The relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms

The aim of the present study was to investigate the relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms. The mathematical language input provided by 35 kindergarten teachers was examined with 9 different input categories. The results of this study indicate that the role of each of these math talk categories is not as straightforward as was hypothesized. Although significant positive relations were found for math talk categories such as cardinality and conventional nominatives, the relations between the categories' calculation and number symbols and children's score on specific number sense tasks were negative. Moreover, a large diversity in math talk was negatively related to kindergartners' number sense acquisition. These results suggest that teachers should be careful and selective with the amount of math talk that they offer to young children.     

Numerosity and number signs in deaf Nicaraguan adults

What abilities are entailed in being numerate? Certainly, one is the ability to hold the exact quantity of a set in mind, even as it changes, and even after its members can no longer be perceived. Is counting language necessary to track and reproduce exact quantities? Previous work with speakers of languages that lack number words involved participants only from non-numerate cultures. Deaf Nicaraguan adults all live in a richly numerate culture, but vary in counting ability, allowing us to experimentally differentiate the contribution of these two factors. Thirty deaf and 10 hearing participants performed 11 one-to-one matching and counting tasks. Results suggest that immersion in a numerate culture is not enough to make one fully numerate. A memorized sequence of number symbols is required, though even an unconventional, iconic system is sufficient. Additionally, we find that within a numerate culture, the ability to track precise quantities can be acquired in adulthood.     

Number-knower levels in young children: insights from Bayesian modeling

Lee and Sarnecka (2010) developed a Bayesian model of young children’s behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children’s behavior. One, the knower-levels theory, is basically a “stage” theory involving real conceptual change. The other, the approximate-meanings theory, assumes that the child’s conceptual knowledge is relatively constant, although performance improves over time. In the second extension, the model is used to ask whether the same latent psychological variable (a child’s number-knower level) can simultaneously account for behavior on two tasks (the Give-N task and the Fast-Cards task) with different performance demands. Together, these two demonstrations show the potential of the Bayesian modeling approach to improve our understanding of the development of human cognition.     

Reducing the gap in numerical knowledge between low- and middle-income preschoolers

We compared the learning from playing a linear number board game of preschoolers from middle-income backgrounds to the learning of preschoolers from low-income backgrounds. Playing this game produced greater learning by both groups than engaging in other numerical activities for the same amount of time. The benefits were present on number line estimation, magnitude comparison, numeral identification, and arithmetic learning. Children with less initial knowledge generally learned more, and children from low-income backgrounds learned at least as much, and on several measures more, than preschoolers from middle-income backgrounds with comparable initial knowledge. The findings suggest a class of intervention that might be especially effective for reducing the gap between low-income and middle-income children's knowledge when they enter school.     

Discriminating the integrated orientation of line segments and its statistical efficiencies

Abstract:  We carried out two experiments to investigate both how efficiencies fluctuate due to the experimental conditions and how we determine the representative efficiency among such various efficiencies in the discrimination task of line orientations. In Experiment 1, line segments were displayed simultaneously and dispersed spatially, while in Experiment 2, line segments were displayed sequentially. In both experiments, statistical efficiencies were calculated. In Experiment 1, efficiencies initially increased as stimulus duration increased, and decreased as the number of lines increased to a point where the efficiencies remained almost stable despite additional changes of stimulus duration or number of lines. In contrast, in Experiment 2, efficiencies were stable for almost all numbers of sequentially displayed lines, except for the condition that four lines were displayed in random positions. These stable efficiencies were approximately 50% in Experiment 1 and 30–50% in Experiment 2. We suggest that these stable efficiencies are varied in the context that human and ideal observers would adopt the same strategy regardless of the experimental conditions.     

The Political Color Line in America: Many “Peoples of Color” or Black Exceptionalism?

