Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States

This study reports findings from comparative samples of sixth-grade Chinese and U.S. students' interpretations of the equal sign. Ninety-eight percent of the Chinese sample correctly answered 4 items indicating conceptions of equality and provided conceptually accurate explanations. In contrast, only 28% of the U.S. sample performed at this level. We examine how teacher preparation materials, students' textbooks and teachers' guidebooks treat equality in each country. U.S. teacher preparation textbooks rarely interpreted the equal sign as equivalence. On the contrary, Chinese textbooks typically introduced the equal sign in a context of relationships and interpreted the sign as “balance,” “sameness,” or “equivalence” and only then embedded the sign with operations on numbers.     

Task-invariant aspects of goodness in perceptual representation.

In two experiments, pairs of Garner's classical 5-dot patterns were presented with an interstimulus interval of 500 ms in a same-different task in which a physical sameness criterion was used: Rotated or reflected versions of the same pattern were rated as different. Patterns varied in "goodness" according to Garner's equivalence set size measure. Both first and second pattern goodness affected reaction time and accuracy. This result and fits of models to reaction time data indicate that equivalence set representations are used in the task, as in a related categorical matching task in previous studies. Two effects were observed that contrast with the categorical matching task: One is a conflict between the need to respond different to patterns that are categorically equivalent under the equivalence set representation; the other is that extra time is needed for rechecking of the representation if pattern structures are hard to distinguish. In combination with previous studies, the present results show that even though the processes differ, the same representational mechanism is used across tasks.     

A reappraisal of the relation between performances of quantitative identity and quantitative equivalence conservation tasks

Previous studies of children's performance on quantitative identity and equivalence conservation problems in the number domain are suggested to be flawed because of the low numbers of items in the arrays. In Experiment 1, children were tested on three different number versions of identity and equivalence conservation tasks. Their performance varied with the number of items and no child was found to pass a large number version of an equivalence conservation task and fail the corresponding version of an identity conservation task. In Experiment 2 the notion that the contextual effect of asking two similar questions might underlie the difference in performance on the two tasks was tested and rejected. The results are discussed in relation to recent analyses of conservation problems.     

Analysis of apparent demonstrations of responding in accordance with relational frames of sameness and opposition

We evaluated whether contextual control over equivalence and nonequivalence and responding by exclusion can explain the outcomes of relational frame theory (RFT) studies on sameness and opposition relations. We trained nine college students to maintain and reverse conditional discriminations with X1 and X2 as contextual stimuli. In Experiment 1, X1 and X2 controlled derived stimulus relations (DSR) analogous to those controlled by Same and Opposite in RFT studies. These results can be explained by at least two hypotheses: X1 and X2 were cues for equivalence and nonequivalence and responding by exclusion, or for sameness and opposition. In Experiment 2, X1 and X2 controlled DSR predicted by the hypothesis that they were cues for equivalence and nonequivalence and responding by exclusion, and not predicted by the hypothesis that they were cues for sameness and opposition. The results of Experiment 2 and the functional equivalence of X1 and X2 with Same and Opposite in Experiment 1 suggest that Same and Opposite were cues for equivalence and nonequivalence and responding by exclusion in RFT studies.     

Using Cognitive Interviewing for the Semantic Enhancement of Multilingual Versions of Personality Questionnaires

We discuss the use of cognitive interviewing with bilinguals as an integral part of cross-cultural adaptation of personality questionnaires. The aim is to maximize semantic equivalence to increase the likelihood of items maintaining the intended structure and meaning in the target language. We refer to this part of adaptation as semantic enhancement, and integrate cognitive interviewing within it as a tool for scrutinizing translations, the connotative meaning, and the psychological impact of items across languages. During the adaptation of a work-based personality questionnaire from English to Arabic, Chinese (Mandarin), and Spanish, we cognitively interviewed 12 bilingual participants about 136 items in different languages (17% of all items), of which 67 were changed. A content analysis categorizing the reasons for amending items elicited 11 errors that affect 2 identified forms of semantic equivalence. We provide the resultant coding scheme as a framework for designing cognitive interviewing protocols and propose a procedure for implementing them. We discuss implications for theory and practice.     

