A method for personalising the blade size for competitors in flatwater kayaking

The intent of this project was to explore the feasibility of personalising the paddle blade size for individual flatwater kayakers based on their power output profiles. Twelve elite male kayakers performed on a kayak ergometer at the same intensity and resistance that they would normally experience while paddling at race pace for 500 m on the water. The kayak ergometer was instrumented so that power profiles could be determined from the instantaneous force and velocity of the representative centre point of the paddle blade. From the power profile information, the researchers calculated a personalised blade size that was expected to improve performance for those kayakers differing more than 5% from the calculated ‘ideal’ size. For the elite kayakers studied, it was recommended that seven of the paddlers should increase their blade size by approximately 5–10%. For the remaining five paddlers, the results indicated that their current blade sizes were within the expected measurement error of their predicted ideal value and should be retained. It is anticipated that this research will provide the theoretical rationale for elite kayakers to see the need to personalise their blade size based on their own muscle power profiles.     

Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification

A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students’ mathematical reasoning, we conduct design research where whole-class mathematical discussions triggered by exploratory tasks play a key role. We take mathematical reasoning as making justified inferences and we consider generalizing and justifying central reasoning processes. Regarding teacher actions, we consider inviting, informing/suggesting, supporting/guiding and challenging actions can be identified in whole-class discussions. This paper presents design principles for an intervention geared to tackle such reasoning processes and focuses on a whole-class discussion on a grade 7 lesson about linear equations and functions. Data analysis concerns teacher actions in relation to design principles and to the sought mathematical reasoning processes. The conclusions highlight teacher actions that lead students to generalize and justify. Generalizations may arise from a central challenging action or from several guiding actions. Regarding justifications, a main challenging action seems to be essential, while follow-up guiding actions may promote a further development of this reasoning process. Thus, this paper provides a set of design principles and a characterization of teacher actions which enhance students’ mathematical reasoning processes such as generalization and justification.     

Changing classroom culture,curricula, and instruction for proof and proving: how amenable to scaling up,practicable for curricular integration,and capable of producing long-lasting effects are current interventions?

This paper is a commentary on the classroom interventions on the teaching and learning of proof reported in the seven empirical papers in this special issue. The seven papers show potential to enhance student learning in an area of mathematics that is not only notoriously difficult for students to learn and for teachers to teach, but also critically important to knowing and doing mathematics. Although the seven papers, and the intervention studies they report, vary in many ways—student population, content domain, goals and duration of the intervention, and theoretical perspectives, to name a few—they all provide valuable insight into ways in which classroom experiences might be designed to positively influence students’ learning to prove. In our commentary, we highlight the contributions and promise of the interventions in terms of whether and how they present capacity to change the classroom culture, the curriculum, or instruction. In doing so, we distinguish between works that aim to enhance students’ preparedness for, and competence in, proof and proving and works that explicitly foster appreciation for the need and importance of proof and proving. Finally, we also discuss briefly the interventions along three dimensions: how amenable to scaling up, how practicable for curricular integration, and how capable of producing long-lasting effects these interventions are.     

Teaching multidigit multiplication: combining multiple frameworks to analyse a class episode

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher’s mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and ascending a priori analysis and an a posteriori analysis. This analysis shows a development of different didactical situations and some links between mathematical knowledge and pertinence. In the conclusion, the contribution of the frameworks from both French and Anglo-American origins is briefly addressed.     

The perceived impact of external evaluation: the system,organisation and individual levels—Estonian case

The purpose of this article is to provide an overview of how the employees of higher education institutions perceive the impact of external evaluations. The study was conducted using the concurrent mixed method and involved 361 employees from Estonian universities and professional higher education institutions. The results indicated that evaluation is mostly deemed necessary at the levels of the organisation and the system; from the personal viewpoint of an employee, positive effects of external evaluations are perceived to a lesser degree. The negative influences mentioned were increased bureaucracy, extra work and stress. Top managers of institutions most often saw the positive influences from external evaluations since they help to implement reorganisations and development activities within an organisation. Managers perceived the positive effects of external evaluations on their everyday work as well, more than other employees did. Researchers felt the positive effects of external evaluations least. Nearly a quarter of all employees of higher education institutions do not perceive the effects of external evaluations on their everyday work at all. Employees of professional higher education institutions perceive the positive effects of external evaluations to a greater extent than employees of universities do, indicating that external evaluation has contributed to the development of their organisations. The differences in opinions of the employees of higher education institutions regarding perceived positive and negative impacts of external evaluations—whether on individual, organisation or system points of view—indicate that employees do not identify closely enough with the organisation and its strategic goals.     

