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.     

Counterfactual comparison modulates fairness consideration in the mini‐ultimatum game: An event‐related potentials study

Existing literature on the mini‐ultimatum game indicates that counterfactual comparison between chosen and unchosen alternatives is of great importance for individual's fairness consideration. However, it is still unclear how counterfactual comparison influences the electrophysiological responses to unfair chosen offers. In conjunction with event‐related potentials’ (ERPs) technique, the current study aimed to explore the issue by employing a modified version of the mini‐ultimatum game where a fixed set of two alternatives (unfair offer vs. fair alternative, unfair vs. hyperfair alternative, unfair offer vs. hyperunfair alternative) was presented before the chosen offer. The behavioral results showed that participants were more likely to accept unfair chosen offers when the unchosen alternative was hyperunfair than when the unchosen alternative was fair or hyperfair. The ERPs results showed that the feedback‐related negativity (FRN) elicited by unfair chosen offers was insensitive to the type of unchosen alternative when correcting for possible overlap with other components. In contrast, unfair chosen offers elicited larger P300 amplitudes when the unchosen alternative was hyperunfair than when the unchosen alternative was fair or hyperfair. These findings suggest that counterfactual comparison may take effect at later stages of fairness consideration as reflected by the P300.     

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.     

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.     

Overcoming fixation with repeated memory suppression

Fixation (blocks to memories or ideas) can be alleviated not only by encouraging productive work towards a solution, but, as the present experiments show, by reducing counterproductive work. Two experiments examined relief from fixation in a word-fragment completion task. Blockers, orthographically similar negative primes (e.g., ANALOGY), blocked solutions to word fragments (e.g., A_L_ _GY) in both experiments. After priming, but before the fragment completion test, participants repeatedly suppressed half of the blockers using the Think/No-Think paradigm, which results in memory inhibition. Inhibiting blockers did not alleviate fixation in Experiment 1 when conscious recollection of negative primes was not encouraged on the fragment completion test. In Experiment 2, however, when participants were encouraged to remember negative primes at fragment completion, relief from fixation was observed. Repeated suppression may nullify fixation effects, and promote creative thinking, particularly when fixation is caused by conscious recollection of counterproductive information.     

医学生临床实习应掌握的几种哲学思维方式

为适应全球卫生事业的迅猛发展,面对医学教育落后于医学发展的现状,转化医学教育迫在眉睫。在第三代“以系统为基础”的教育改革中,培养医学生的哲学思维无疑是其重要环节之一。思维方式必须在医学生步入临床时就要开始正确培养,一旦开始阶段就养成不正确的思维方式、不但会导致医疗过程中的失误,而且再想改变将会有很大难度。本文通过对医学哲学重要性的探讨,剖析医学生哲学思维的不足,阐述了医学生,临床实习过程中应掌握的几种哲学思维方式。旨在提高医学生的哲学理念,促进以岗位胜任能力为导向的医学教育转型发展。     

Online Primary Sources in Religious Studies: Active Learning Exercises for Information Literacy Instruction

Online primary sources are a valuable resource for undergraduate students in religious studies courses. They provide firsthand, factual information about the beliefs and practices of religious traditions, movements, cults, and so on. In addition, they are readily and freely accessible online. Given their value as an information resource, undergraduate students need to be able to identify primary sources and understand how to use them in academic research. The purpose of this article is to describe activities for information literacy instruction that focus on primary sources in religious studies. These activities are intended as a resource for academic librarians who are teaching—or who plan to teach—undergraduate students how to identify and use primary sources.