We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally…

In this article, the author shares the Menu Writing project, designed to promote a meaningful, real-world connection to mathematics with the lives of students. The rationale for developing this project was two-fold: (1) to connect school mathematics to students' lived experiences to encourage and sustain students' interest, motivation, and…

Computational thinking has been popularized in the last decade, particularly with the emphasis on coding education in K-12 schools. The core idea of computational thinking has a close relationship with technology and engineering education (TEE). TEE has emphasized the use of computing skills to solve problems, and integrative STEM education…

Working with language-independent logic structures can help students develop both inductive and deductive reasoning skills. The Japanese publisher Nikoli (with resources available both in print and online) produces a treasure trove of language-independent logic puzzles. The Nikoli print resources are mostly in Japanese, creating the extra…

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;…

Presents a developmental approach to teaching programing at all educational levels which stresses concepts rather than syntax; provides motivation, relevant examples, and activities; proceeds from concrete to pictorial to abstract according to age and experience of learners; and utilizes increasingly complex activities building upon and extending…

Recognizing similarities between our relationship to music and to other people reveals significant educational implications. Emotional responses are inseparable from the understanding which is a necessary condition for any fully educational activity. This brings out the importance of reasoning in music education. Such importance is usually…

Describes an Israeli reading program for disadvantaged adolescents based on verbal exercises using informative, literary, and speculative texts to improve their reading comprehension and cognitive functions. (HOD)

The Philosophy for Children Program was introduced to a class of deaf fifth graders as an instructional approach for reasoning skills. The program is intended to develop analytic skills required for intellectual functioning (including concept development, generalization, inference making, question formulation, and analogies). The program's major…

As part of a study of ecology, students in a second and third grade classroom developed board games. The research, creation, rule making, naming, and testing of several games are described. The games' levels of abstraction, presentation of factual information, content, and potential for sustained interest are considered. (LB)

This article presents 10 practical teaching procedures to encourage students to develop formal reasoning skills. A twelfth-grade English course is used as an example. Procedures include pretesting, sequencing instruction, providing students with concrete experiences, discussing reasoning patterns and forms of argumentation, assigning argumentative…