Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

Using Content Analysis to Compare a U.S. Urban Teacher Residency to a Finnish Teacher Education Program

In the United States, how to provide a high-quality education to all students has been a focal discussion, especially in urban settings. One potential solution that has emerged to confront this issue involves urban teacher residency (UTR) programs that provide innovations concerning the recruitment, preparation, and retention of teachers in high-need urban schools. In this study, we conducted a content analysis and compared steering documents of a UTR program in California with materials from a teacher-training program in Finland. Despite differences in both the legislative and local contexts under which the two programs operate, we found many similarities in both the steering documents and course offerings of these two teacher-training programs. For example, both promote aspects of social justice and are research-based. Furthermore, both offer a variety of types of courses, such as those emphasizing the pedagogical bases of education and research studies in education.

     

Transformative Social and Emotional Learning (SEL): Toward SEL in Service of Educational Equity and Excellence

This article seeks to develop transformative social and emotional learning (SEL), a form of SEL intended to promote equity and excellence among children, young people, and adults. We focus on issues of race/ethnicity as a first step toward addressing the broader range of extant inequities. Transformative SEL is anchored in the notion of justice-oriented citizenship, and we discuss issues of culture, identity, agency, belonging, and engagement as relevant expressions of the Collaborative for Academic, Social and Emotional Learning 5 core competencies. We also point to programs and practices that hold promise for cultivating these competencies and the importance of adult professional development in making these efforts maximally effective for diverse children and youth. We conclude by offering a few next steps to further advance transformative SEL research and practice.     

Social Justice in Sport and Exercise Psychology: A Position Statement

ABSTRACT

There are varied approaches that have been used in sport for development (SFD) projects. This article is focused on the move by sport and exercise psychology researchers toward community-based SFD projects where marginalized groups are centralized. The authors have chosen two of their projects to exemplify different approaches to SFD. An initial project with an Aboriginal community is critically examined to reveal cultural missteps that perpetuated cultural colonization–something antithetical to community capacity building. The second project is then considered because of its closer alignment with cultural praxis and community capacity building. This second project focuses on the initial developments of a YMCA physical activity project designed to meet the needs of forced immigrants (a self-titled name developed by the refugee community members) and the staff who work with them. We culminate with five postulates proposed for SFD project teams derived from our vantage in sport and exercise psychology, where community engagement and eventual self-governance are imperatives.     

Attitudinal Survey Characteristics Impacting Participant Responses

Abstract

Research suggests that certain characteristics of survey items may impact participants’ responses. In this study we investigated the impact of several of these characteristics: vague wording, question-versus-statement phrasing, and full-versus-partial labeling of response options. We manipulated survey items per these characteristics and randomly administered the manipulated and nonmanipulated items to two groups of respondents. We examined differences in responses via multiple groups confirmatory factor analysis (MGCFA) and found differences in factor means, slopes (indicating differing discrimination), and/or intercepts (indicating differing response extremity) for all conditions. Implications for survey construction are discussed.     

Changing Minds With the Story of Adaptation: Strategies for Teaching Young Children About Natural Selection

Research Findings: Educational guidelines recommend a delayed, piecemeal approach to instruction on adaptation by natural selection. This approach is questionable given suggestions that older students’ pervasive misunderstandings about adaptation are rooted in cognitive biases that develop early. In response to this, Kelemen et al. (2014) recently showed that young children can learn a basic yet comprehensive explanation of adaptation by natural selection from a picture storybook intervention. However, this research was conducted in a laboratory-based setting with children from middle and higher socioeconomic backgrounds. To further explore the intervention’s efficacy, this investigation examined whether Kelemen et al.’s (2014, Experiment 2) findings extend to a more diverse sample of children tested in a more naturalistic setting, namely, after-school programs. After a 10-min picture storybook reading that described adaptation within a fictitious but realistic mammal species, 5- to 6- and 7- to 8-year-old children’s learning of adaptation was examined. Results revealed that younger and older children benefitted from the intervention; however, older children displayed pronounced learning and generalization. Practice or Policy: Findings confirm that children are capable of learning complex biological ideas and that comprehensive storybook interventions are simple but powerful teaching tools. Implications for instruction on natural selection are discussed.