The Role of Mathematics Teachers' Content Knowledge in their Teaching: A Framework for Research applied to a Study of Student Teachers

The authors develop and explain a framework toguide research on the relationship betweenmathematics teachers' knowledge of content andtheir teaching. The framework istwo-dimensional. The dimensions are (a) theelements of teaching and (b) the processes ofteaching in which knowledge of content is ofconsequence. The interplay between the elementsof teaching and the processes of teaching isdiscussed theoretically, consideringconnections to existing literature about therole of teachers' subject matter knowledge.Three vignettes from the authors' work withpre-service secondary mathematics teachersinvestigate further the relationship betweencontent knowledge and effective mathematicsteaching. The vignettes also serve toillustrate the complexity of investigationsinto this relationship. Direction is offeredfor use of the framework in future research.     

Teaching practices of the undergraduate introductory biomechanics faculty: a North American survey

Instruction and assessment strategies of undergraduate introductory biomechanics instructors have yet to be comprehensively examined. The purpose of this study was to identify the current instruction and assessment practices of North American undergraduate introductory biomechanics instructors and equipment needed for effective instruction in lecture and laboratory sessions. One hundred and sixty-five respondents (age: 42.5 ± 10.3 years) who currently teach or have taught an introductory biomechanics course in North America were recruited by electronic mail. Subjects completed a web-based survey, consisting of 60 open- and closed-ended questions. Pearson's correlation coefficients were used to assess relationships between instructor's familiarity with either the Biomechanics Concept Inventory or the NASPE Guidelines for Undergraduate Biomechanics, and instructor and course characteristics (number of years teaching, age, faculty rank, number of quizzes given, etc.) A number of variables were significantly (p < 0.05) correlated. Answers to open-ended questions were processed using content analysis, with results categorized in content areas including: instructor and course characteristics; lecture instruction; assessment and equipment; laboratory instruction; assessment and equipment; and instructor's perspectives. Many active learning strategies for lecture and laboratory instruction were identified by faculty. Limited student preparation and limited resources were noted as the instructor's most common challenges.     

Significant and meaningful effects in sports biomechanics research

Errors in statistical analysis of multiple dependent variables and in documenting the size of effects are common in the scientific and biomechanical literature. In this paper, I review these errors and several solutions that can improve the validity of sports biomechanics research reports. Studies examining multiple dependent variables should either control for the inflation of Type I errors (e.g. Holm's procedure) during multiple comparisons or use multivariate analysis of variance to focus on the structure and interaction of the dependent variables. When statistically significant differences are observed, research reports should provide confidence limits or effect sizes to document the size of the effects. Authors of sports biomechanics research reports are encouraged to analyse and present their data accounting for the experiment-wise Type I error rate, as well as reporting data documenting the size or practical significance of effects reaching their standard of statistical significance.     

Confidence crisis of results in biomechanics research

Many biomechanics studies have small sample sizes and incorrect statistical analyses, so reporting of inaccurate inferences and inflated magnitude of effects are common in the field. This review examines these issues in biomechanics research and summarises potential solutions from research in other fields to increase the confidence in the experimental effects reported in biomechanics. Authors, reviewers and editors of biomechanics research reports are encouraged to improve sample sizes and the resulting statistical power, improve reporting transparency, improve the rigour of statistical analyses used, and increase the acceptance of replication studies to improve the validity of inferences from data in biomechanics research. The application of sports biomechanics research results would also improve if a larger percentage of unbiased effects and their uncertainty were reported in the literature.