Presents a technique for multiplying two-digit numbers whose tens digits are equal and whose units digits have a sum of 10. Then various mental calculations with other types of two-digit and larger numbers are discussed. (MNS)

Relations among the number and types of strategies used by 89 college students when estimating, quantitative ability, and computational estimation ability were investigated. Students of relatively high quantitative ability were found to be better estimators and used more strategy types. (MP)

The performance on a battery of cognitive tests of an individual with extraordinary ability at mental arithmetic was studied. Implications of the rather ordinary test performance of Shakuntala Devi in contrast with her calculating speed are discussed with reference to memory and information processing. (SLD)

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

Research has been done to look at the benefits of BILOG over LOGIST as well as the potential issues that can arise if transition from LOGIST to BILOG is desired. A serious concern arises when comparability is required between previously calibrated LOGIST parameter estimates and currently calibrated BILOG estimates. It is imperative to obtain an…

The Statistical Analysis System was used to program a statistical procedure developed by K. J. Levy (1975). The focus was on Dunnett-like pairwise multiple comparisons among sample variances. An example using data from G. Glass and K. Hopkins (1996) is used to illustrate a computer run with this program. (Author/SLD)

Analyzes objections to the computational paradigm recently proposed by several cognitive scientists, suggesting that their objections are grounded in objections to specific properties of representations as they are used in various psychological theories. Discusses five properties that can be added to mediating states and examines their importance…

Three studies examined three- to six-year olds' understanding of cardinality independent of counting order. Found that more children expected different order count to yield same number when they did not have to count than when they counted or monitored puppet's counting. More children predicted that recounting would yield the same number than the…

We evaluated Samaniego and Reneau's 1994 novel weight method for eliciting subjective probability estimates. Experiment 1 replicated their experiment (subjects weighed their prior estimate against 10 new observations), with an additional weight judgment against 50 observations. In Experiment 2, subjects gave prior estimates to questions in a…

Bases such as 5 and 12 provide the same structural place value benefits as base 10. However, when numbers less than one are concerned, base 10 provides friendly decimals for the most common fractions of half, quarter, three-quarters. Base 5 is not user friendly at all in this regard. Base 12 would provide nice dozenimals(?) for the same…

The Bernoulli polynomials are generalized and some properties of the resulting generalizations are presented.

A general cubic equation ax[cubed] + bx[squared] + cx + d = 0 where a , b , c , d [is a member of R], a [not equal to] 0 has three roots with two possibilities--either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of…

These proceedings contain the papers of the 16th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2019), held during November 7-9, 2019, which has been organized by the International Association for Development of the Information Society (IADIS) and co-organised by University Degli Studi di Cagliari, Italy.…

Reciprocal determinism is a central premise of Bandura's (1986) social cognitive theory. Studies of the relationship between self-beliefs and performance tend to draw on this or related theories and usually endorse the notion of reciprocal determinism at a substantive-theoretical level. However, attempts to model this postulated mutual influence…

The widely used PASCO laboratory equipment is an excellent way to introduce students to many topics in physics. In one case, PASCO's equipment may be too good! Various experiments exist for calculating the kinetic coefficient of friction by measuring the acceleration of a sliding object under some constant force. With ever more accurate equipment,…