Within initial teacher education there is increasing pressure to enhance the use of assessment data to support students to improve their knowledge and skills, and to determine what standards they meet upon graduation. For such data to be useful, both programme designers and students require meaningful and comprehensive assessment reports on…

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…

Explores mathematical methods children use to find answers for themselves. Describes some methods used for multiplication and subtraction problems. (YP)

Since the mid-1960s a new approach has dominated American research in the area of mathematics education -- information-processing theory. The author examines several examples of research in this new tradition and sketches the general features of an emerging information-processing psychology of teaching. Information-processing studies that employ…

Honors the contribution of Efraim Fischbein to the study and analysis of probabilistic thinking. Summarizes Fischbein's early work, then focuses on the role of intuition in mathematical and scientific thinking; the development of probabilistic thinking; and the influence of instruction on that development. (Author/MM)

The educational background of students termed "limited English proficient" (LEP) is discussed, with consideration of how that background might affect the LEP student's learning of arithmetic. Reasons why knowledge of background is important are first noted. Then examples of different ways to read and write numerals and differing subtraction and…

Discusses histories of three current issues in the psychology and pedagogy of mathematical thinking: (1) the notion of a "prescriptive method"; (2) "associationism" as an explanation for learning; and (3) Gestaltism. Reviews theoretical perspectives that emerged starting in the mid-twentieth century, including behaviorism,…

Presents results of a diagnostic analysis of mathematics and science achievement data for Black students collected by the National Assessment of Educational Progress. Identifies the taxonomic level (knowledge, skills, comprehension, application, and analysis) and content area of exercises on which Black students perform below the national average.…

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…

Discusses a performance assessment tool that entails open-ended tasks requiring students not only to provide answers but to show their solution processes. Discusses several areas to address in developing open-ended tasks. Areas include the need to assess important mathematical content and cognitive processes, use of effective prompts, and use of…