Various ways to determine rational number size: an exploration across primary and secondary education

European Journal of Psychology of Education - Understanding rational numbers is a complex task for primary and secondary school students. Previous research has shown that a possible reason is...     

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.     

Validation and profile of Chinese pre-service teachers’ technological pedagogical content knowledge scale

Researchers state that teachers in different contexts reported different technological pedagogical content knowledge (TPACK). This phenomenon may partially be explained by cultural differences. Based on this consideration, the development and validation of the Chinese pre-service teachers’ technological pedagogical content knowledge (CTPCK) scale is described in this article. The sample was split into two subsamples on random basis (n1 = 229, n2 = 207) for the purpose of conducting (1) exploratory factor analysis (EFA) and (2) confirmatory factor analysis (CFA), respectively. After the EFA, the CTPCK scale excluded six items and included eight factors with 42 items. Reliability and correlations were discussed. The findings revealed that the CTPCK scale was a valid and reliable instrument for measuring the TPACK of Chinese pre-service teachers’ knowledge with or without linking educational technology.     

Resistance to Confounding Style and Content in Scoring Constructed-Response Items

An assumption that is fundamental to the scoring of student-constructed responses (e.g., essays) is the ability of raters to focus on the response characteristics of interest rather than on other features. A common example, and the focus of this study, is the ability of raters to score a response based on the content achievement it demonstrates independent of the quality with which it is expressed. Previously scored responses from a large-scale assessment in which trained scorers rated exclusively constructed-response formats were altered to enhance or degrade the quality of the writing, and scores that resulted from the altered responses were compared with the original scores. Statistically significant differences in favor of the better-writing condition were found in all six content areas. However, the effect sizes were very small in mathematics, reading, science, and social studies items. They were relatively large for items in writing and language usage (mechanics). It was concluded from the last two content areas that the manipulation was successful and from the first four that trained scorers are reasonably well able to differentiate writing quality from other achievement constructs in rating student responses.     

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.