The interface between mathematics and design and technology in secondary schools

ABSTRACT

This article suggests that there are important connections between design and technology and mathematics curricula and that these are not fully made in the United Kingdom National Curriculum. Using three examples, the authors show how there are real opportunities in design and technology teaching for incorporating mathematical learning, but that all too often these are lost because they are not made explicit. Again, the authors argue that too much mathematics teaching is dominated by abstract investigation rather than practical problem‐solving. They conclude by suggesting that teaching should transcend subject boundaries and be concerned with real‐life situations.     

The developmental and professional activities of female international soccer players from five high-performing nations

ABSTRACT

We study the developmental and professional activities engaged in by 86 female adult soccer players from the senior national teams of Australia, Canada, England, Sweden, and the United States of America. Players completed the Participation History Questionnaire (PHQ) to elicit the amount and type of activities engaged in across their developmental and professional years, including milestones, soccer-specific activity and engagement in other sport activity. Greater specialisation than diversification characterised their childhood developmental activities, including all players starting in soccer in childhood and accumulating more hours in soccer activity than other sports during this period. However, interindividual variation further characterised these childhood activities, with a proportion of players diversifying into other sports and/or soccer play to a greater or lesser degree during childhood when compared to the other players. The amount of coach-led soccer practice increased for all players across their development culminating in an average of 15–16 h/wk across a 40-week season in early adulthood. In contrast, the amount of engagement in other sports and soccer peer-led play varied between players but generally decreased across adolescence to negligible amounts in late adolescence. Findings are commensurate with the deliberate practice framework and early engagement.     

The Empirical Attitude, Material Practice and Design Activities

This article is an argument about something that is both important and severely underemphasized in most current science curricula. The empirical attitude, fundamental to science since Galileo, is a habit of mind that motivates an active search for feedback on our ideas from the material world. Although more simple views of science manifest the empirical attitude through relation of theories to data, we describe more recent philosophical scholarship that characterizes the relation of theories to data through phenomena (regularities in nature’s behavior that can be identified and characterized through data). This view highlights the centrality of material practice, in which scientists design data collection events to inform phenomena. Thus manifestation of the empirical attitude in science is characterized as a design endeavor that involves considerably sophisticated coordination among theories, phenomena, data, and data collection events. If we want students to learn how to participate in such work, curricula should break down these complex processes into more basic components at least at the outset. Our recommendation is to begin with design activities that can focus on the empirical attitude initially without the complex coordination with phenomena and data. We present an example of such an activity and share results that suggest design activities can target the empirical attitude and be built upon in curricula to gradually include coordination with phenomena and theories.     

Examining the potential of critical and Kaupapa Māori approaches to leading education reform in New Zealand’s English-medium secondary schools

This paper discusses expectations, policies and practices that currently underpin education within the New Zealand context. It acknowledges the ongoing failure of this policy framework to positively influence reform for Indigenous Māori students in regular, state-funded schools and highlights the need for extensive change in the positioning and expectations of educators if Māori learners are to realize their true potential. The paper then considers leadership models to reimagine and lead a transformative educational reform that aims to include the aspirations and contributions of all members of the school’s communities, especially those who have historically been marginalized. Finally it considers the implications of this model for international application.     

Bivariate functional principal components analysis: considerations for use with multivariate movement signatures in sports biomechanics

Sporting performance is often investigated through graphical observation of key technical variables that are representative of whole movements. The presence of differences between athletes in such variables has led to terms such as movement signatures being used. These signatures can be multivariate (multiple time-series observed concurrently), and also be composed of variables measured relative to different scales. Analytical techniques from areas of statistics such as Functional Data Analysis (FDA) present a practical alternative for analysing multivariate signatures. When applied to concurrent bivariate time-series multivariate functional principal components analysis (referred to as bivariate fPCA or bfPCA in this paper) has demonstrated preliminary application in biomechanical contexts. Despite this, given the infancy of bfPCA in sports biomechanics there are still necessary considerations for its use with non-conventional or complex bivariate structures. This paper focuses on the application of bfPCA to the force-angle graph in on-water rowing, which is a bivariate structure composed of variables with different units. A normalisation approach is proposed to investigate and standardise differences in variability between the two variables. The results of bfPCA applied to the non-normalised data and normalised data are then compared. Considerations and recommendations for the application of bfPCA in this context are also provided.