Never mind the gap: Formative assessment confronted with Dewey's and Gadamer's concept of experience

The notion of “closing the learning gap” is widely used in the conceptualisation of formative assessment. It builds on an unarticulated assumption that students' learning can and should be controlled towards predefined outcomes. This article discusses this control assumption in the light of the concept of the American philosopher John Dewey and the German philosopher Hans-Georg Gadamer. Their conceptualisation challenges the idea of learning as a linear and controllable process that results in stable and predictable outcomes. Using the concept of experience, we argue that learning follows a continuous circular movement where previous experiences condition future interpretations and that every experience changes the subject. This process of change is both unpredictable and diverse and requires that attention is paid to the uniqueness of each situation and to students as subjects. Following the discussion, we propose a model for considering the extensiveness and rigidity of formative assessment practices and that authors pay attention to whether they conceptualise formative assessment in a way that promotes student and teacher “gap closing” and control.     

浅谈数学概念教学

数学是由概念与命题等内容组成的知识体系,是一门以抽象思维为主的学科,因此概念是数学基础知识和基本技能教学的核心。学生数学素养差,关键表现在对数学概念的理解、应用和转化等方面的不足。文章指出了现行中学数学概念教学中可能出现的弊端,并根据学生的认知特点及数学本身的特征介绍了如何进行数学概念教学的几种方法。     

数学概念的理解问题

对数学概念的理解问题是数学学习理论中的重要理论问题．就刻划数学概念理解的重要概念——数学概念的心理表征和数学概念理解的认知基础进行分析，从而对数学概念的理解问题有更深入的认识。     

Understanding mathematical literacy: The contribution of research

Amid the current ‘math wars’ in the United States, research evidence is being both demanded and attacked by all sides. A recent study designed to synthesize the literature on mathematics learning and to provide research-based recommendations, advice, and guidance developed an elaborated view of mathematical literacy, termed mathematical proficiency in the study report. Mathematical proficiency can serve as a focus for both research and practice, avoiding the extreme positions with respect to the goals of mathematics learning that are so often found in disputes over school mathematics. The study also demonstrated how research could be synthesized so that evidence from research might be used more productively for changing school mathematics in ways that would yield greater mathematical literacy for all.     

Didactic use of concept mapping in higher education: applications in medical education

This paper describes the use of concept mapping for didactic purposes in higher education at the university level, namely, in medical schools. The first study involved the use of concept mapping to evaluate students' self learned knowledge of subject matter during their clerkship in a department of surgery. The individually constructed cognitive maps facilitated learning by being used in group discussions with the tutor, to identify correct ideas as well as misconceptions, and to convey the tutor's view, and thereby facilitated learning. The second, unrelated study employed concept mapping to evaluate an inservice Orientation Workshop for medicine school faculty. The cognitive structure characteristics of the participants and their congruence with those of the workshop teachers were assessed. These provided evidence regarding the attainment of the workshop's objectives for different kinds of participant. For example, by using concept mapping in planning instruction or preparing materials for teaching, teachers become learners. Potential didactic uses in higher education are discussed in light of these studies.     

Transfer effects of mathematical literacy: an integrative longitudinal study

European Journal of Psychology of Education - Mathematical literacy (ML) is considered central to the application of mathematical knowledge in everyday life and thus is found in many comparative...     

Evaluating the effectiveness of interactive computer tutorials for an undergraduate mathematical literacy course

This article describes a study of learning when students used interactive spreadsheet‐based computer tutorials in a mathematical literacy course. It foregrounds theories relating to the role of computer technology (and specifically spreadsheets) as a mediator for learning of mathematics. It outlines the application of quantitative methods involving pre‐ and post‐testing of students, both in the computer laboratory and in the lecture sessions, and discusses factors constraining the experimental design and the usefulness of the results. There are indications that the data reveal real differences between the learning experiences in the lecture sessions and the computer laboratories. It appears that in some respects the computer tutorials were more effective in conveying the concepts than the lecture sessions were. A method of analysing and representing the data, that tracks the extent of learning of concepts through the pre‐ and post‐tests, was developed. It allows for the performance of sub‐groups of students to be examined separately. This analysis shows that simple definitions of disadvantage (such as having English as a second language) are inadequate to account for the poor performance of students in the lower quartile.     

Reading graphs: Contributions to an integrative concept of literacy

In contrast to past educational research that views graph-related activities in terms of mental ability, I offer a conceptualization of graphing as a semiotic activity. This move provides a more viable account not only of individual experiences, familiarity and socio-cultural factors during graph reading, but also of errors committed by students and 'experts' alike. I outline a model of semiotic activity that contains two elements not present in other semiotic theories: the process of parsing the perceptual field to construct relevant signs and the grounding of a sign through the dialectic of sign-to-referent and referent-to-sign movements. This model of semiotic activity also implies an integration of research on graphing (and other sign-related activities) into a more general concept of literacy.     

Young people's readings of a political cartoon and the concept of multimodal literacy

This article uses young people's responses to a newspaper cartoon as a way of exploring the concept of multimodal literacy. The discussion draws on data from a study which aimed to elicit the geopolitical views of 16–19-year-olds in a multi-ethnic British city by using cartoons as a way of encouraging them to talk about their thoughts and feelings towards recent political events. We argue that, contrary to popular perceptions, political cartoons are complex and polysemous and require a particular form of literacy. This not only encompasses the ability to read visual grammar, but also an understanding of the cartoon genre and how it is constructed, with a view to conveying particular meanings within a specific social and cultural context.     

