How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively,…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

The move from additive to multiplicative thinking requires significant change in children's comprehension and manipulation of numerical relationships, involves various conceptual components, and can be a slow, multistage process for some. Unit arrays are a key visuospatial representation for supporting learning, but most research focuses on 2D…

Today, almost all introductory physics textbooks include standardized "rules" on how to find the number of significant figures in a calculated value. And yet, 30 years ago these rules were almost nonexistent. Why have we increased the role of significant figures in introductory classes, and should we continue this trend? A look back at…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

Binomial coefficients are used to prove two conjectures concerning the partitioning of an N-dimensional space. (MP)

Students have the opportunity to verbalize relationships that demonstrate the acquisition of good number sense. They are to develop clues about the answer to a problem without computing or telling the answer, and to state or write several things they know about the answer to each problem. (MNS)

This mathematics textbook, written in Portuguese, is designed for second graders. Developed from objectives set forth by the National Portuguese Materials Development Center, it follows closely the objectives and methodology of major curricula used in schools of the United States. The thirteen chapters deal with: numeration (0-999); addition with…

Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

This mathematics textbook, written in Portuguese, is the third book of a Mathematics Program in Portuguese. It is designed for third graders. It closely follows the objectives and methodology of the major curricula used throughout the schools in the United States. The 11 chapters deal with: numeration (0-999,999); addition with and without…

This teachers manual accompanies a mathematics textbook, written in Portuguese, for third graders. It closely follows the objectives and methodology of the major curricula used throughout the schools in the United States. The 11 chapters deal with: numeration (0-999,999); addition with and without regrouping; subtraction with and without…

This document is part 2 of the workbook for grade 4 pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

This teacher's manual accompanies a mathematics textbook for second graders, written in Portuguese. Developed from objectives set forth by the National Portuguese Materials Development Center, it follows closely the objectives and methodology of major curricula used in schools of the United States. Consideration was given to the Portuguese child's…

Discusses ways that calculators and computer microworlds, such as LOGO and Shape Makers, can be used as tools for exploration, problem solving, and empowerment in school mathematics. Includes suggestions for classroom activities. (Contains 12 references.) (MKR)