Students’ images of mathematics

Students’ judgments about “what counts” as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as mathematical, and how they make their judgments. Students completed a photo sorting activity; took, viewed, and captioned their own photos of mathematics; viewed and commented on classmates’ photos; and participated in a small group discussion. Across multiple sources of data, findings showed that students attended to two major features of photos and activities when making judgments: surface cues present in the photos, such as numbers and money, and the possibility for mathematical action. Some students looked for the possibility of mathematics, while others asked if mathematics was necessary. Students also gave higher ratings to activities with which they had personal experience. The article concludes with possible implications for practice.     

Investigating teachers’ images of mathematics

Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be used to express already-held perceptions about the nature of mathematics. In addition to providing a way of talking about current views of mathematics, the analogous dimensions of metaphors can prompt new ways of thinking about these images. In this article, I consider the use of metaphors as a strategy for explicating elementary teachers’ views of mathematics. I claim that the investigation of metaphors of mathematics helped create a shared communicative space and enhanced the quality of the discussion with the teachers. In particular, our exploration of the metaphor mathematics is a language encouraged a consideration of the humanistic dimensions of mathematics and contributed to a varied re-imaging of mathematics.     

Students’ images of two-variable functions and their graphs

This paper presents a conceptual analysis for students’ images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of one-variable functions to graphs of two-variable functions. To evaluate the viability of this learning trajectory, we use data from two teaching experiments based on tasks intended to support development of the schemes in the HLT. We focus on the schemes that two students developed in these teaching experiments and discuss their relationship to the original HLT. We close by considering the role of covariational reasoning in generalization, consider other ways in which students might come to conceptualize graphs of two-variable functions, and discuss implications for instruction.     

Students’ images and their understanding of definitions of the limit of a sequence

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students’ images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the ɛ–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.     

Student teachers’ conceptions of sustainable development: the starting-points of geographers and scientists

Postgraduate student teachers’ conceptions of sustainable development were elicited using a questionnaire completed by the entire cohort of geography (N = 21) and science (N = 40) students starting the University of Oxford Post Graduate Certificate in Education (PGCE) secondary course. Responses were analysed in three ways: (i) development of categories to capture features of sustainable development; (ii) scrutiny of individual responses for the presence or absence of key features (specifically environmental, economic and social factors); and (iii) in contrast to these grounded approaches, examination of the responses in light of a pre-specified framework. Notable findings were: (i) the large numbers recognizing the centrality of environmental (87%), economic (69%) and social (49%) factors—about a third highlighted all three factors (the geographers significantly more so than the scientists), while a further third mentioned two of them; (ii) when compared with the pre-specified framework, the aspects of sustainable development largely missing were to do with preservation of diversity, and with uncertainty and precaution in action; (iii) only one response contained an aesthetic element; and (iv) when comparing education for sustainable development with environmental education, the most frequent view identified the former as broader. The findings are related to contemporary literature in the field and some implications for PGCE learning are considered.     

Do images influence assessment in anatomy? Exploring the effect of images on item difficulty and item discrimination

Anatomists often use images in assessments and examinations. This study aims to investigate the influence of different types of images on item difficulty and item discrimination in written assessments. A total of 210 of 460 students volunteered for an extra assessment in a gross anatomy course. This assessment contained 39 test items grouped in seven themes. The answer format alternated per theme and was either a labeled image or an answer list, resulting in two versions containing both images and answer lists. Subjects were randomly assigned to one version. Answer formats were compared through item scores. Both examinations had similar overall difficulty and reliability. Two cross‐sectional images resulted in greater item difficulty and item discrimination, compared to an answer list. A schematic image of fetal circulation led to decreased item difficulty and item discrimination. Three images showed variable effects. These results show that effects on assessment scores are dependent on the type of image used. Results from the two cross‐sectional images suggest an extra ability is being tested. Data from a scheme of fetal circulation suggest a cueing effect. Variable effects from other images indicate that a context‐dependent interaction takes place with the content of questions. The conclusion is that item difficulty and item discrimination can be affected when images are used instead of answer lists; thus, the use of images as a response format has potential implications for the validity of test items. Anat Sci Educ © 2012 American Association of Anatomists.     

