Developing a Learning Progression for Curriculum,Instruction, and Student Learning: An Example from Mathematics Education

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.     

大学生的冲动性特质与自杀意念的关系:一个有调节的中介模型

以应激-易感模型为依据考察冲动性特质与自杀意念的关系,并在此基础上提出一个有调节的中介模型,探讨负性生活事件影响的中介作用以及家庭环境的调节作用。采用巴瑞特冲动性量表、青少年生活事件量表、家庭环境量表、贝克自杀意念量表对902名大学生进行集体施测,旨在考察负性生活事件的影响对大学生冲动性特质与自杀意念的中介作用以及家庭环境的调节作用,结果表明:(1)冲动性特质和负性生活事件的影响能正向预测大学生的自杀意念;(2)负性生活事件的影响在冲动性特质和自杀意念之间起中介作用;(3)负性生活事件影响的中介作用和冲动性特质的直接作用受家庭环境的调节。这些结果对于综合解释环境与个体因素对自杀意念的作用与机制具有重要意义。     

MOTILITY,AGGRESSION, AND THE BODILY I: AN INTERPRETATION OF WINNICOTT

Among the central ideas associated with the name of Winnicott, scant mention is made of motility. This is largely attributable to Winnicott himself, who never thematized motility and never wrote a paper specifically devoted to the topic. This paper suggests both that the idea of motility is nonetheless of central significance in Winnicott's thought, and that motility is of central importance in the development and constitution of the bodily I. In elaborating both these suggestions, the paper gives particular attention to the connections between motility, continuity, aggression, and creativity in Winnicott's work.     

Nature Gives Us Strength: Exposure to Nature Counteracts Ego-Depletion

Previous research rarely investigated the role of physical environment in counteracting ego-depletion. In the present research, we hypothesized that exposure to natural environment counteracts ego-depletion. Three experiments were conducted to test this hypothesis. In Experiment 1, initially depleted participants who viewed pictures of nature scenes showed greater persistence on a subsequent anagram task than those who were given a rest period. Experiment 2 expanded upon this finding by showing that natural environment enhanced logical reasoning performance after ego-depleting task. Experiment 3 adopted a two- (depletion vs. no-depletion) -by-two (nature exposure vs. urban exposure) factorial design. We found that nature exposure moderated the effect of depletion on anagram task performance. Taken together, the present studies offer a viable and novel strategy to mitigate the negative impacts of ego-depletion.     

A first grade student’s exploration of variable and variable notation / Una alumna de primer grado explora las variables y su notación

Abstract

This paper presents a case study of a first grade student to illustrate the diversity of her understandings related to variables and variable notation. While prior research has documented secondary school students’ difficulties with variables and variable notation, we identify many productive understandings in this much younger student, leading us to question the prevailing argument that students might have difficulties with variables due mostly to their own limitations. We draw our data from a teaching experiment that explored functional relationships. Individual interviews were carried out with a subset of the students in the experiment prior to, as well as mid-way through and at the end of the experiment. This paper focuses on a set of three interviews with one of the first grade students. We illustrate the shifts that occurred in the student’s understandings about variables and variable notation across as well as within each of the three interviews.     

Changing epistemologies under conditions of social change in two Arab communities in Israel

The study of epistemic thinking focuses on how people understand and coordinate objective and subjective aspects of knowing and make sense of multiple and discrepant knowledge claims. Typically described in terms of normative development, cross‐cultural studies show differences in epistemic development and characteristics of epistemic thinking. This study focuses on within‐culture variations of epistemic thinking, with the assumption that social change will produce changes in development. Arab society in Israel has undergone notable change over the last half century. In this cross‐sectional research design, cross‐generational comparison and rural–urban comparison were used as proxies for longitudinal social change. Three generations of Muslim Arab women in a village in Israel (20 adolescents, 20 mothers and 20 grandmothers) and 20 Muslim Arab adolescents from a large, mixed city in the same region responded to six dilemmas invoking epistemic thinking. Village adolescents were more subjectivist than their mothers and grandmothers. Sociodemographic characteristics representing greater exposure to diverse people and ideas accounted for generational differences. Both urban and rural adolescents tended towards subjectivist perspectives, and they did not differ. Parents' education levels emerged as the sociodemographic variables most consistently related to epistemic thinking. Epistemic thinking mediated the relationship between generation and gender role/cross‐sex relation values.     

