Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

The possible use of a calendar algorithm was assessed in DBC, an autistic "savant" of normal measured intelligence. Testing of all the dates in a year revealed a random distribution of errors. Re-testing DBC on the same dates one year later shows that his errors were not stable across time. Finally, DBC was able to answer "reversed" questions that…

Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…

Curriculum modification strategies, particularly curriculum adaptations and augmentations, have been identified as important to enable learners with disabilities to achieve access to and progress in the general curriculum. There is, however, relatively little research on the effect of these strategies with students with intellectual and…

This article explores the relationship between research and teaching, arguing that each of them is both a demanding science and an imaginative art, and that they both manifest the values and processes of learning, the open mind and the open heart, as it were. This is a rather different proposition from the notion that "evidence" can be "applied"…

The present study investigates the development of children's ability to make inferences about a peer's mental state. In this study 48 eight-year-old children, 49 ten-year-old children and 44 adults observed and analyzed short video sequences, extracts from a socio-cognitive interaction between two children working on a mathematical task. The…

A problem solving strategy, Thinking Aloud Pair Problem Solving (TAPPS), developed by Arthur Whimbey to help students monitor and understand their own thought process is presented. The TAPPS strategy encouraged the students interact verbally with each other to solve chemistry problems and improve the achievements in chemistry.

We report on a two-year NSF-funded project to strengthen connections among science, technology, engineering, and mathematics (STEM) disciplines. One component of this project was to produce some initial data on the effectiveness of Interdisciplinary Lively Applications Projects (ILAPs) in teaching science and engineering undergraduates. ILAPs are…

The author describes 10 classroom activities that are designed to promote reading comprehension and organizational skills in the context of solving math problems. These lessons help students to clarify the information within math problems, identify what operations are necessary, and express their solutions more accurately and precisely. A…

This paper discusses the curriculum and students' and teachers' conceptions of proof. It goes on to discuss university students' difficulties with proving related to understanding and using definitions and theorems, understanding the structure of a proof, knowing how to read and check proofs, knowing and using relevant concepts, bringing…

"Every Child" is Australia's premier early childhood publication, aimed at anyone involved in the care and education of children from birth to eight years--in particular child care professionals, teachers, child care students and the parents of young children. Published quarterly, it contains informative and entertaining articles on such…

"Progress in Mathematics[C] 2006" is a new core curriculum for students in kindergarten through grade 6. "Progress in Mathematics[C] 2006" differs substantively from "Progress in Mathematics[C] 2000" in both content and assessment material. "Progress in Mathematics[C] 2006" uses a sequence of systematic…

The Maui Hawaii Educational consortium (the Maui School District and Maui Community College) sought scientifically based evidence for the effectiveness of the "Cognitive Tutor" ("CT") Algebra I Curriculum to inform adoption decisions. Decision makers were particularly interested in whether the use of the "CT" program…

Teacher-learner relationships are founded on the fundamental human need of knowing that another person genuinely cares. Students know when they are recognized, understood, and respected for their unique abilities and interests by their teachers. Teachers who believe in their students' abilities demonstrate that they care by placing the learners at…

This paper describes a content upgrading course on Secondary School Algebra which was planned and conducted for in-service mathematics teachers who are trained to teach mathematics at lower secondary level (ages 13 to 14). In order to be an effective mathematics teacher, one needs to know a great deal of mathematical knowledge on top of good…