高职学院教师工作情况评价的数学模型

如何科学、合理地评价教师的工作,以利于充分调动广大教师的积极性,一直是学院教学管理部门研究的课题,也是广大教师密切关注的问题.本文将构建评价教师工作情况的指标体系并运用层次分析法建立了评价教师工作的数学模型,提出了一种定量的评价方案,供大家参考。     

Mathematical development: the role of broad cognitive processes

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that calculation complexity was predicted by long-term retrieval and working memory; calculation fluency was predicted by perceptual processing speed, phonetic coding, and visual processing; problem solving was predicted by fluid reasoning, crystallised knowledge, working memory, and perceptual processing speed. Younger students’ problem solving skills were more strongly associated with fluid reasoning skills, relative to older students. Conversely, older students’ problem solving skills were more strongly associated with crystallised knowledge skills, relative to younger students. Findings are consistent with the theoretical suggestion that broad cognitive processes play specific roles in the development of mathematical skills among children and adolescents. Implications for educational psychologists are discussed.     

Leading Undergraduate Research Projects in Mathematical Modeling

Abstract

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived from calculus, but can be suitably modified to solve more complex problems; and finally provide pointers on how to train students through the UR process that can help to impact student’s future academic and non-academic careers.     

人鬼之恋--《星愿》与《人鬼情未了》比较刍议

悲剧与文化、人物与象征、叙事与造型及爱的诠释四点对两部中西方同是描写人鬼之恋的影片,进行了深入的探示,以使观众对这两部电影有更深的了解.     

The role of schools in explaining individuals’ subject choices at age 14

Abstract

The subjects that young people study from age 14 onwards may have important consequences for their future academic and labour market outcomes. These decisions are shaped by the schools in which they find themselves. Schools also face constraints of their own. This paper explores the extent to which individuals’ decisions are affected by the school they attend and to what extent this is affected by the composition of schools in terms of academic attainment, gender, and socioeconomic background. We use multi-level variance decomposition models applied to administrative data on the subjects that young people in mainstream state-funded schools in England study between ages 14 and 16. Our results highlight the important role that constraints on schools play in subject choice decisions. We also note the particular role of attending a non-selective school within a selective schooling district.     

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。     

Student perceptions of predictability of examination requirements and relationship with outcomes in high-stakes tests in Ireland

Entirely predictable examinations are ones for which the questions are known in advance. Some assessments are designed this way, but in public examinations, predictability is subtler. Students familiarise themselves with the requirements broadly: likely topics that will come up, question formats and how to maximise their marks. If students can predict what they have to do, they can memorise performances, such as essays, and restrict their learning to fit only with examination requirements. The danger is that this focus could undermine curriculum aims. Further, examinations that are overly predictable might produce results that do not generalise to other performances or have predictive validity. This paper presents part of a broader project investigating whether the Higher Level Irish Leaving Certificate (LC) examinations were too predictable. Here, the development of a rating scale for students’ views of examination predictability is described. Data were collected from 1002 Irish LC students taking higher level examinations in biology (n?=?536), English (n?=?749) and geography (n?=?387). Students’ views on predictability of the examination could be grouped consistently across subject areas into three factors: valuable learning, predictability and narrowing of the curriculum. Belief that narrowing of the curriculum was a good examination preparation tactic had a negative relationship with examination scores and perceived learning value of examinations was positively associated with students’ scores in biology and English. These findings indicate that the scoring system rewards students who believe they must study the discipline broadly.     

A science need: Designing tasks to engage students in modeling complex data

In this information age, the capacity to perceive structure in data, model that structure, and make decisions regarding its implications is rapidly becoming the most important of the quantitative literacy skills. We build on Kaput’s belief in a Science of Need to motivate and direct the development of tasks and tools for engaging students in reasoning about data. A Science of Need embodies the utility value of mathematics, and engages students in seeing the importance of mathematics in both their current and their future lives. An extended example of the design of tasks that require students to generate, test, and revise models of complex data is used to illustrate the ways in which attention to the contributions of students can aid in the development of both useful and theoretically coherent models of mathematical understanding by researchers. Tools such as Fathom are shown as democratizing agents in making data modeling more expressive and intimate, aiding in the development of deeper and more applicable mathematical understanding.

The impact of learning difficulties and socioemotional and behavioural problems on transition to postsecondary education or work life in Finland: a five-year follow-up study

Learning difficulties have been found to dilute the possibilities that young adults have in their educational careers. However, during the last few decades, education has become increasingly important for employment and overall life satisfaction. In the present study, we were interested in the effects of mathematical and reading difficulties and socioemotional and behavioural problems (measured at age 16) on three educational situations at age 21: delayed graduation from upper secondary education, short educational trajectory and not being engaged in education, employment or training (NEET). The participants (N = 597; 304 females, 293 males) were one age cohort of ninth graders in general education classes, who were followed for five years after completion of compulsory education. This time frame included two different transition phases: first, from comprehensive education to upper secondary education, and second, from upper secondary education to further studies or to working life. Structural equation modelling was used as analysis method. The findings show that mathematical and reading difficulties as well as socioemotional and behavioural problems had significant long-term effects on the participants’ educational careers. New in part was that these learning difficulties seemed to have somewhat divergent emphases on the three investigated life situations: (1) mathematical difficulties, more strongly than reading difficulties, caused the students to attain lower levels of education, (2) mathematical difficulties and socioemotional problems predicted a student ending up in the NEET group and (3) reading difficulties and behavioural problems predicted delayed graduation from upper secondary education.     

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.