Multiple representations as sites for teacher reflection about mathematics learning

This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.     

Learning with multiple representations: Extending multimedia learning beyond the lab

The present study extended multimedia learning principles beyond the lab to an ecologically valid setting (homework). Eighteen information cards were used to perform three homework tasks. The control group students learnt from single representation (SR) cards that presented all information as printed text. The multiple representation (MR) group students received the same information, but each card contained either printed text or an informationally equivalent graphic such as a chart or graph. The MR group students performed better than the SR group students on accuracy of their homework answers and on subsequent posttest retention and transfer, and used more information cards while learning. The improved MR group students' performance is discussed in relation to two alternative possible explanations – the nature of the information sources and students' motivation to learn.     

Learning about earthquakes: getting serious about authenticity in computer-supported learning

The discovery or re-construction of scientific explanations and understanding based on experience is a complex process, for which school learning often uses shortcuts. On the basis of the example of analyzing real seismic measurements, we propose a computer-facilitated collaborative learning scenario which meets many of the requirements for authentic learning, knowledge construction, and collaboration. The implementation of the learning environment called SeisModes is based on a general platform for supporting collaborative modeling activities. SeisModes provides a tool to allow students collaboratively learn about earthquakes and thus reduce the fears they might have concerning them. First formal evaluations showed the approach motivates students.     

Learning about and learning from expert teachers

Studies of expertise in teaching have been informative, despite problems. One problem is determining the relative roles of talent vs. deliberate practice in the acquisition of expertise. When studying teachers, however, a third factor must be considered, that of context. The working conditions of teachers exert a powerful influence on the development of expertise. A second problem is that of definition because expertise in teaching takes different forms in different cultures, and its characteristics change by decade. A distinction is drawn between the good teacher and the successful teacher, characteristics of expertise that are often confused. A prototypical model of expertise is described and found to identify teachers who were both good and successful. Discussed also is the importance of understanding adaptive or fluid expertise, automaticity and flexibility. Finally, the development of teacher expertise is seen as an increase in agency over time.     

Lifelong learning: Implications for institutions

Lifelong learning poses a large number ofthreats and opportunities for the traditionalhigher education institutions. Not justprogramme offerings and means of delivery willhave to be restructured, but, morefundamentally, universities and colleges willhave to rethink and reshape their businessconcept, that is: their way of creating valueand maintaining their competitive edge overother providers in the education system.It will be argued that a business concept thatis based on the idea of creating value throughenhancing differentiation requires highereducation providers to move as much as they canto a student-centered provision of educationand training. This has far-reachingconsequences for the curriculum, the concept ofresearch, the interaction with students, andthe relationships with other institutions inthe education system. It may very well lead toan education system in which there is room forsome universities to transform themselves intodual-sector institutions, that contain both ahigher education part and a vocational part.     

论学习型社会中的自学考试

在多年的发展中,自学考试为个人成才和社会发展作出了重要贡献。当前其现实处境:数量基础受损,价值认可不高,社会风气不良,监管机制不全。在学习型社会建设中,自学考试将呈现良好的发展趋势:完善制度创新建设,面向农村发展服务,加快互通认证步伐,构建终身教育体系。     

Assessment matters: Learning about learning communities: Consider the variables

Learning communities come in many forms. Indiana University's Gary Pike shares four research‐based lessons to guide the assessment of all of them.     

Adult development: Implications for teaching and learning

This paper presents the background and issues emanating from an adult studies curriculum for adult students. The experimental nature of this program is analyzed in the context of three recent trends in higher education. First, individuals in their thirties, forties, and fifties are returning to college in increasing numbers. Second, adult development theory and research is a fairly new body of knowledge suggesting interesting implications for teaching and learning. Third, adults returning to college tend to seek out nontraditional models of higher education. Empire State College, established in 1971 as the alternative unit of the State University of New York, illustrates this trend.The adult studies curriculum and instructional design are subsequently analyzed in terms of four theoretical perspectives: (1) life cycle theory, (2) ego development, (3) moral development, and (4) adult learning style. Implications for teaching and learning and issues for further research conclude the article.     