Assessing handwriting speed of children biliterate in English and Chinese

The assessment of multiliterate handwriting performance is rarely reported despite increased globalization. The present study describes the psychometric properties of a handwriting speed test developed for children who are biliterate in English and Chinese. This included interrater reliability, test-retest reliability, interitem correlation, construct validity, and concurrent validity. The test's reliabilities between two raters and over a 1-wk. interval were high with ICCs ranging from .89 to .99. Interitem correlation between the English and Chinese items was .87. The presence of age trends but not sex differences was a positive indicator of the test's validity. Correlations of .91 and 1.00 between the Chinese and the English items of the Handwriting Assessment Tool with the Chinese Handwriting Speed Test and Handwriting Speed Test, respectively, provided evidence of concurrent validity. These preliminary results showed the Handwriting Assessment Tool is reliable and is a potentially useful handwriting test for children biliterate in English and Chinese. The feasibility of assessing biliterate handwriting speed performance with the same set of scoring criteria for different writing systems was supported.     

Developing equivalent Chinese and English scale‐point labels for rating scales used in survey research

Rating scales are the most frequently‐used response tool in surveys, and the scale levels are commonly described with words [verbal scale‐point labels (VSPL)]. In this study, Chinese VSPL were identified which employ five‐point scales that are psychometrically equivalent to English VSPL. In several bilingual studies, a total of 61 Chinese and 44 English items addressing intensity, frequency, and agreement rating modalities were tested. For each VSPL, three aspects were measured: position between minimum and maximum, familiarity, and appeal. The correspondence between pertinent Chinese and English words was also assessed. Based on these findings, we recommend specific VSPL that are best‐suited for achieving equivalence between Chinese and English in rating scales.     

The Cultural Adaptation of the Youth Quality of Life Instrument-Research Version for Latino Children and Adolescents

We reviewed the Spanish translation of the Youth Quality of Life Instrument-Research Version (YQOL-R) and culturally adapted the measure with Puerto Rican and Mexican American children and adolescents. The YQOL-R is a self-reported measure that includes four domains: Sense of Self, Social Relationships, Environment, and General Quality of Life. A total of 10 focus groups were conducted with children aged 9 to 11, adolescents aged 12 to 17, their parents, and mental health providers. Five focus groups were conducted in San Diego, California and five in San Juan, Puerto Rico. Eligible participants were recruited from children’s outpatient psychiatry clinics. We followed an iterative and recursive process in reviewing changes and modifications to the instrument using a bilingual committee and a Multi National Bilingual Committee. Greater semantic, content, and technical equivalence of the Spanish and English versions for the YQOL-R was achieved for the two largest U.S. Latino subgroups: Mexican Americans and Puerto Ricans. The cultural adaptation process revealed several important issues regarding the measurement of quality of life in different age groups. Additional items for school, relationships (both family and friends) and spare time suggested the need for a future children’s version of the instrument. For the adolescents, additional items were suggested in the areas of sexuality, intergenerational conflict and acculturative stress.     

Assessing Measurement Invariance of the Children's Depression Inventory in Chinese and Italian Primary School Student Samples

This study tested the measurement invariance of Children's Depression Inventory (CDI) and compared its factorial variance/covariance and latent means among Chinese and Italian children. Multigroup confirmatory factor analysis of the original five factors identified by Kovacs revealed that full measurement invariance did not hold. Further analysis showed that 4 of 21 factor loadings, 14 of 26 intercepts, and 12 of 26 item errors were noninvariant. Factor variance and covariance invariant tests revealed significant differences between Chinese and Italian samples. The latent factor mean comparison suggested no significant difference across the two groups. Nevertheless, the finding of partial metric and scalar invariance suggested that observed mean differences on the CDI items cannot be fully explained by the mean differences in the latent factor. These results suggest that researchers and practitioners exercise caution when gauging the size of the true national population differences in depressive symptoms among Italian and Chinese children when assessed via CDI. In addition to providing needed evidence on the use of the CDI in Italian and Chinese children specifically, the methods used in this research can serve more generally as an example for other cross-cultural assessment research to test structural equivalence and measurement invariance of scales and to determine why it is important to do so.     

