Presented is a method of teaching adding and subtracting as an interrelated series of patterns using a number line. Examples of the use of this method as well as the materials necessary are discussed. Applications of the method to multiplication and division are given. (CW)

One method of making magic squares using a prolongated square is illustrated. Discussed are third-order magic squares, fractional magic squares, fifth-order magic squares, decimal magic squares, and even magic squares. (CW)

Described is a study of second grade classes that participated in a year-long project in which instruction was generally compatible with a socioconstructivist theory of knowledge and recent recommendations of the National Council of Teachers of Mathematics. Methods, results, and implications for mathematics instruction are discussed. (CW)

Four activities are described which focus on consumer awareness and judgment using data collection and judgment skills involving data from footwear. Worksheets for data collection and activities at home and at school are included. A set of ratings of sneakers from "Consumer Reports" magazine is provided. (CW)

Performance of 5 students (ages 8 and 10) with moderate intellectual disability was compared as they received the DISTAR Arithmetic instructional intervention and a Discrimination Learning Theory (DLT) intervention not requiring a fast-paced verbal student response. Academic engagement and skill mastery were greater during the DLT intervention.…

Reviewed is an integrated approach to teaching place-value concepts. A semi-integrated approach is proposed which may provide a more effective implementation of the technique. (CW)

Indicates the shortcomings of paper-and-pencil tests. Reports the effect of an interview-and-teaching method for students who obtained correct answers by a mechanical process but lacked a conceptual foundation. Five references are listed. (YP)

Urban Canadian sixth-graders (n=84) were tested on 80 arithmetic word problems developed as part of a larger set to reflect individual differences in problem solving. Problems varied in complexity of language and amount of extraneous information present. Results indicated substantial internal consistency and concurrent validity relative to…

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

Presents 3 examples for setting teacher's aims in Japanese and American mathematics classrooms. Provides 10 guidelines for teachers who would like to include more mathematical dialogue and encourage the expression of conceptual splatter in their classrooms. (YP)

Provides methods of teaching negative number operations, including addition, subtraction, and multiplication. Presents examples and activities for the operations. (YP)

Investigated problem-solving perseverance of (n=40) students in grades 6 and 10 while solving nonroutine number problems. Students who were ultimately successful were more inclined than others to be flexible in their use of strategies. (40 references) (Author/MKR)

Describes a computer program for arithmetic in which the use of the operationalized cognitive apprenticeship methods was studied together with effects of modelling and coaching on student performance. Results showed that adult basic education students make little use of optional materials in a computer program. (Author/JKP)

Interviews with in-service elementary teachers (n=32) who were asked to solve multiplicative problems showed that teachers who solved problems relationally reasoned in terms of ratio and proportion concepts, whereas teachers who arrived at correct solutions without the concepts did so using a trial-and-error method. (24 references) (Author/MKR)