The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics…

This issue of the journal contains abstracts and critiques of ten research reports. They address such topics as: (1) characterizing the Van Hiele levels of development in geometry; (2) children's ideas about commutativity in the early elementary arithmetic program; (3) two children's anticipations, beliefs and motivations about mathematics; (4) a…

The theme of the sixth annual meeting of the North American Chapter of Psychology of Mathematics Education was "The Importance of Psychological Models for Research in Mathematics Learning." The conference proceedings contain papers organized around five major topics. In the first section, eight papers on the learning of arithmetic are…

This study investigated the effectiveness of LOGO's turtle graphics in both providing a model of systematic thought and in teaching simple geometry to young children in the second grade. The treatment given to 25 second grade students in the experimental group consisted of programming with LOGO's turtle graphics using four Apple II+…

Described is research which sought to prove the hypothesis that mental models tend to preserve their autonomy with regard to the originals they are meant to represent. The results of this investigation involving 200 Israeli students are presented. (CW)

Responds to Crowley's and Wilson's articles on the reliability of the van Hiele Geometry Test. Discusses the issue of the difficulty of trying to maximize content validity while minimizing measurement error. (YP)

Investigates the relationship between the strategies used by preservice elementary teachers in geometric problem solving and two primary mental abilities--spatial visualization and formal reasoning. Reports that the two abilities were related to problem-solving performance, and the strategies used were related to achievement in the geometry…

In the research described in this document, the goal was to develop definite theoretical characterizations of understanding in a specific domain of problems. Some performance that provides persuasive evidence of understanding was chosen, and hypotheses about cognitive structures and processes that cause the performance to occur were developed.…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

Provides an alternative analysis of the reliability associated with the van Hiele Geometry Test based on the assumption that the norm-referenced reliability coefficients provided by the developers were inappropriate. Discusses the agreement coefficient and the kappa coefficient. (YP)

Presented is a study which focused on using turtle graphics programing for geometric problem solving. The goal was to investigate changes in children's mathematical knowledge and results indicate that the LOGO environment enriched children's geometric conceptualizations and sophistication of their geometric thinking. (KR)

The papers presented in these proceedings are organized into seven categories: (1) number and number operations (13 papers); (2) spatial representation and geometrical understanding (10 papers); (3) developing and/or using models of mathematical learning (15 papers); (4) mathematical concept formation (17 papers); (5) the mathematical learning…

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)

Reported is whether and how mathematics has changed during the 75 years of the Mathematical Association of America's (MAA) existence. The progress of mathematics is organized into 9 concepts, 2 explosions, and 11 developments. (KR)