The major targets of number agreement in English are pronouns and verbs. To examine the factors that control pronoun number and to test pronouns against a psycholinguistic account of how verb number arises during language production, we varied the meaningful and grammatical number properties of agreement controllers and examined the impact of…

Everyone is familiar with the concept that the cube and octahedron, dodecahedron and icosahedron are dual pairs, with the tetrahedron being self-dual. On the face of it, the concept seems straightforward; however, in all but the most symmetrical cases it is far from clear. By using the computer and three-dimensional graphics programs, it is…

The authors investigated how 2-digit Arabic numerals are named by looking at the effects of masked primes on the naming latencies. Target numerals were named faster when prime and target shared a digit at the same position (e.g., the target 28 primed by 18 and 21). In contrast, naming latencies were slower when prime and target shared 1 or 2…

The enumeration of small numbers of objects (approximately 4) proceeds rapidly, accurately, and with little effort via a process termed subitization. Four experiments examined whether it was possible to subitize the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

This paper presents a qualitative study that investigated two third-grade students' understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as…

This article describes the experiences of a group of primary-grade students and their teacher as they explore negative numbers over the course of two years. It is just one example of how a problem-solving environment contributes to discussion and understanding in mathematics. (Contains 3 figures.)

A criterion-referenced computerized test is expressed as a statistical hypothesis problem. This admits that it can be studied by using the theory of optimal design. The power function of the statistical test is used as a criterion function when designing the test. A formal proof is provided showing that all items should have the same item…

Mathematics is not only taught because it is useful. It should be a source of delight and wonder, offering pupils intellectual excitement and an appreciation of its essential creativity. In this article, the author discusses four basic principles that he currently believes: (1) All children can do mathematics; (2) Active participation is required…

Deaf people have difficulty reading and remembering English script because of its sound-based orthography. Logographs (e.g., kanji, Arabic numerals) should not pose the same challenge because they are based on meaning, not sound. Little research has been conducted to test this theory's validity cross-culturally. The present study was an attempt to…

The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.

This article describes how children learn the basic addition and subtraction facts, why many have difficulty mastering these basic skills, and what teachers can do to prevent or overcome these learning difficulties.

AN ATTEMPT WAS MADE TO ASSESS THE EFFECTS ON ADULT LEARNING OF DIFFERENTIALLY STRUCTURED INTRODUCTORY COGNITIVE LEARNING TASKS AND MATERIALS, AND THE INTERACTION OF INTELLIGENCE WITH THE EXPERIMENTALLY MANIPULATED MATERIAL AND TASK CATEGORIES. ABOUT 96 ADULTS WHO WERE UNFAMILIAR WITH THE CONCEPT OF NUMBER BASES WERE CLASSIFIED ACCORDING TO A 4X3X4…

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…