Lost in (cyber)space: finding two adolescent boys hiding from their own humanity

This article explores the intense psychological effects of compulsive Internet use, which has become increasingly common among adolescent boys and young men. Two cases are presented and discussed to illustrate some of the psychic distortions around thinking and feeling, as these occurred in the analysis of a mid‐adolescent boy and of another patient in later adolescence. A kind of narcissistic omnipotence grounded in magical thinking appeared to take root in their minds, and it led to an avoidant pattern in relationships because of such strong wishes for both distance and control. A short review of the conceptual origins of magical thinking underscores its continued relevance because so many now engage with the Internet. In addition, Anzieu's idea of the ‘skin ego’ is applied to the clinical case material to provide a theoretical framework for the developmental challenges that can appear in adolescent boys who seek to use the Internet as a form of psychic container. Emerging problems that immersion in the Internet might bring into our practices, for example the depleting effects of massive projective identification, are considered and discussed, along with the obvious ways in which using the Internet can be beneficial for connecting with others, for creating new platforms of expression, and for education.     

Event detail and confidence in gambling: The role of counterfactual thought reactions

Differences in people’s reactions to the same events described with full vs. sketchy information are examined. It is hypothesized that differences in counterfactual thought reactions to varying levels of event detail shape confidence in, and willingness to gamble on similar, future events. In three experiments, participants were presented with different types and levels of event detail about their performances on a trivia test, on several games of blackjack, or on gambling on a professional horse race. Upward counterfactual thoughts were observed more frequently in response to losing events containing high levels of detail and specificity. Importantly, counterfactual thought frequency also mediated the relationships between event detail and the level of confidence in and willingness to gamble on similar, future events. Evidence also indicates that this relationship is based on the hindsight bias that results from counterfactual thinking. Results are discussed in terms of cognitive processes and decision making research.     

The Role of the Dominant Social Paradigm in the Quality of Life/Environmental Interface

In this examination of the relationship between quality of life and the environment, it is argued that a broad framework within which the relationship can be established is required. The framework used is that of the dominant social paradigm (Pirages & Ehrlich, 1974) that contains political, economic, and technological institutions. It is these institutions that determine both the quality of life and environmental constructs within any society. The paper integrates these three areas in a single model that hypothesizes a particular relationship between the dominant social paradigm, the environment, and quality of life.     

Creative thinking and collective mobilisation in the Muslim world

ABSTRACT

To what extent does openness to new ideas and creativity (ONIC) help explain the elite-challenging collective mobilisation in the Muslim world? Are religious Muslims who are open to creative and innovative thinking more or less likely to engage in pro-democratic collective action? Analysing 16 Muslim-majority countries, this study advances the debate of Muslim contentious politics by systematically examining the extent to which ONIC explains the variation in high-risk, pro-democratic collective mobilisation. A quad-dimensional analysis of creativity indicates that ONIC is an empirically distinctive measure to capture openness and creative thinking. The evidence further suggests that, ceteris paribus, Islamic religiosity and ONIC are not mutually exclusive and that both are positively associated with collective protests. Notably, ONIC does appear to intervene to mediate the positive relationship between Islam and engagement in high-risk collective action, implying that the effects of religiosity may not be independent from how Muslims position themselves towards being open to novel ideas or creativity. The findings also demonstrate that an individual-level ONIC may be boosting the likelihood of protest engagement among more devout individuals in Islamic societies.