"Give an example" tasks invite students to consider mathematical concepts in relation to their properties according to the data collected by interviews and a questionnaire asking students' strategies for generating the example. Examines how these tasks contribute to the construction of links which in turn lead to construction of more webbed and…

The difficulties and misconceptions that many students experience when learning to visualize graphs of functions are discussed. Specifically, the inability to make accurate connections between symbolic and graphical representations, the lack of understanding about scale and scaling, and the confusion caused by transformations are examined with…

Explores the learning opportunities that might be created in mathematics instruction if reading were reconceptualized as described in the NCTM statement on communication. Develops the notion of "reading to learn mathematics" by enunciating and illustrating its key components. (44 references) (MDH)

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

Describes how a mathematics teacher's knowledge level can be supported or justified by a criterion different from test scores of teacher's students, namely the ability of the teacher to justify teaching practices by appealing to concurrent learning method. Two examples are provided that formalize theoretical justifications as practical arguments…

Provides ethnographic information about preservice teachers and their formative relationships to diagnostic teaching and letter writing within the school mathematics curriculum. Also, indicates that elementary school students benefit from letter writing as it relates to mathematics attitudes and achievement levels. (nine references) (JJK)