback in exploratory learning systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment…

Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…

The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

In 2001, the Chinese Ministry of Education issued Guidelines for Preschool Education (GPE) (trial version) to call on early childhood practitioners to use a child-centered and play-based approach to teaching and learning. The guidelines also include mathematics within the science domain and described its standards in a way that significantly…

Small-group cooperative learning provides an alternative to both traditional whole-class expository instruction and individual instruction systems. The procedures described in this volume are realistic, practical strategies for using small groups in mathematics teaching and learning with methods applicable to all age levels, curriculum levels, and…