中国人人格量表（QZPS）的编制过程与初步结果

旨在编制能够反映中国人人格结构特点的中国人人格量表（QZPS）。文中首先分析了直接采用或修订西方人格量表的问题和潜在危险,以及目前国内使用的各种人格量表存在的局限;按照人格研究的“词汇学假设”,根据杨国枢和王登峰（1999）以及后来的研究所确定的中国人人格结构的七因素模型,提出了QZPS的编制原则和操作程序。按照人格特质形容词的含义编写测量项目,并根据小因素和大因素的含义对项目进行修改,初步确定了1600多个项目。经2280名被试的评定,初步筛选出409个项目。再经1099名被试评定,确定了215个项目构成QZPS,测量中国人人格的7个维度和18个小因素。文中还报告了对QZPS的项目分析的结果     

Sound symbolism facilitates early verb learning

Some words are sound-symbolic in that they involve a non-arbitrary relationship between sound and meaning. Here, we report that 25-month-old children are sensitive to cross-linguistically valid sound-symbolic matches in the domain of action and that this sound symbolism facilitates verb learning in young children. We constructed a set of novel sound-symbolic verbs whose sounds were judged to match certain actions better than others, as confirmed by adult Japanese- as well as English speakers, and by 2- and 3-year-old Japanese-speaking children. These sound-symbolic verbs, together with other novel non-sound-symbolic verbs, were used in a verb learning task with 3-year-old Japanese children. In line with the previous literature, 3-year-olds could not generalize the meaning of novel non-sound-symbolic verbs on the basis of the sameness of action. However, 3-year-olds could correctly generalize the meaning of novel sound-symbolic verbs. These results suggest that iconic scaffolding by means of sound symbolism plays an important role in early verb learning.     

Because it's there! Why some children count,rather than infer numerical relationships

Two experiments are described that investigate the ability to infer the number of items in one-to-one corresponding sets for two age groups. We assess the influence of set size, the visibility of sets, and the way in which set equivalence is derived – pairing versus sharing – using a repeated-measures design. Three-year-olds are largely restricted to inferring number after separating out conceptually paired items. In contrast, four-year-olds are able to make appropriate inferences about shared items, but they typically prefer to count those items if they are visible. Moreover, the size of corresponding sets affects children's propensity to count rather than infer. Children count more often on larger sets. The ability to infer number using cardinal extension is associated most strongly with sharing proficiency, although counting skills also play an important part. We discuss how the data reveal an emerging understanding of the relationship between one-to-one correspondence and cardinality.     

Levels of phonological awareness in three cultures

This study focused on syllable phoneme onset levels of phonological awareness in relation to reading of Chinese and English in kindergarten and first-grade children from Xian (China), Hong Kong, and Toronto, cultures that differ substantially in approaches to reading instruction. English syllable awareness among native Chinese speakers was as good as or better than that among English speakers, indicating that the Chinese language may promote syllable-level awareness in children. Hong Kong children recognized significantly more words in both English and Chinese but were significantly poorer than the Xian children in both syllable and phoneme onset deletion tasks, suggesting that Pinyin training (given in Xian only) may promote phonological awareness even at the syllable level. In both Xian and Hong Kong, measures of syllable awareness consistently predicted Chinese character recognition better than did phoneme onset awareness. In contrast, English word recognition was predicted differently by syllable and phoneme onset awareness across cultures. These results underscore the roles of both language and writing system in understanding levels of phonological awareness.     

Gender Differences in Attitudes Toward Women as Sales Managers in the People's Republic of China

The present study promulgates a research stream in the area of understanding women's position in the management of the Chinese sales force. The study investigates attitudes toward women as sales managers held by Chinese salespeople. Male salespeople consistently rated the female sales managers lower than did female salespeople on three sets of attitude items. This finding indicates the presence of male resistance to women in sales management positions.     

