Analyzed students' reasoning with fractions. Found that skilled students applied strategies specifically tailored to restricted classes of fractions and produced reliable solutions with a minimum of computation effort. Results suggest that competent reasoning depends on a knowledge base that includes numerically specific and invented strategies,…

Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

This is an effective drill and practice activity that does not use consumable materials. It does not teach math facts, algorithms or concepts. It provides immediate feedback to the learner and can be easily modified for use in many curriculum areas. It is self correcting because the student can identify errors without assistance and provides…

Reports the third grade and seventh grade results of the fourth mathematics assessment of the National Assessment of Educational Progress. Summarizes the major results of the performance on number, operations, and word problem items. Some examples of data are given. (PK)

Using license plates and telephone numbers for teaching probability ideas involving counting rules is suggested. How each is useful is illustrated in some detail. (MNS)

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

In this paper, a contextual approach to teaching Mathematics at the pre-university level is recommended, and an example is illustrated. A "context" in the form of a real common mathematical problem is presented to the students. Different approaches to tackle the problem (from topics within and outside the syllabus) can be elicited from students.…

Behavioral objectives are listed for the primary, intermediate and junior high mathematics curriculum in the Mesa Public Schools (Arizona). Lists of specific objectives are given by level for sets, symbol recognition, number operations, mathematical structures, measurement and problem solving skills. (JP)

This article describes a valuable lesson that university mathematics faculty members learned from fifth grade and middle school teachers in a professional development workshop. The goal of the workshop was to show how models for whole number operations could be linked to models for rational numbers and to connect the traditional algorithms to the…

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…