Audrey's acquisition of fractions: A case study into the learning of formal mathematics

National standards for teaching mathematics in primary schools in the Netherlands leave little room for formal fractions. However,a newly developed programme in fractions aims at learning formal fractions. The starting point in the development of this curriculum is the students’ acquisition of `numeracy infractions’. In this case study we describe the growth in reasoning ability with fractions of one student in this newly developed programme of 30 lessons during one whole school year. In the study we found indications that the programme and its teaching stimulated the progress of an average performer in mathematics. Moreover we found arguments as to what extent formal operations with fractions suits as an educational goal. This revised version was published online in July 2006 with corrections to the Cover Date.     

A framework for designing interactive multimedia to scaffold young children's understanding of historical chronology

Young children's understanding of thehistorical past is often characterised by alack of temporal differentiation and a sense oftotal discontinuity with the present. Researchhas suggested that this situation may be causedin part by their formation of inappropriaterepresentations when solving problems ofchronology. To help children construct moreappropriate external representations forparticular tasks and reason more effectivelywith them about chronological concepts, weinvestigated the role that interactivemultimedia might play in scaffoldingteacher-led activities in the classroom. Inthis paper we report on our conceptual designand pedagogical approach to developingeffective dynamic, interactive representationsand activities at the computer interface, aimedat bridging the conceptual gap between concreteexperience and abstract concepts. Evaluationsof the software built using this frameworkshowed that the program was well received bychildren and teachers alike, and that it wasable to facilitate children's understanding of,and ability to reason about, chronology.     

The Thinking Frames Approach: a case study of inclusion using student‐generated multiple‐representations

Many teachers struggle to provide equitable opportunities for students with special educational needs (SEN) to learn science concepts in the inclusive classroom. This study examines the experience of teaching in an inclusive classroom using a conceptual change approach, the Thinking Frames Approach (TFA), incorporating the use of discrepant events, social construction of scientific conceptions followed by the production of multiple student‐generated representations of their understanding. An in‐depth case study is presented of the experience of Wayne, a student with complex SEN and the effect on his behaviour and science learning based on video/audio recordings of lessons, teacher journal entries, student artefacts, questionnaire results and interviews. It was found that there were positive effects for Wayne's learning using this approach including improved behaviour, greater feelings of self‐efficacy, increased participation in small group and class discussions and improved outcomes on the same assessment tasks as peers. It is suggested that the structured approach of the TFA, the communication of understanding in different modalities, particularly drawing, and the support of peers enabled Wayne to more deeply engage in construction of understanding and may provide teachers with an easy and effective approach to authentic inclusion where real conceptual gains are made by all students.     

谈在高校理论教育中贯彻"三个代表"的基本思路

本文认为“三个代表”为高校理论教育及时地指明了方向,并按“三个代表”的要求审视了当前高校理论教育的现状,提出了在高校理论教育改革中贯彻“三个代表”重要思想的基本思路。     

Identifying processes underlying the multimedia effect in testing: An eye-movement analysis

Test items become easier when a representational picture visualizes the text item stem; this is referred to as the multimedia effect in testing. To uncover the processes underlying this effect and to understand how pictures affect students' item-solving behavior, we recorded the eye movements of sixty-two schoolchildren solving multiple-choice (MC) science items either with or without a representational picture. Results show that the time students spent fixating the picture was compensated for by less time spent reading the corresponding text. In text-picture items, students also spent less time fixating incorrect answer options; a behavior that was associated with better test scores in general. Detailed gaze likelihood analyses revealed that the picture received particular attention right after item onset and in the later phase of item solving. Hence, comparable to learning, pictures in tests seemingly boost students' performance because they may serve as mental scaffolds, supporting comprehension and decision making.     

The effect of external representation on constructing computer models of complex phenomena

Computer modeling – creating executable modelsof science domains – has been recognized as animportant teaching method. Still not much isknown about the factors making modelingenvironments effective in use. We investigatethe effect of different externalrepresentations on the construction of computermodels. Representations can significantlyinfluence the processes of modeling. In orderto find the specific benefits of two differentrepresentations, we compare dyads working on acollaborative modeling task using a text-basedmodel representation, in which correctequations are required to make the model run,with others using a graphical representation,in which the model is built by qualitativelylinking variables. The learners, secondaryschool students and modeling novices, workedwith the representations on a task in thedomain of physics. Results indicate that thetwo representations induce differentbehaviours, which are appropriate for differentphases of the modeling process.     

Being-in-the-World and the Horizons of Learning: Heidegger, Wittgenstein, and Cognition

The work of Heidegger and Wittgenstein still influences research and development in such areas as sociology of science, cognitive science, and design of computer-based work environments. The purpose of this article is to show how the writings of Heidegger and Wittgenstein can be used to: (a) throw new light on studies of real-time learning in school science, (b) understand the situated nature of cognition during science activities, and (c) inform the design of new learning environments. Two case studies are used to illustrate the fruitfulness of such an approach.     

“三个代表”思想与高校党的建设

高校是中国先进社会生产力的重要源泉 ,是中国先进文化的生产者和推动器 ,与中国最广大人民群众的根本利益息息相关。因此 ,高校党委要把贯彻、落实江泽民同志“三个代表”重要思想作为加强高校党的建设 ,办好高等学校的关键来抓。要紧密结合高校实际 ,着眼大局 ,理解内涵 ,明确定位 ;遵守规范 ,把握导向 ;抓好基础 ,持之以恒 ;勇于校正 ,自觉防范。     

On Understanding the Notion of Limits and Infinitesimal Quantities

In this paper we explore the influence of students’ personalized notion of ‘small’ numbers based on real life experiences on their understanding of limits. Tests were conducted on two samples of students. The first sample, consisting of students in the XII grade, had been taught limits using an informal approach (i.e., without recourse to the definition) and the second sample, consisting of first year undergraduates, had been taught the formal definition of limits. Our research points out that most students in both samples round off to zero such ‘small numbers’ while evaluating limits wherever such numbers might occur because they perceive limit as a process of approximation.     

Notions of intelligence and social-educational identity

This study examined whether notions of intelligence tend to maintain a group’s social-educational identity. A sample of academically and vocationally educated parents were asked to give their opinions of a statement proposing that a theoretical university education enables people to gain a deeper understanding of most matters. It was found that only among the academic parents, support for the statement tended to amplify endorsement of a general, individualised and essentialistic representation of intelligence.