Qualities Underlying the Definitions of Gender

Dimensions underlying the definition of items as feminine and masculine were examined in a set of three studies. Items chosen by children as belonging to males or females were used as the initial stimuli. These included traditionally stereotyped items such as a hammer and an iron, as well as more metaphorically related items such as bears and flowers. The raters in all three studies were undergraduates (70% White, 30% minorities). In Study 1, the items were rated using a set of 40 common adjectives. Three factors resulted: two related to masculine items and one to feminine items. In Study 2, a subset of the adjectives were used to rate abstract paintings that had been designated feminine or masculine by another group of adults. In Study 3, a set of stimuli were developed using the adjectives from the previous two studies. The items were rated as feminine or masculine and matched the initial coding of the adjective. The new items were also rated on the same adjectives by another set of adults. Again, the masculine adjectives were assigned to masculine items and feminine to feminine items. There was excellent agreement across three different sets of stimuli on the underlying dimensions of gender definition, even using items that were not traditionally stereotyped.     

The semantics of secrecy: young children's classification of secret content

The authors explored whether young children can distinguish potential secrets from nonsecrets by their content, as can older children, adolescents, and adults. Ninety children, 4, 5, and 6 years old, rated the secrecy of items from an adult-validated list of personal information about an age- and gender-appropriate puppet. Two factors of the children's data corresponded to the adult categories of nonsecrets and secrets, and a third factor corresponded to surprises. All ages rated surprises as significantly more secret than nonsecret items; however, the surprise items contained linguistic cues to secrecy. A tendency to rate nonsecrets as secret decreased with age, but only the 6-year-olds rated secrets other than surprises as significantly more secret than nonsecrets. Thus, children acquire the implicit rules defining secret content from a somewhat later age than that reported for the cognitive or behavioral capacities for secrecy.     

Sameness of Fregean sense

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.     

Montserratian mothers’ and English teachers’ perceptions of teaching and learning

After the explosion of a previously dormant volcano in Montserrat (an island in the Caribbean, in the Leeward Islands of the West Indies, overseas territory of the UK) in 1996, about 3000 people emigrated to England. As the children settled into English schools, the pattern of underachievement observed with previous West Indian immigrants started to repeat itself. However, a new fact emerged: Montserratian parents were unhappy with the standards of mathematics and science in English schools, which they considered low. This paper reports a case study of how two Montserratian mothers and their four children perceived English schools. The parents, a Montserratian and an English teacher were interviewed about their views of teaching and learning. The parents were also videotaped while helping their children with homework; the English teacher watched one of these tapes and commented on the session.The interviews and videos were analysed by themes. The interpretation of the themes identified in the interviews was later checked against the events in the homework sessions. Different implicit conceptions of school emerged from the analysis: Montserratian schools appear to fit an ‘interdependent’ style of socialisation whereas English schools fit a more ‘independent’ style. These implicit conceptions of schooling resulted in misunderstandings between teachers and parents, who did not perceive each other as truly helping the children. Differences were also observed in implicit teaching and learning aims. These differences seem to explain the Montserratian parents’ perceptions of a low standard of work being asked of their children in English schools.It is suggested that teachers of immigrant children would find it useful to understand pupils’ and parents’ implicit conceptions of schools when they receive immigrants in their community. Their communication with parents might work better if it fits with the parental expectations and parents have time to learn the ways of schooling in the host country.     

Prototypical Behaviour Patterns of Social Intelligence: An Intercultural Comparison between Chinese and German Subjects

By using the Act Frequency Approach (Buss & Craik, 1980), Chinese subjects (N = 31) generated a list of acts (specific behaviours) considered to represent social intelligence. These acts were rated by Chinese subjects (N = 39) and German subjects (N = 29) for prototypicality. A comparison of results showed that the construct of social intelligence is culture dependent. For the Chinese, social intelligent behaviours seem to reflect the classical traditions and ideals of Confucianism. Acts that received the highest scores were those that described conforming to and fulfilling expected roles, and acts in which the wellbeing of the entire society was described as being more important that the desires of an individual. This was especially true for older subjects and for women. Items controlling for socially desirable behaviour and social engagement showed clear differences between the two cultures; as expected, the German subjects rated these items lower, whereas the Chinese subjects found both items to be high prototypical of social intelligence.