Group time treasures: Implications for learning

Meaningful group times have been a hallmark of quality early childhood programs for many years. Stimulating group experiences present a wealth of opportunities for everyone involved. Adults are better able to monitor children's skills and enjoy their ongoing growth. Group activities also may set the stage for an abundance of adventures as young children grow and learn in all areas of their development (Bredekamp, 1986).Pauline Davey Zeece and Marcia Corr are at the Department of Human Development and the Family, University of Nebraska-Lincoln in Lincoln, Nebraska.     

How do Students Feel about Grammar?: The Framework and its Implications for Teaching and Learning

Grammar's place in English teaching seems to be constantly under review. This paper reflects on the status and methods of grammar teaching at the moment. In particular, it explores both the positive and negative impact of the Key Stage 3 Framework for Teaching English on teaching and learning. It goes on to analyse the writer's experiences of teaching grammar as a student teacher, and asks whether the methods we are using today are adequate for the needs of young writers.     

Web 3.0: Implications for Online Learning

The impact of Web 3.0, also known as the Semantic Web, on online learning is yet to be determined as the Semantic Web and its technologies continue to develop. Online instructors must have a rudimentary understanding of Web 3.0 to prepare for the next phase of online learning. This paper provides an understandable definition of the Semantic Web and its terminology, and then explores possible implications of Web 3.0 on online learning. The foundation of the Semantic Web is data integration. By using metadata, “display only” data is converted to meaningful information which can be located, evaluated, and delivered by software agents. Web 3.0 technologies will assist online instructors in the areas of course development, learner support, assessment, and record keeping. Online students will benefit from learning personalization and knowledge construction powered by the Semantic Web.     

Bilingualism and symbolic abstraction: Implications for algebra learning

Much of the research on bilingualism and math learning focuses on the potential challenges that bilinguals and language learners may face. The current line of research took an alternative approach and explored whether a bilingual advantage may emerge for a novel algebraic problem solving task that requires symbolic thought, the Symbol Math task. No differences were seen between bilingual and monolingual samples on basic math or executive control tasks; however, a bilingual advantage was seen in performance on the Symbol Math task across two experiments. The results suggest that bilingualism may improve the ability to engage in more abstract or symbolic thought processes, which may have important implications for algebra learning.     

Visual Learning and the Brain: Implications for Dyslexia

ABSTRACT— The central and peripheral visual fields are structurally segregated in the brain and are differentiated by their anatomical and functional characteristics. While the central field appears well suited for tasks such as visual search, the periphery is optimized for rapid processing over broad regions. People vary in their abilities to make use of information in the center versus the periphery, and we propose that this bias leads to a trade-off between abilities for sequential search versus contemporaneous comparisons. The parameter of periphery-to-center ratio (PCR) describes the degree of peripheral bias, which evidence suggests is high in many people with dyslexia. That is, many dyslexics favor the peripheral visual field over the center, which results in not only search deficits but also (more surprisingly) talents for visual comparison. The PCR framework offers a coherent explanation for these seemingly contradictory observations of both deficit and talent in visual processing. The framework has potential implications for instructional support in visually intensive domains such as science and mathematics.     

Personal Epistemology Research: Implications for Learning and Teaching

The ideas that individuals hold about knowledge and knowing have been the target of research programs with disparate names, such as epistemological beliefs, reflective judgment, ways of knowing, and epistemological reflection, all of which appear to be a part of a larger body of work on “personal epistemology.” Epistemological perspectives are salient in numerous academic experiences, have been shown to be related to learning in various ways, influence reasoning and judgment throughout our lives, and have implications for teaching. Yet this work has remained outside the mainstream of educational psychology and cognitive development. This paper addresses three main questions: (1) What is personal epistemology research and how is it conceptualized? (2) How are individuals' conceptions of epistemology related to learning and instruction? (3) Given what we know about personal epistemology, what might educators do? Suggestions are also provided for future research and theoretical development.     

An international comparative study of practicum mentors: Learning about ourselves by learning about others

Teachers who mentor student teachers on practicum play a critical role in teacher education. However, it is widely reported that these teachers are poorly prepared and lack sufficient knowledge for mentoring. And what is known about mentoring is largely drawn from idiosyncratic single-context studies. In an attempt to extend the scope of this knowledge, this study draws on the Mentoring Profile Inventory (www.mentoringprofile.com) to chart how mentors conceive of their work within and across six international contexts. The outcome is a comparative analysis that highlights what is ‘particular’ versus what is ‘general’ across contexts that has not been previously reported.