Developing mathematical fluency: comparing exercises and rich tasks

Achieving fluency in important mathematical procedures is fundamental to students’ mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way? This paper reports three quasi-experimental studies carried out in a total of 11 secondary schools involving altogether 528 students aged 12–15. In each study, parallel classes were taught the same mathematical procedure before one class undertook traditional exercises while the other worked on a “mathematical etude” (Foster International Journal of Mathematical Education in Science and Technology, 44(5), 765–774, 2013b), designed to be a richer task involving extensive opportunities for practice of the relevant procedure. Bayesian t tests on the gain scores between pre- and post-tests in each study provided evidence of no difference between the two conditions. A Bayesian meta-analysis of the three studies gave a combined Bayes factor of 5.83, constituting “substantial” evidence (Jeffreys, 1961) in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data support the conclusion that the mathematical etudes trialled are comparable to traditional exercises in their effects on procedural fluency. This could make etudes a viable alternative to exercises, since they offer the possibility of richer, more creative problem-solving activity, with comparable effectiveness in developing procedural fluency.     

Student observations: Introducing iPads into university classrooms

This paper explores the growing trend of using mobile technology in university classrooms, exploring the use of tablets in particular, to identify learning benefits faced by students. Students, acting on their efficacy beliefs, make decisions regarding technology’s influence in improving their education. We construct a theoretical model in which internal and external factors affect a student’s self-efficacy which in turn affects the extent of adoption of a device for educational purposes. Through qualitative survey responses of university students who were given an Apple iPad to keep for the duration of a university course we find high levels of self-efficacy leading to positive views of the technology’s learning enhancement capabilities. Student observations on the practicality of the technology, off-topic use and its effects, communication, content, and perceived market advantage of using a tablet are also explored.     

Subject-oriented test construction

Conclusion The substance of the case which has been presented is not that any of the procedures that are currently used to develop tests should be discarded but that a richer source of data should be used to make judgements about the validity of tests. It has been argued that the production of valid tests requires a subject-oriented approach and that interviews are a valuable source of information for assisting in the development of such tests. Interviews can be used in the initial exploration of the ways in which potential subjects perceive an area of knowledge, in the trialling of test items and even in the final administration of the completed test. One added bonus of such an approach is that it helps to bring together in a complementary fashion research paradigms which are more often seen to be in competition with one another.     

Helping Children to Develop as Writers: Supporting,Showing, Responding

How can we help children develop as writers once they have begun to master the complexities of the writing system and begun to understand how they can compose their own texts? Colin Peacock proposes some answers to these questions on the basis of a small-scale research project in one school. Key issues which emerged were the need to develop motivation, to give children opportunities to write, to respond to their difficulties and to show them what counted as success.     

The Adequacy of Privacy: The European Union Data Protection Directive and the North American Response

The recently passed European Directive on the Protection of Personal Data aims to harmonize European data protection law at a higher level of protection than exists now. It represents a European consensus on a standard for personal privacy and a model for countries without data protection laws. The protracted process for agreement and ratification, however, has produced a document with many derogations and ambiguities, reflecting the wider moves towards 'subsidiarity' within the European Union. Of concern to North America is the stipulation that transborder data flow may not be permitted unless the receiving country can demonstrate an 'adequate' level of protection. While the process through which this provision will be interpreted and applied is so far found to be complicated and unclear, nevertheless European authorities will be reluctant to tolerate 'data havens,' a fact that should concern North American business that relies on the unimpeded flows of personal data from and to Europe. Neither Canada nor the United States can claim 'adequate' data protection according to the European standard. However, Canadian efforts through the Canadian Standards Association and the Federal Information Highway Advisory Council signal an attempt to fashion a more comprehensive policy framework for privacy than the more incremental and reactive approach of the United States. This divergence is explained by key cultural, economic, and political factors within Canada, which have caused a different reaction to the extraterritorial effects of the European Union's Data Protection Directive.     

Leading in the age of post-socialist education transformations: Examining sustainability of teacher education reform in Latvia

As the former socialist countries of Southeastern/Central Europe and the former Soviet Union have embarked on their journeys from authoritarian to democratic societies in the early 1990s, education systems across the region have experienced major changes. From curriculum revision to education finance reforms, virtually no aspect of the education systems has remained untouched. While all post-socialist reform efforts have striven for large-scale, sustainable change, some initiatives were more successful than others, and many reform efforts were short-lived. Focusing on pre-service teacher education reform in Latvia, this article seeks to understand how educational leadership contributes to sustainability of educational reform in the dynamic context of post-socialist education transformation processes.     

Using micro-sensor data to quantify macro kinematics of classical cross-country skiing during on-snow training

Abstract

Micro-sensors were used to quantify macro kinematics of classical cross-country skiing techniques and measure cycle rates and cycle lengths during on-snow training. Data were collected from seven national level participants skiing at two submaximal intensities while wearing a micro-sensor unit (MinimaxX^?). Algorithms were developed identifying double poling (DP), diagonal striding (DS), kick-double poling (KDP), tucking (Tuck), and turning (Turn). Technique duration (T-time), cycle rates, and cycle counts were compared to video-derived data to assess system accuracy. There was good reliability between micro-sensor and video calculated cycle rates for DP, DS, and KDP, with small mean differences (Mdiff% = ?0.2 ± 3.2, ?1.5 ± 2.2 and ?1.4 ± 6.2) and trivial to small effect sizes (ES = 0.20, 0.30 and 0.13). Very strong correlations were observed for DP, DS, and KDP for T-time (r = 0.87–0.99) and cycle count (r = 0.87–0.99), while mean values were under-reported by the micro-sensor. Incorrect Turn detection was a major factor in technique cycle misclassification. Data presented highlight the potential of automated ski technique classification in cross-country skiing research. With further refinement, this approach will allow many applied questions associated with pacing, fatigue, technique selection and power output during training and competition to be answered.