Student perceptions of the fairness of grading procedures: a multilevel investigation of the role of the academic environment

The purpose of this study is to examine the effects of assessment method (essays vs. examinations) and instruction method (seminars vs. lectures) on student perceptions of the fairness of the assessment process. Department-specific combinations of these factors give a unique profile to the assessment process and to the way students interact with faculty. It is argued that the conditions thus created place students in some departments in a more advantageous position when it comes to meeting justice-related expectations. The variables of interest are procedural justice (PJ) and informational justice (IJ). For PJ, aspects regarding the amount of control students can exert on the grading process (PJ-C) are distinguished from aspects regarding the perceived validity of grading procedures (PJ-V). The sample consists of 1549 students from 48 departments of a German university. Analysis is done via multilevel mixed effects models. Models also check for cross-level interactions between effects of the academic environment and student socioeconomic status (SES). Results show that PJ-C and PJ-V are significantly affected by the assessment method. Higher proportions of essays relative to examinations in a department lead to higher ratings of PJ-C, while they decrease ratings of PJ-V. Ratings of IJ are higher as well if assessment is more essay-based, although this only affects low-SES students. Regarding the instruction method, a higher proportion of seminars was found to significantly increase PJ-C and IJ. Again, effects on IJ are moderated by parental SES. Policy implications for reducing feelings of injustice are discussed.     

Effects of student-facilitated learning on instructional facilitators

We investigated perceptions about learning strategy use and instructional roles among a sample of high needs adolescents (n = 230) who acted as near-peer instructional facilitators. The sample was drawn from science and mathematics classes in nonselective public secondary schools in New York City. Students participated in an inschool intervention that draws on social constructivism, theory and research on metacognition and learning strategies, role theory, and empirical findings from the peer-to-peer learning literature to promote advanced achievement among students who act as facilitators. Using a pre- and post-test single group design, we surveyed student instructional facilitators before and after program participation and related their perceptions about learning strategy use and perceptions about teaching roles to data about academic achievement. We found no survey gains in student perceptions about learning strategies or instructional roles between pre-survey (fall) and post-survey (spring). We found small but significant effects of individual perceptions about learning strategies and teaching roles on academic gains among instructional facilitators. The study also suggests that an in-school near-peer facilitated learning program can be an effective means to raise achievement in urban high schools. The study provides partial support for theories that hold that metacognition and role perceptions are involved in the academic gains of instructional facilitators, as gains in these dimensions were small compared to achievement gains.     

Effects of a rubric for mathematical reasoning on teaching and learning in primary school

Rubrics are assessment tools that help students gain complex competencies. Our quasi-experimental study aimed to evaluate whether rubrics help teachers teach and assess mathematical reasoning in primary school and whether such an instrument might support student learning. In two Swiss cantons, 762 students in 44 5th- and 6th-grade primary classes worked on their reasoning competencies, and half of them additionally employed our standards-based rubric. All of the teachers received a 1-day training and participated in the final project evaluation. To standardise and support the teachers during the implementation phase, they received a detailed curriculum. An achievement test and questionnaires for students and teachers were administered before and at the end of the intervention. The results of our quantitative longitudinal analyses indicate that the rubric fosters the teachers’ perceived diagnostic skills but only indirectly impacts their use of formative feedback. Based on the students’ perceptions, however, we observed a direct effect of the rubric on formative feedback and student self-assessment. Effects on students’ outcomes could not be observed, but there are indications of effects mediated by self-regulation and self-efficacy.