By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

A first grade teacher in a rural elementary school in upper East Tennessee observed that her students needed a better way to improve their computation skills than those of traditional instructional methods. The school system's new Mathematics textbook was correlated with commercial Mathematics software. The teacher wanted to find out if using this…

The equivalence of multiple-choice (MC) and constructed response (discrete) (CR-D) response formats as applied to mathematics computation at grade levels two to six was tested. The difference between total scores from the two response formats was tested for statistical significance, and the factor structure of items in both response formats was…

Reviews the principles of Monte Carlo calculation and random number generation in an attempt to introduce the direct and the rejection method of sampling techniques as well as the variance-reduction procedures. Indicates that the increasing availability of computers makes it possible for a wider audience to learn about these powerful methods. (CC)

Magic squares are used both as a vehicle for arithmetic drill and the development of mathematical concepts for second-grade students. By searching for patterns within the squares, additional number concepts are developed along with the concept of symmetry. (JP)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

Computational skills in multiplication and division are reinforced and practice is provided on these worksheets on estimating, finding factors, and determining divisibility. (MNS)

The effectiveness of the Multisensory Basic Fact Program to teach addition facts to 115 remedial groups in grades two through six in Australian schools was studied. Performance increased between pre- and posttests and was maintained on the retention test. (MNS)

A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

Investigation of the relationship between systematic computational errors and achievement among native Indian children indicated a significant relationship between error type and achievement in multiplication but not in addition or subtraction. In multiplication, high achievers tended to make nonsystematic errors; low achievers tended to make…

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

A way to use tongue depressors in a model of multiplication is presented. The original intent was to use the sticks to teach about fractions, but "mistakes" in student responses led to new ideas. It is felt that teachers should use the model in teaching multiplication. (MP)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

Pre-experimental interviews conducted with three children to investigate three aspects of the nature of counting are detailed. Sixteen findings related to the counting of perceptual items are summarized. (MP)