A machine learning approach to investigating the effects of mathematics dispositions on mathematical literacy

Mathematics competency is fast becoming an essential requirement in ever greater parts of day-to-day work and life. Thus, creating strategies for improving mathematics learning in students is a major goal of education research. However, doing so requires an ability to look at many aspects of mathematics learning, such as demographics and psychological dispositions, in an integrated way as part of the same system. Large-scale assessments such as the Programme for International Student Assessment (PISA) provide an accessible and large volume of coherent data, and this gives researchers the opportunity to employ data-driven approaches to gain an overview of the system. For these reasons, we have used machine learning to explore the relationships between psychological dispositions and mathematical literacy in Australian 15-year-olds using the PISA 2012 data set. Our results from this strongly data-driven approach re-affirm the primacy of mathematics self-efficacy and highlight novel complex interactions between mathematics self-efficacy, mathematics anxiety and socio-economic status. In this paper, we demonstrate how education researchers can usefully employ data-driven modelling techniques to find complex non-linear relationships and novel interactions in a multidimensional data set.     

数学分析中极限概念的教学策略研究

数学分析是高等院校数学类专业的主干课程。极限理论是数学分析课程的基本理论,而极限概念是极限理论的核心内容,因此搞好极限概念的教学具有重要的现实意义。采用定量和定性相结合的基本方法,首先对极限概念的教学方法进行综述,然后对极限概念教学难的主要原因进行了分析。在此基础之上,提出了一些极限概念的具体教学策略。     

The scientist as Cracker-Barrel Philosopher: Implications for the concept of scientific literacy

This study aims to identify an internally consistent and readily teachable philosophical approach to the nature and practice of science. The primary sources are anecdotal material and oral reflections prepared for the popular media by and about an eminent contemporary scientist, the late physicist Richard Feynman. Examples of real people working on technological problems can provide a useful foil to the customary study of great men in the history of science, yet both of these approaches can have serious drawbacks. Feynman's anecdotal reflections provide an excellent middle ground case study: a pure scientist, yet with a personal background anchored in practical problems, who combines the traditional credentials of authority with an endearing humanity. There are striking similarities between the account of the nature of science, technology, and good teaching implied by Feynman's musings and that expressed more abstractly in the recent American Association for the Advancement of Science report,Science for All Americans.     

高等数学概念学习应注重规律

通过大量例子说明学习高等数学概念时应从概念引入、概念理解、概念应用、概念巩固诸方面注重规律.     

Humanization of education in Pakistan through Freire’s concept of literacy

Pakistan is an underdeveloped country, full of socio-economic problems where a few oppress and exploit many. One of the most significant reasons, in this context, is the high illiteracy rate in the country. However, can high literacy rates guarranty peace, prosperity, and justice in any society? Clearly, not. There are several countries where the literacy rate is very high yet it remains relatively under-developed. However, it is also a fact that the countries where the literacy rate is high have been able to emerge as economic powers. In this regard, Freire’s concept of literacy education is very helpful in that it is essentially hopeful in nature and it is this optimism which gives it the potential to transform oppressive situations.     

Heuristic literacy development and its relation to mathematical achievements of middle school students

The relationships between heuristic literacy development and mathematical achievements of middle school students were explored during a 5-month classroom experiment in two 8th grade classes (N = 37). By heuristic literacy we refer to an individual’s capacity to use heuristic vocabulary in problem-solving discourse and to approach scholastic mathematical problems by using a variety of heuristics. During the experiment the heuristic constituent of curriculum-determined topics in algebra and geometry was gradually revealed and promoted by means of incorporating heuristic vocabulary in classroom discourse and seizing opportunities to use the same heuristics in different mathematical contexts. Students’ heuristic literacy development was indicated by means of individual thinking-aloud interviews and their mathematical achievements – by means of the Scholastic Aptitude Test. We found that heuristic literacy development and changes in mathematical achievements are correlated yet distributed unequally among the students. In particular, the same students, who progressed with respect to SAT scores, progressed also with respect to their heuristic literacy. Those students, who were weaker with respect to SAT scores at the beginning of the intervention, demonstrated more significant progress regarding both measures.     

新时期学前教育专业学生的数学素养意识与分析

2017年以后我国高考改革,实行文理不分科发展趋势,与此同时社会、家长对幼儿教师数学素养的要求也会更高。指出我国幼儿教师数学素养的意义,给出数学素养的含义,根据对我国目前部分地区幼儿教师数学素养的问卷调查分析,可以看出幼儿教师在数学知识能力、数学教学技能、数学教育观念等方面存在问题,并提出学前教育专业学生数学素养的培养措施,为学前教育专业课程建设与教学改革提供参考依据。     

从“大”教学论到“微”教学论

教学论学科难以发挥对教学实践的影响力,是因为教学论研究依然受到了大教学论思维方式和框架体系的束缚;教学论学科发展需要返本开新,反思大教学论的贡献与局限;教学论要发展,必须从大教学论思维方式和框架体系中走出来,从追求发现把一切事物教给一切人们的全部(或统一)艺术的大教学论转向追求建立把不同的内容教给不同的人的多样化的科学理论的微教学论;微教学论的产生需要经过进入教学现场-观察教学现象-提出教学问题与假设-构建教学干预方案-通过以课为例的行动研究验证假设-提炼总结具体教学规律的理论建构过程。     

Pedagogical and Didactic Aspects of the New Hauptschule

Northrhine-Westphalia, with 17 million people the largest of the eleven Länder (states) of the Federal Republic of Germany, issued revised curriculum programs for all its schools between 1966 and 1968. The most interesting changes occurred in the secondary school for those children (about 60% of the age group) whose parents do not enroll them at age 10 in a Realschule (semiacademic) or a Gymnasium (academic). These children formerly remained in the Volksschule for a total of eight years; but now the upper half of this school, expanded by one year, is called Hauptschule and is designed to offer more substantial education than previously, including a foreign language (English). The same pattern is followed in all the other West German Länder.