Portrayals of science and scientists,and ‘science for citizenship’

There are increasing calls in the science education community for ‘science for citizenship’ as an important goal for the school science curriculum of the 21st century. The potential influence of portrayals of science and scientists in popular culture on the achievement of this goal is explored in this paper through a review of the literature. We develop a framework of important questions citizens ask in considering personal and social decision making in relation to science and technology issues, and how portrayals of science and scientists might contribute to this decision making process.     

Fusion of ERT images based on Dempster-Shafer’s evidence theory

In this paper, an electrical resistance tomography（ERT） imaging method is used as a classifier, and then the Dempster-Shafer＇s evidence theory with fuzzy clustering is integrated to improve the ERT image quality. The fuzzy clustering is applied to determining the key mass function, and dealing with the uncertain, incomplete and inconsistent measured imaging data in ERT. The proposed method was applied to images with the same investigated object under eight typical current drive patterns. Experiments were performed on a group of simulations using COMSOL Multiphysics tool and measurements with a piece of porcine lung and a pair of porcine kidneys as test materials. Compared with any single drive pattern, the proposed method can provide images with a spatial resolution of about 10% higher, while the time resolution was almost the same.     

The role of visualization in learning from computer‐based images

Among the sciences, the practice of geology is especially visual. To assess the role of spatial ability in learning geology, we designed an experiment using: (1) web‐based versions of spatial visualization tests, (2) a geospatial test, and (3) multimedia instructional modules built around QuickTime Virtual Reality movies. Students in control and experimental sections were administered measures of spatial orientation and visualization, as well as a content‐based geospatial examination. All subjects improved significantly in their scores on spatial visualization and the geospatial examination. There was no change in their scores on spatial orientation. A three‐way analysis of variance, with the geospatial examination as the dependent variable, revealed significant main effects favoring the experimental group and a significant interaction between treatment and gender. These results demonstrate that spatial ability can be improved through instruction, that learning of geological content will improve as a result, and that differences in performance between the genders can be eliminated.     

必修五 Unit 1 Great scientists

一、完形填空 阅读下面短文，掌握其大意，然后从1-10各题所给的A、B、C和D项中。     

Children’s images of beauty: environmental influences on aesthetic preferences

This article reports on a recent study that explored children’s aesthetic preferences. Authors of previous studies in this area have concluded children have a relatively narrow range of preferences based on judgments about their responses to images. In other contexts, researchers have investigated children’s perspectives on their environments and created opportunities for them to take photographs in response to research tasks. This study is the first to draw on both approaches in order to develop a clearer understanding of children’s aesthetic preferences. Fifty-one children in two primary schools were asked to find and photograph images to represent their perceptions of beauty. In order to investigate whether or how children’s environments influenced their preferences, the schools were located in contrasting urban and rural areas. The article explores several contrasts between the two sets of images and offers explanations for these contrasts. It suggests that previous studies may have underestimated the diversity of children’s aesthetic preferences and that social, cultural and environmental factors may explain the differences between children’s aesthetic preferences. The article concludes that both researchers and teachers could adopt similar methods to develop our understanding of children’s perspectives, identities and experiences.     

Internal conflicts of Emily Dickinson—A study of the images of boat and sea in Dickinson's poems

The peculiar images,the boat and the sea,often recur in the poems of Emily Dickinson,the great American poet,which well reflect her internal conflicts,the conflicts between being an autonomous woman and being a passionate yet submissive woman.In her poems,the sea is a symbol of the male-dominated society or an individual man.While the little boat is the epitome of Dickinson:sometimes it wants to be strong-willed and clear of its destination,sometimes it just wants to moor in the sea and enjoy the calmness.The paper tends to reveal the psychological struggle of Emily Dickinson and show the whole image of her as an individual through the analysis of the images of boat and sea in Dickinson’s poems.     

