Rhymes are often useful teaching devices for small children, and can even become a creative resource for teaching mathematics. The students and their teachers can change many of them to better fit their environment and/or extend the rhyme so that higher numbers are involved. A number of rhymes and folk tales lend themselves to more detailed…

This classroom scholarship report is based on the teaching experience using Davydov's mathematics curriculum, which was developed in the former Soviet Union. While "from arithmetic to algebra" is the normally accepted instructional sequence in school mathematics, Davydov's curriculum is laid out "from algebra to arithmetic," focusing on algebraic…

Manipulatives are the way to our future and the way to new knowledge. No matter where we turn or what we do, we as a society are using some form of manipulative in our lives. Mathematics is changing all of the time from basic arithmetic to basic calculus. Therefore, children in today's classroom deserve to have that extra tool to help them grasp…

NCTM Past President Cathy L. Seeley shares her messages on today's most relevant topics and issues in education. Based on Cathy L. Seeley's award-winning NCTM President's Messages, and including dozens of new messages, this must-have K-12 resource offers straight talk and common sense about some of today's most important, thought-provoking issues…

This study examined the effects of extra time on the reading comprehension performance of a heterogeneous group of adults with reading disabilities. Sixty-four adults participated. A clinic that assesses learning disabilities identified 22 as reading disabled, and 42 as normal readers. The 64 adults took a reading comprehension test under both…

This paper articulates a perspective on learning to discuss ways in which students develop personal sense and negotiate meaning in a middle school algebra context. Building on a sociocultural perspective that incorporates mental objects, learning is described as a mutually dependent process involving personal sense making and the public…

Calculators can be used in primary schools in a number of situations. They are most beneficial when working with large numbers, dealing with real data that leads to complex calculations, performing repetitive calculations, developing concepts, estimating and checking, problem solving, and looking for patterns and/or relationships. But what if the…

Problem-posing abilities of 54 third graders who displayed different patterns of achievement in number concepts and novel problem solving were investigated in this paper. The children were administered a problem-posing pretest followed by an instructional program (for half the sample) and a delayed posttest. Among the findings are the limited…

This book contains activities and projects designed to be congruent with three underlying philosophies: the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards; Howard Gardner's multiple intelligences; and manipulatives, activities, and projects. The introduction contains information about educational reforms; multiple…

Defining better implicit models of children's actions in a series of situations is of paramount importance to understanding how knowledge is constructed. The objective of this study was to analyze the implicit mental models used by children in complex change problems to understand the stability of the models and their evolution with the child's…

Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…

A series of puzzle-type activities combining arithmetic reasoning and geometric figures is described and illustrated. (SD)

The first four chapters of a 14-chapter, three-volume work on arithmetical applications are contained in this document. Each chapter details the "use classes" of one broad arithmetical concept. (A "use class" of a concept is a set of examples of real world uses of the concept which share a common structure). Each chapter…