The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

Describes second graders' responses to finding the sum of the numbers from 1 through 10 after reading the book, Ten Black Dots. Includes student work demonstrating their problem solving. (MKR)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

Presents results from an Australian study examining whether children who use cognitive strategies in solving simple addition questions develop greater proficiency in addition than children who do not use such strategies. Describes the subjects, instruments, procedure, and instructional treatment. Concludes that the development of cognitive…

Summarized are the findings from five studies carried out in Australia in 1979-80. First was a cross-sectional survey designed to determine the memory capacity of a population of children in grades 1-3. The second study investigated performance differences on a variety of mathematically related developmental tasks for the same group. Data from…

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

Three studies on the development of number concepts (counting, addition, subtraction, and place value) in seven- to nine-year-olds considered low attainers in mathematics were conducted. The search for a descriptive framework, the development of a diagnostic assessment instrument, and a longitudinal study are reported. (MNS)

Presents two seasonally related investigations involving arithmetic series to develop critical thinking: (1) the number of candles needed for the eight nights of Hanukkah, and (2) the number of presents given during "The Twelve Days of Christmas." Students also calculated the amount of money needed to buy all the presents. (MDH)

Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

Recent research suggests that many middle school students approach mathematical story problems with strategies that are not based on possible meanings for the operations, yielding success for one-step problems, but providing a weak background for approaching algebra story problems. This document reports the findings and the materials developed by…