Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

英文手机短信翻译的格式塔意象再造及审美再现

英文手机短信分为文学体和非文学体两大类。依据接受美学理论,手机短信文本的意义是一种动态生产物,具有开放性和召唤结构。收信人在阅读的具体过程中,通过发挥想象力去填补“空白”,从整体上理解接受原文的信息,在大脑中形成一个格式塔意象。译者在翻译过程中,首先应充分理解、接受原文信息,并进行格式塔意象再造,然后,最大限度地再现短信原文的韵律美、形式美、形象美、修辞美、模糊美和幽默美。     

Social working memory: Memory for another rat's spatial choices can increase or decrease choice tendencies

In two experiments using a radial-arm maze, pairs of rats made choices among eight maze locations, each containing a large quantity of one of two food types. The choices made by 1 rat affected the choices made by the other rat. Under most conditions, visits by 1 rat increased the tendency of the other rat to subsequently choose that maze location. However, the effect depended on the quality of the food available in a particular location. When it was possible for the rats to observe each other on the maze arms and a rat had experienced that a location contained the less preferred food type, a previous visit to that location by the foraging partner decreased the tendency to visit that location. These effects are attributed to working memory for the spatial choices of another rat, and they indicate that memory produced by a rat’s own visit to a maze location is integrated with memory for the behavior of another rat to determine spatial choice     

Relationships between student characteristics and self‐, peer and tutor evaluations of oral presentations

There are many influences on how assessors grade themselves and others. Oral presentations are useful for exploring such factors in peer, self‐ and tutor marked assessments, being rapidly completed and assessed, commonly used in HE and very difficult to anonymize. This opportunistic study examined the effects of gender and level of attainment on the triangulation of marks awarded to student presenters. Grades generated by peer assessment were associated more strongly with tutor‐awarded marks than those from self‐assessment. For self‐assessment there was a strong effect of gender (female students undervalued their performance compared with tutor grades). Peer assessment produced higher marks than from tutors, perhaps because of the close‐knit community developed during residential courses. For tutor marks, the greatest variability was at the lower end of the scale, whereas peer assessors were most variable when marking students who self‐evaluated or peer assessed highly. Students awarded a narrower range of marks to peers compared with tutors, but when self‐assessing used a larger range. Presentations by students who admitted to little sleep the night before received lower grades from both peers and tutors, but this was not reflected by self‐assessments, suggesting they were unaware of their poorer performances. Sessions with fewer talks (four rather than seven) reduced the ‘dip’ in marks previously observed in the middle of sessions. Findings are discussed in the context of bias in this mode of assessment.     

PhD students’ work conditions and study environment in university- and industry-based PhD programmes

During the last 10 years, new models of funding and training PhD students have been established in Denmark in order to integrate industry into the entire PhD education. Several programmes have been conducted where it is possible to co-finance PhD scholarships or to become an employee as an industrial PhD in a company. An important question is what impact these new conditions will have on the PhD students’ training, work conditions and study environment. In this article, the new type of programmes will be presented together with data analysis of PhD students’ work conditions and study environment in various programmes mainly based on a research project from 2006. The results of this study show no significant difference between PhD students in a traditional university PhD programme and PhD students in an industrial programme concerning working environment. However, the study shows significant differences in the intercultural dimension, where foreign PhD students are significantly more satisfied with their study environment compared with Danish PhD students. In general the workload is very high and the environment is stressful for all PhD students.     

Contextual effects on predicting risk for reading difficulties in first and second grade

This study utilized early reading assessment data from a randomized trial of 210 urban and rural schools in Texas to examine contextual effects on risk prediction in first and second grade. The primary objective was to examine the roles of (a) individual differences, (b) the grade 1 classroom, and (c) the pairing of first and second grade teachers in determining grade 2 outcomes in word reading and fluency. A second objective was to investigate whether the administration format of the assessment (paper, paper plus desktop, handheld plus desktop) or the level of teacher support (web mentoring, no mentoring) moderated the prediction. These moderator variables proved not to be significant. Subsequent analyses found that a combination of student pretest and mean of pretest classroom was a better predictor than student pretest alone. Additionally, the effect of student scores varied by teacher-pair. On average, intraclass correlations (ICCs) ranged from 6% to 17%. Differences in ICCs at the classroom level were much greater than at the school level, and differences in urban schools were twice that of rural schools.     

The Effects of Faculty Demographic Characteristics and Disciplinary Context on Dimensions of Job Satisfaction

This study applies Kalleberg’s framework to better understand the effects of diverse demographic faculty characteristics on dimensions of job satisfaction. We also extend his work and the work of others to explore the contextual effects of academic disciplines on faculty job satisfaction. We find that women are consistently less satisfied than their male colleagues and that the effect of being female varies by discipline on levels of job satisfaction. We also find race/ethnicity has mixed effects on dimensions of job satisfaction but the effects of race/ethnicity tend to be constant across discipline. Our findings hold important implications for those seeking to understand the experiences of college faculty from diverse demographic backgrounds.     

Problem-based learning in the fifth, sixth, and seventh grades: Assessment of students' perceptions

This study examined the effects of students' characteristics (gender, age, and first-language spoken at home) on their perceptions about problem-based learning (PBL). The study revealed that students from the fifth, sixth and seventh grades perceived PBL in a positive way but there were significant differences between the grades. The resources identified by students as the most useful to their self-directed learning in the PBL unit varied between these grades. However, other parameters such as gender and first-language spoken at home did not have effects on students' perceptions.     

Effortful Control, Surgency, and reading skills in middle childhood

We examined the associations between components of temperament and children’s word and pseudo-word reading skills, in a school-age sample using a within-family internal-replication design. We estimated the statistical prediction of word and pseudo-word reading in separate regression equations that included the main effects of, and two-way interaction between, Surgency and Effortful Control. Children with better Effortful Control scores showed better reading skills. Surgency was unrelated to reading skills, but moderated the effect of Effortful Control. The positive association between reading skills and Effortful Control was present only for children who were low in Surgency. Thus, reading achievement in school-age children is optimized by strong Effortful Control, but these processes may be disrupted for those children who are high in Surgency.     

Why Don't More Students Major in IS?

The large increases in the number of information systems (IS) majors about 10 years ago have been matched by equally large decreases in IS enrollments over the last few years. This article addresses the question of why students choose any major in general, and why students no longer choose to become an IS major in particular. We used a validated survey instrument and the responses from 163 students to examine this question in detail. Not surprisingly, we found that "genuine interest" in the subject was the most salient factor affecting the decision to major in IS. More surprising were what factors did not appear to influence this decision—for example, the promise of good job salaries, job security, the advice of others, or even the image of those who become IS professionals. Students seem aware that information technology employment opportunities exist; if job and salary issues contribute to choosing majors  other than IS , it is due to the perception of an unfavorable work/salary ratio for our field rather than one of job security or availability. That is, the amount of work to get an IS degree (the perception of harder-than-average courses) combined with (for many students) the perception of an undesirable amount of continuous training to keep an IS career just do not seem to balance with salary levels. These findings have important implications for the recruiting efforts of IS faculty seeking to attract more IS majors.