Despite the successes of the civil rights movement, a largely impermeable color line continues to restrict African Americans from assimilation into the broader American society. In the meantime high rates of immigration have produced an increasingly culturally diverse population. A "people of color" hypothesis suggests that the color line the new immigrants face resembles that imposed on African Americans. A "black exceptionalism" hypothesis suggests instead that the color line will be more porous for them, allowing for greater assimilation over successive generations, including a gradual weakening of politicized racial and ethnic group consciousness. Using data from Los Angeles County Social Surveys, we find that the largest new immigrant group, Latinos, like blacks, show strongly group-interested policy preferences and strong group consciousness. However, both effects are stronger for recent Latino immigrants than for the U.S.-born. We conclude that the new immigrant groups are increasingly likely to assimilate politically into the broader society in future generations, whereas a rather strict color line will continue to restrict blacks and maintain their distinctiveness.     

一位阿拉伯数字的空间表征

数字数量的空间表征问题是认知心理学领域的研究热点之一。本研究采用Fischer等人的实验范式,探讨了较浅程度加工时一位阿拉伯数字在水平和垂直方向上的空间表征,结果发现:(1)对数字进行较浅程度的加工(仅仅注视数字)时,在水平方向上出现了SNARC效应,即激活了数字在水平方向上的空间表征,数字数量按照小、中、大的顺序自左而右地映射到心理数字线上;(2)对数字进行较浅程度加工时,在垂直方向上没有出现SNARC效应,即未激活数字在垂直方向上的空间表征。     

Are Line Lengths Critical to the Discrimination of Axisymmetric Pairs of Figures from Disoriented Identical Pairs?

I examined whether the lack of a difference in line lengths made the discrimination of axisymmetric (Ax) pairs of figures from disoriented identical (Idr) pairs difficult. Three basic pair types were prepared: Idr, Ax, and nonidentical/nonaxisymmetric (Nd) pairs. To avoid confusion arising from structural differences, all pairs of figures were set to be mutually isomorphic. Two figures of a pair were controlled to have the same line lengths of respective figural components (Experiment 1) or the same lengths of individual line segments (Experiment 2) in experiments where participants decided if the figures were the same/different. Experiment 1 showed longer latencies for Ax pairs than for Nd pairs, indicating that these feature values alone did not cause difficulty in discrimination. Experiment 2 showed that only Nd pairs with all line segments having the same lengths for the two figures had the same latencies as Ax pairs. The sameness of individual line segments in simple pairs of figures made discrimination difficult.     

Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

Previous studies showed that children learning a language with an obligatory singular/plural distinction (Russian and English) learn the meaning of the number word for one earlier than children learning Japanese, a language without obligatory number morphology (Barner, Libenson, Cheung, & Takasaki, 2009; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007). This can be explained by differences in number morphology, but it can also be explained by many other differences between the languages and the environments of the children who were compared. The present study tests the hypothesis that the morphological singular/plural distinction supports the early acquisition of the meaning of the number word for one by comparing young English learners to age and SES matched young Mandarin Chinese learners. Mandarin does not have obligatory number morphology but is more similar to English than Japanese in many crucial respects. Corpus analyses show that, compared to English learners, Mandarin learners hear number words more frequently, are more likely to hear number words followed by a noun, and are more likely to hear number words in contexts where they denote a cardinal value. Two tasks show that, despite these advantages, Mandarin learners learn the meaning of the number word for one three to six months later than do English learners. These results provide the strongest evidence to date that prior knowledge of the numerical meaning of the distinction between singular and plural supports the acquisition of the meaning of the number word for one.     

Eye Movements Reveal Mental Looking Through Time

People often make use of a spatial “mental time line” to represent events in time. We investigated whether the eyes follow such a mental time line during online language comprehension of sentences that refer to the past, present, and future. Participants' eye movements were measured on a blank screen while they listened to these sentences. Saccade direction revealed that the future is mapped higher up in space than the past. Moreover, fewer saccades were made when two events are simultaneously taking place at the present moment compared to two events that are happening in different points in time. This is the first evidence that oculomotor correlates reflect mental looking along an abstract invisible time line during online language comprehension about time. Our results support the idea that observing eye movements is likely to “detect” invisible spatial scaffoldings which are involved in cognitively processing abstract meaning, even when the abstract meaning lacks an explicit spatial correlate. Theoretical implications of these findings are discussed.