Mathematical engineering and mathematical change 1

In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception of mathematical knowledge, in particular mathematical growth.     

Specialization of the motor system in infancy: from broad tuning to selectively specialized purposeful actions

In executing purposeful actions, adults select sufficient and necessary limbs. But infants often move goal‐irrelevant limbs, suggesting a developmental process of motor specialization. Two experiments with 9‐ and 12‐month‐olds revealed gradual decreases in extraneous movements in non‐acting limbs during unimanual actions. In Experiment 1, 9‐month‐olds produced more extraneous movements in the non‐acting hand/arm and feet/legs than 12‐month‐olds. In Experiment 2, analysis of the spatiotemporal dynamics of infants’ movements revealed developmental declines in the spatiotemporal coupling of movements between acting and non‐acting arms. We also showed that the degree of specialization in infants’ unimanual actions is associated with individual differences in motor experience and visual attention, indicating the experience‐dependent and broad functional nature of these developmental changes. Our study provides important new insights into motor development: as in cognitive domains, motor behaviours are initially broadly tuned to their goal, becoming progressively specialized during the first year of life.     

Testing an integrated model of the work–family interface in Chinese employees: A longitudinal study

The purpose of this study was to examine an integrated model of the work–family interface (WFI) linking work–family demands (workload and family conflict), resources (supervisory support and family support) and role satisfaction in a Chinese context. The four‐factor structure of WFI comprises direction of influence (work to family vs family to work) and types of effect (work–family conflict vs work–family enrichment). A longitudinal design was used to collect data from 409 Chinese employees at three time points, separating measures of antecedents (T1), WFI (T2) and outcomes (T3) in time. The results based on structural equation modelling (SEM) reveal that: (1) the direction and types of effect were two underlying dimensions of the WFI, supporting the four‐factor structure; (2) demands were more strongly related to conflict, while resources were more strongly related to enrichment; (3) work–family conflict and enrichment were related to role satisfaction, regardless of the direction of influence.     

Fitting direct covariance structures by the MSTRUCT modeling language of the CALIS procedure

This paper demonstrates the usefulness and flexibility of the general structural equation modelling (SEM) approach to fitting direct covariance patterns or structures (as opposed to fitting implied covariance structures from functional relationships among variables). In particular, the MSTRUCT modelling language (or syntax) of the CALIS procedure (SAS/STAT version 9.22 or later: SAS Institute, 2010) is used to illustrate the SEM approach. The MSTRUCT modelling language supports a direct covariance pattern specification of each covariance element. It also supports the input of additional independent and dependent parameters. Model tests, fit statistics, estimates, and their standard errors are then produced under the general SEM framework. By using numerical and computational examples, the following tests of basic covariance patterns are illustrated: sphericity, compound symmetry, and multiple‐group covariance patterns. Specification and testing of two complex correlation structures, the circumplex pattern and the composite direct product models with or without composite errors and scales, are also illustrated by the MSTRUCT syntax. It is concluded that the SEM approach offers a general and flexible modelling of direct covariance and correlation patterns. In conjunction with the use of SAS macros, the MSTRUCT syntax provides an easy‐to‐use interface for specifying and fitting complex covariance and correlation structures, even when the number of variables or parameters becomes large.     

Longitudinal trajectories of bicultural identity integration in recently immigrated Hispanic adolescents: Links with mental health and family functioning

This study examined, in a sample of recently immigrated Hispanic adolescents in Miami and Los Angeles, the extent to which bicultural identity integration (BII; involving the ability to synthesise one's heritage and receiving cultural streams and to identify as a member of both cultures) is best understood as a developmental construct that changes over time or as an individual‐difference construct that is largely stable over time. We were also interested in the extent to which these trajectories predicted mental health and family functioning. Recent‐immigrant 9th graders (N = 302) were assessed 6 times from 9th to 12th grade. Latent class growth analyses using the first 5 timepoints identified 2 trajectory classes—one with lower BII scores over time and another with higher BII scores over time. Higher heritage and US identity at baseline predicted membership in the higher BII class. At the 6th study timepoint, lower BII adolescents reported significantly poorer self‐esteem, optimism, prosocial behaviour and family relationships compared with their higher BII counterparts. These findings are discussed in terms of further research on the over‐time trajectory of biculturalism, and on the need to develop interventions to promote BII as a way of facilitating well‐being and positive family functioning.     

The Ontology of Musical Versions: Introducing the Hypothesis of Nested Types

This article explores the ontological nature of musical versions. I assume the widespread view that type/token ontologies offer the best explanation of the repeatable nature of works of music. However, I show that traditional type/token theories, which distinguish only between two levels of objects, face two problems when applied to the phenomenon of musical versions. First, they are not able to accommodate the familiar intuition of our musical practices that the work versioned is repeated in its versions’ performances. Second, they are not able to distinguish between two different phenomena of our practices: the phenomenon of a work's versions and the phenomenon of works inspired by, or derived from, other works. These undesirable consequences are entailed, under traditional two‐level type/token theories, by the nature of types as ontologically thin entities. I defend that the hypothesis of nested types, a multiple‐level type/token theory, can avoid these two problems while preserving the theoretical virtues of traditional two‐level type/token theories and structural monism—the most widely shared view about the individuation of musical works, according to which musical works are individuated by one, and only one, sound structure.     

Group‐based discrimination,national identification,and British Muslims’ attitudes toward non‐Muslims: the mediating role of perceived identity incompatibility

In two studies, we tested a model in which the perceived (in)compatibility of being British and Muslim (identity incompatibility) was expected to mediate between group‐based discrimination and the identifications and attitudes of British Muslims. In Study 1 (N = 76), anti‐Muslim discrimination was associated with lower national identification and more negative attitudes toward non‐Muslims, and these relationships were mediated by perceived identity incompatibility. In Study 2 (N = 70), we additionally found that anti‐Muslim discrimination predicted stronger endorsement of Islamic group rights, and this relationship was also mediated by perceived identity incompatibility. The studies highlight the importance of group‐based discrimination in shaping the perceived (in)compatibility of being British and Muslim, and, in turn, the identifications and attitudes of British Muslims.