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.     

Time perspective and sleep problems

In this study of 137 university students, we examined the relationships among the five dimensions of the Zimbardo Time Perspective Inventory and three scales that measure aspects of sleep problems. All of the Zimbardo Inventory dimensions correlated significantly with each of the sleep problem-related scales. These data suggest that concern about time, regardless of the specific nature of individuals' time perspective, and certain sleep problems are significantly related.     

三支论式及因明学说实质之辨析

本文从卢卡西维茨关于亚氏三段论的分析出发,针对学术界中“三支论式”是三段论推理、充分条件假言推理、假言转为三段论推理或外设三段论推理等观点,从工具的使用到工具的锻造这一角度,进行了分析研究。笔者提出了一些与传统看法不同的观点,并在此基础上得出了“三支论式”及因明学说的实质是论证而不是推理的新见解。     

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.