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.     

White Religious Educators Resisting White Fragility: Lessons From Mystics

Abstract

Decades of work in dismantling racism have not yielded the kind of results for which religious educators have hoped. One primary reason has been what scholars term “white fragility,” a symptom of the structural racism which confers systemic privilege upon White people. Lessons learned from Christian mystics point to powerful ways to confront and resist the siren call of such formation and instead to make resisting racism an integral part of Christian identity for White people.     

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.     

Narrative Career Counselling for People with Refugee Backgrounds

For people with refugee backgrounds, pursuing a meaningful career in their country of resettlement is important for their successful integration. However, for many, achieving this is a challenging process. Career counsellors may have a role to play in facilitating the transition and integration of people with refugee backgrounds, and narrative career counselling has much to offer. This article discusses the impact of prolonged transition under difficult circumstances on people with refugee backgrounds, and the potential contribution of narrative career counselling in assisting them. In particular, it identifies cultural considerations for narrative career counsellors who work with people with refugee backgrounds.     

School principals’ views of teacher evaluation policy: lessons learned from two empirical studies

Teacher evaluation accountability policies are emerging worldwide. This study examines principals’ perceptions of teacher evaluation in terms of commonalities and differences arising from two research projects conducted in Portugal and in the US. Perceptions of school principals in regard to a new policy on teacher evaluation as well as its perceived effects at school and conditions for its implementation will be analysed. Findings point to the challenges and successes of coping with mandated accountability measures in two different contexts. Principals balanced perceived conflicting goals, sought maintenance of positive teacher relationships and school culture and managed the tensions of policy implementation and the making sense of its effects at school. Implications of the findings are discussed.     

Reading to Learn or Learning to Read? Engaging College Students in Course Readings

Despite instructors' belief that class readings are integral to the learning process, only 20–30% of undergraduate students complete required readings. Failure to complete course reading has been associated with declines in exam and research performance. This article first offers a brief review of the literature on why students do not complete course readings: 1) unpreparedness, 2) lack of motivation, 3) time constraints, and 4) an underestimation of reading importance. We then identify approaches that encourage students to read, enjoy reading, and develop metacognitive knowledge, shown to improve learning.     

Using the Content of Online Privacy Notices to Inform Public Policy: A Longitudinal Analysis of the 1998-2001 U.S. Web Surveys

In the United States, Congress has had a long-standing interest in consumer privacy and the extent to which company practices are based on fair information practices. Previously, public policy was largely informed by anecdotal evidence about the effectiveness of industry self-regulatory programs. However, the Internet has made it possible to unobtrusively sample web sites and their privacy disclosures in a way that is not feasible in the offline world. Beginning in 1998, the Federal Trade Commission relied upon a series of three surveys of web sites to assess whether organizations post online privacy disclosures and whether these disclosures represent the U.S. definition of fair information practices. While each year's survey has provided an important snapshot of U.S. web-site practices, there has been no longitudinal analysis of the multiyear trends. This study compares a subset of equivalent individual-level web-site data for the 1998, 1999, 2000, and 2001 web surveys. Implications for using this type of research to inform public policy are discussed.