The author emphasizes the importance of concepts and mathematical form in a discussion of understanding mathematics. (MN)

Discussion about the nature and varieties of mathematical understanding is presented. Symbolic understanding is defined as a mutual assimilation between a symbol system and a conceptual structure, that is dominated by the conceptual structure. (MP)

This paper discusses the benefits of teaching literature through levels of understanding so that teachers can more quickly and efficiently determine the operational levels of individual students. The seven levels of understanding and some of the generic questions by which they can be determined are: (1) perceptual level: "What happened, when,…

This researcher investigated the relationship of hierarchical classification processes in subjects categorized as to developmental level as defined by Piaget's theory, and explored the validity of the hierarchical model and test used in the study. A hierarchical classification test and a battery of four Piaget-type tasks were administered…

The problems of using formalistic methods in the instruction of mathematics to elementary level children are discussed. Precision in mathematical language is not seen as a useful instructional tool, and functional modes of communication are stressed. (MP)