The give-"n" task is widely used in developmental psychology to indicate young children's knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and…

Number-recognition tasks, such as the how-many task, involve set-to-word mapping, and number-creation tasks, such as the give-n task, entail word-to-set mapping. The present study involved comparing sixty 3-year-olds' performance on the two tasks with collections of one to three items over three time points about 3 weeks apart. Inconsistent with…

Recent research has found that linguistic cues may affect children's number word acquisition. Two studies were undertaken to evaluate the use of singular/plural markings and small number words in Chinese and English and its effect on children's number concepts. The first study utilized the CHILDES data and investigated how singular/plural markings…

A mother tracked her preschooler's number word development daily from 18 to 49 months of age. Naturalistic observations were supplemented with observations during structured (Kumon) training and microgenetic testing. The boy's everyday use of "two" did not become highly reliable and selective for 10 months (at 28 months), emerged later than that…

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…

Little research has focused on an informal understanding of subtractive negation (e.g., 3 - 3 = 0) and subtractive identity (e.g., 3 - 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1 - 1 = 2). Recognition of a small…

Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…

Memorizing the basic number combinations, such as 9 + 7 = 16 and 16 - 9 = 7, is a punishing and insurmountable task for children with difficulties learning mathematics. Two perspectives on such learning lead to different conclusions about the primary source of this key learning difficulty. According to the conventional wisdom (the Passive Storage…

Fifteen trainable mentally retarded students (four-six years old) were generally capable of rule-governed and other counting skills, and some could mentally compare numbers and choose the larger. Some Ss demonstrated a basic form of problem solving: they used the addition identity and commutativity principles to shortcut computational effort.…

The study examined the effectiveness of a tutoring program on counting and number skills for trainable mentally retarded (TMR) and educable mentally retarded (EMR) students (5-14 years old). Experimental Ss received individualized instruction based on counting games while control Ss received instruction on objectives not related to counting.…

Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…

The study investigated whether 15 children (ages 6-21) with IQs from 31 to 66 could spontaneously invent more efficient calculational procedures and abstract basic arithmetic relationships after individualized tutoring in computation. Experimental subjects were given training that focused on accurate computation but specific relationships and…

Four three-year-old girls were studied in seven sessions during a three-month period for their performance on rote and object counting tasks. Two exhibited behavior consistent with underlying stable-order and uniqueness principles. (MNS)

Developmental patterns and interrelationships of various informal skills, reading and writing of numerals, and a range of base ten/place value concepts/skills were examined in a study involving 78 primary school children from four schools who were individually examined in a standardized interview. A total of 23 tasks were administered and…

Eleven retarded children with mental ages (MA) less than 4.5 years were examined to evaluate whether there is a critical MA for learning basic counting principles and how an understanding of counting develops. Results are discussed in terms of individual needs. (MNS)