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.     

SCHOOL RACIAL CLIMATE AND THE ACADEMIC ACHIEVEMENT OF AFRICAN AMERICAN HIGH SCHOOL STUDENTS: THE MEDIATING ROLE OF SCHOOL ENGAGEMENT

This investigation utilized an integrative model of development for ethnic minority children and a process model of engagement to explore whether three dimensions of school engagement (behavioral, emotional, and cognitive) mediated relationships between school racial climate, academic performance, and educational aspirations. A total of 139 African American students were recruited from a high school in the southeastern United States. Findings revealed an indirect association between perceptions of racial fairness and academic achievement indicators through behavioral and cognitive engagement. Behavioral and cognitive engagement also mediated relationships between youths’ perceived peer discrimination and academic achievement indicators. No significant indirect associations between teacher discrimination and academic achievement through school engagement dimensions were found. Study limitations, future directions, and implications are discussed.     

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.     

Regulating research: The problem of theorizing community on LambdaMOO

This article considers ongoing attempts to regulate or even ban researchon LambdaMOO. Industry, private individuals, and research institutionshave supported MOOs, or multi-user object-oriented worlds. The earlyresearch on MOOs by Pavel Curtis, who was one of the key designers,suggests that these systems are part of a research project and have beenresearched since they were originally designed. However, a group ofMOOers have grown increasingly uncomfortable about the quotation ofcertain texts on web sites and academic journals and the potentiallypanoptic effect of research. Some of these practices have breachedcommunity conventions. Yet, such things as testing, invisibly watching,freely quoting characters, and ignoring certain rules have always beenaspects of the system. The dispute over research ethics and theparticipation of varied researchers within this setting indicate thatdiverse values are represented among MOOers and different expectationsexist about how the MOO might be a community. The term ``community' andthe presumption that online characters are people may have alsoincorrectly informed the research debate by making it seem that onlinesettings provide immediate access onto spaces, bodies, and individuals.Many MOOers may believe that research threatens individuals andcommunity. However, critical histories and analysis are needed in orderto explain the system to new users and encourage alternative forms ofdevelopment. Such work can only be produced if online systems are opento research and critique.     

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.     

The role that schools hold in supporting young people with selective mutism: a systematic literature review

Schools are expected to hold an increasingly central role in co-ordinating support for children with mental health needs. However, the role that schools hold in supporting pupils with selective mutism (SM) is complex. Through a Critical Interpretive Synthesis (CIS), this review explores the multidimensional role which educational settings hold in supporting children with SM. Key databases were searched (PsycInfo, British Education Index, Education Resources Information Center, British Library EThOS and Google Scholar) and a conceptual map, informed by experienced practitioners, guided additional purposive searching with a focus on conceptual saturation. A total of twenty-four papers were identified following a further process of appraisal. Reciprocal Translational Analysis (RTA) found that schools hold a tripartite role in supporting children with SM: this incorporated developing a shared understanding of the disorder, engaging in effective (and often multi-professional) planning, and offering direct support through adapting provision and facilitating individual intervention. Through realising this role, schools and educational settings might transform the support currently available for children and young people with SM. Implications for practice, policy and future research also emerged. This included a clear need for enhanced teacher understanding of SM, arguably at the level of initial teacher training (ITT).     

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.     

A Behind‐the‐Scenes Guide to School‐Based Research

Schools are an important context for both basic and applied scientific research. Unlike the laboratory, however, the physical and social conditions of schools are not under the exclusive control of scientists. In this article, we liken collecting data in schools to putting on a theatrical production. We begin by describing the large cast of characters whose collaborative efforts make school‐based research possible. Next, we address the critics, including the university Institutional Review Board (IRB) and school administrators, whose feedback often improves the final study design. We then turn our attention to set building, stage directions, and rehearsals—key steps in the iterative process of refining study procedures. We end with a discussion of the day of data collection itself and activities that take place after the curtain drops. Throughout, we make recommendations based on our recent experience collecting data at several high schools.     

In search of consolidation of short-term memory in nonhuman animals

Wixted (Annual Review of Psychology, 55, 235 – 269, 2004) has argued that forgetting is due to consolidation failure. Previous research with humans and nonhuman animals has reported evidence for consolidation in intermediate or long-term memory (LTM). The present study examines whether consolidation occurs in short-term memory in pigeons. Delayed matching-to-sample accuracy was reduced when retroactive interference (an extraneous task in Experiment 1 or houselight illumination in Experiment 2) was interpolated in the retention interval. Accuracy was not greater, however, when interference occurred at the end of the retention interval, as compared with when it occurred at the beginning. That is, there was no evidence for consolidation in short-term memory for pigeons. We did find, however, the beginning–end effect originally reported by Roberts and Grant (Journal of Experimental Psychology: Animal Behavior Processes, 4, 219–236, 1978) and the recovery from forgetting reported by White and Brown (Journal of the Experimental Analysis of Behavior, 96, 177–189, 2011). The results are discussed in relation to temporal distinctiveness theory as an alternative to consolidation.