Denoising of Chinese calligraphy tablet images based on run-length statistics and structure characteristic of character strokes

INTRODUCTION As an art form, Chinese calligraphy has a long history of several thousand years. Many ancient cal- ligraphy work created by former famous calligraphers were carved on stone tablets, and calligraphy docu- ments were produced by rubbings. The most imme- morial tablets we could look with reverence are “Shigu” stone tablets (left of Fig.1) which appeared about 2500 years ago in Warring States Period. The rubbed calligraphy document images however may look noisy, due to natur…     

The positioning of students in newly qualified secondary teachers’ images of their ‘best teaching’

Asking newly qualified teachers (NQTs) to provide images of their ‘best teaching’, and encouraging subsequent reflection on these images, has the potential to enhance their understanding of themselves as teachers as they explore their often unconsciously held assumptions about students and classrooms. This paper reports aspects of a study of 100 New Zealand secondary NQTs as they constructed and explained images of themselves when ‘teaching at their best’ at three points over the first 18 months of full-time teaching. The article shows how these images of ‘best teaching’ may represent the NQTs’ pedagogical creed, and explores the nature of relationships and ways of working with students described within this developing pedagogy. It concludes by indicating implications from this study for teacher education pedagogies and programmes.     

Is a picture always worth 1000 words? Website images of classrooms and perceptions of the institution

Learning Environments Research - When classroom facilities are out of date, students complain (Habaci et al., in Procedia Soc Behav Sci 64:58-64 2012, https://doi.org/10.1016/j.sbspro.2012.11.008...     

Differences between experts’ and students’ conceptual images of the mathematical structure of Taylor series convergence

Taylor series convergence is a complicated mathematical structure which incorporates multiple concepts. Therefore, it can be very difficult for students to initially comprehend. How might students make sense of this structure? How might experts make sense of this structure? To answer these questions, an exploratory study was conducted using experts and students who responded to a variety of interview tasks related to Taylor series convergence. An initial analysis revealed that many patterns of their reasoning were based upon certain elements and actions performed on elements from the underlying mathematical structure of Taylor series. A corresponding framework was created to better identify these elements and how they were being used. Some of the elements included using particular values for the independent variable, working with terms, partial sums, sequences, and remainders. Experts and students both focused on particular elements of Taylor series, but the experts demonstrated the efficiency and effectiveness of their reasoning by evoking more conceptual images and more readily moving between images of different elements to best respond to the current task. Instead of moving between images as dictated by tasks, students might fixate on “surface level” features of Taylor series and fail to focus on more relevant features that would allow them to more appropriately engage the task. Furthermore, how experts used their images, supports the idea that they were guided by formal theory, whereas students were still attempting to construct their understanding.     

Do we need more scientists? A long‐term view of patterns of participation in UK undergraduate science programmes

This paper reports the findings from an ESRC funded study which examined patterns of participation in higher education science programmes. Using data on applications and acceptances to university, the paper describes trends in the numbers of candidates who choose to study science and science‐related degree programmes in the UK over the last two decades. Two main findings emerge. The first shows that overall the sciences have retained their share of the undergraduate population during a period in which the sector has expanded rapidly. We find no evidence of a ‘swing’ from science. Indeed it is not the case that undergraduates are not studying science, rather, it is the type of science courses they are studying which has changed. The second finding suggests that large and small‐scale initiatives to increase recruitment to the sciences have had little lasting impact on the higher education participation data.     

From the Horse's Mouth: Why scientists’ views are crucial to nature of science understanding

Written in response to criticism of our work by Fouad Abd-El-Khalick, this position paper reaffirms and reinforces our position about the need to broaden and enrich the scope of nature of science (NOS) oriented curricula by exposing students to the voices of practising scientists. While Abd-El-Khalick's motivation for promoting the so-called consensus view of NOS is rooted in issues of assessment (or ‘benchmarking', as he calls it), we argue that the major reason for teaching about NOS is its contribution to what Shen calls civic and cultural scientific literacy. We are critical of the consensus view for its philosophical naivety, failure to reflect contemporary scientific practice and potential for confusing students, and we re-state our view that it is important to expose students to a diversity of practice among the sub-disciplines of science. We argue that richer NOS understanding and a more authentic view of scientific practice can be achieved through direct and indirect contact with scientists at the cutting edge of research and development, which we characterise as learning about scientists, learning from scientists and learning with scientists.     

Thomas Hardy and his Tess of the d’Urbervilles:Analysis of the images of birds in Tess of the d’ Urbervilles

The article gives a brief introduction of Thomas Hardy and His Tess of the d’Urberville, the image of birds in Tess of the d’Urberville and its importance for illustrating the theme has also been analyzed.