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.     

The dynamics of connecting universities,non-governmental organizations and community members by means of academic projects directed at people in need

In this article we discuss an action research experience that took place from 2002 to 2015. We analyze the inception and progress of several project-based learning-centered academic courses that were aimed at developing the project management skills of graduate and undergraduate students. The experience involved approximately 1800 students from two universities and 40 community partners. The students developed real-life projects on behalf of institutions and non-governmental organizations located in the area that help people in need; we refer to these agencies as ‘community partners.’ We analyze the development of the course from a systemic perspective, making use of causal loop diagrams in order to understand the main driving dynamics. We discuss the results achieved by these projects and the benefits brought to the community partners. We also present testimony from the community partners themselves. We conclude by presenting the lessons we learned over the years we have been running this course.     

Immigrant girls as caregivers to younger siblings: a transnational feminist analysis

This article employs a transnational feminist lens to examine the experiences of racialised immigrant girls who provide care for their younger siblings. The article draws on findings from a participatory action research study in Victoria, British Columbia, Canada to examine the role that immigrant girls’ caregiving practices play in transnational families’ social, economic, and cultural survival. It argues that greater attention should be given to the diverse and complex contexts, consequences, costs, and contributions of immigrant girls’ caregiving labour.     

Inspiratory muscle warm-up and inspiratory muscle training: separate and combined effects on intermittent running to exhaustion

In the present study, we examined the independent and combined effects of an inspiratory muscle warm-up and inspiratory muscle training on intermittent running to exhaustion. Twelve males were recruited to undertake four experimental trials. Two trials (Trials 1 and 2) preceded either a 4-week training period of 1 × 30 breaths twice daily at 50% (experimental group) or 15% (control group) maximal inspiratory mouth pressure (PImax). A further two trials (Trials 3 and 4) were performed after the 4 weeks. Trials 2 and 4 were preceded by a warm-up: 2 × 30 breaths at 40% PImax. Pre-training PImax and distance covered increased (P < 0.05) similarly between groups after the warm-up (~11% and ~5-7% PImax and distance covered, respectively). After training, PImax increased by 20 ± 6.1% (P < 0.01; d = 3.6) and 26.7 ± 6.3% (P < 0.01; d = 3.1) when training and warm-up were combined in the experimental group. Distance covered increased after training in the experimental group by 12 ± 4.9% (P < 0.01; d = 3.6) and 14.9 ± 4.5% (P < 0.01; d = 2.3) when training and warm-up interventions were combined. In conclusion, inspiratory muscle training and inspiratory muscle warm-up can both increase running distance independently, but the greatest increase is observed when they are combined.     

How full is your luggage? Background knowledge of zoo visitors regarding sharks

For the general population, sharks have a reputation that does not really fit with their biological and ecological nature. Informal surveys often classify sharks as dangerous, aggressive and/or man-eaters. This apparent common knowledge seems difficult to detach from the conscience of many worldwide zoo visitors, even with the help of shark-focused educational programmes. As so, how can zoos and aquariums contribute to a change in this paradigm? Are the education and conservation strategies effective to the average zoo visitor? In this study, young visitors’ perceptions regarding sharks were assessed with the goal of identifying a valid Learning Progression, thus helping to update and develop different and more effective educational strategies and methodologies. The study took place at Zoomarine, an oceanographic park located in southern Portugal, with visitors aged between 8 and 16. A case study was conducted using a qualitative research approach (drawings and interviews) resulting in a Learning Progression Hypothesis. The proposed Learning Progression is composed of three knowledge levels for the participants’ biological perceptions regarding sharks. The results of this study showed a clear predominance of anthropomorphic and anthropocentric visions, as well as a utilitarian view of sharks and ecosystem, thus conditioning the visitors’ epistemological knowledge.     

Physiological aspects of competitive cross-country skiing.

The physiological demands of cross-country skiing require competitive skiers to have high maximal oxygen uptakes and anaerobic thresholds. Anaerobic capacity has a relatively less important role, but may be of greater importance today with the faster race velocities resulting from the new skiing techniques of ski skating. Although use of the ski skating techniques results in faster race velocities than the classical techniques, it has been found that under some conditions the double-pole technique is more economical than other skiing techniques. It is suggested that this results from a more effective storage and recovery of elastic energy, a greater proportion of the forces being directed along the line of travel, and a lower air resistance due to greater trunk and hip flexion with the double-pole technique. The greater economy of the double-pole technique suggests that this may be advantageous in certain race conditions if the upper body is adequately prepared. The greater propulsive forces generated with the upper body with ski skating also suggest that training of the upper body should receive more emphasis. The potential cardiovascular adaptations from cross-country ski training appear to be similar for the classical and skating techniques, yet training specificity is important for optimal performance.     

PARTY IDENTIFICATION AND ATTITUDES TOWARDS HOMOSEXUALS IN GREAT BRITAIN

Legislative activity and controversy concerning the issue ofhomosexual rights and practices has intensified in Britain overthe last decade. Despite this increase in intensity, however,the question of mass public opinion in relation to homosexualrights and practices has received little empirical investigation.In an effort to remedy this situation, this paper focuses onthe influence of party identification in determining publicattitudes towards homosexuals. Using data from the British SocialAttitudes Surveys, the results suggest that although party identificationexerts an independent and statistically significant effect onattitudes towards homosexuals, in all cases, however, theseeffects are both secondary and variable. Other equally, if notmore salient, determinants include: gender, education, age,occupation, and type of homosexual relationship. Of these varioussocio–demographic variables, both age and education standout as having the strongest and most consistent effect. In otherwords, at least as far as current British society is concerned,anti-homosexual views are most prevalent among both older individualsas well as the lesser educated.