Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

Discussed is the importance of incorporating calculators and computers into the primary grades. Number concepts, counting skills, place-value, basic operations, problem-solving, and higher order thinking skills can be reinforced by using calculators and computers along with manipulatives. (KR)

Discusses the use of calculators to calculate multiple operations. Describes calculating procedures and provides four different types of examples. (YP)

Describes the process through which four high-achieving second graders constructed their knowledge and misconceptions of rounding concepts gained from using computer-based practice sessions which provided full solutions to examples but without verbal explanations. (31 references) (MKR)

Describes a wide range of activities based on a grade-number theme of "two" in second grade, "three" in third grade, and "four" in fourth grade. (MKR/SW)

Discusses ways teachers can encourage students to construct useful meanings for the fractional unit. Provides three examples of representations of common fractions and illustrates misconceptions in fraction problems. Includes a brief summary of constructivist mathematics education and an example in which a teacher misunderstands a fractional unit.…

Presents a study that analyzed errors made by randomly chosen fourth grade students (25 of 57) while using the division algorithm and investigated the effect of remediation on identified systematic errors. Results affirm that error pattern diagnosis and directed remediation lead to new learning and long-term retention. (MDH)

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Normally achieving students (n=119) and students with mild handicaps (n=83) in grades 3-6 were instructed to create and answer computation items similar to samples given. Students with mild handicaps understood item characteristics enough to create like items, though averaging three years behind normal achievers. A sample instructional activity is…

Presented are simple activities that can be completed by students at home with the help of a parent. Activities include the topics of sorting, patterning, counting and numbers, geometry, adding, subtracting, and measuring. Each activity describes a series of sequenced tasks related to one of the topics. (KR)

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

A class of 32 fourth graders, who studied inverse operations in grades 1-3, was given 3 written tests, each followed by an interview, to see how well they could simplify computations using inverse operations. Most could not evaluate 28 + 75 - 75, for example, without performing all operations. (GW)

The present study explores the experience of two young Gypsy girls in solving school arithmetic tasks in interaction with an adult who supports their participation. Along with learning the use of arithmetic tools, a basic element concerning the experience of the two girls as they try to gain entry into the school practice is learning about…

This article discusses how children learn to understand the decimal system in very concrete ways, while having fun using beads. When counting the beads, the children learn 5,491 is not simply "five thousand four hundred and ninety-one" but actually 5 thousands, 4 hundreds, 9 tens, and 1 unit. They begin to understand that as they get 10 units,…

This microgenetic study investigated similarities and differences in use and discovery of addition strategies in children with and without mild mental retardation across 24 sessions. Nine children with mild mental retardation in third through fifth grade classrooms and 14 children without mental retardation in kindergarten classrooms were tested…