基于概念的教育资源元素材聚类方法研究

针对教育资源元素材种类多、独立性强等特点，研究了概念聚类方法解决领域知识的分类和归并问题，并实现了概念的动态聚类算法和归并算法，分析了该算法的效率和聚类准确性．     

工程类专业课讨论式教学方法探讨

根据工程类专业课的特点和学生的学习心理,本文提出把工程类专业课教学作为一个综合课堂讲授和其他实践性教学环节的系统过程来考虑,尝试并总结出提高工程类专业课教学效果的一些有效的教学方法。这些方法一方面强调教师的课堂讲授要与学生的课堂讨论紧密结合,并通过实践提出了安排教学讨论的“课尾十分钟法”。另一方面注意实践性教学环节对课堂讲授的补充与强化作用。这些措施在实际应用中增强了学生的学习主动性、提高了教学的总效果。     

Exploring college students’ mental representations of inferential statistics

We report a case study that explored how three college students mentally represented the knowledge they held of inferential statistics, how this knowledge was connected, and how it was applied in two problem solving situations. A concept map task and two problem categorization tasks were used along with interviews to gather the data. We found that the students’ representations were based on incomplete statistical understanding. Although they grasped various concepts and inferential tests, the students rarely linked key concepts together or to tests nor did they accurately apply that knowledge to categorize word problems. We suggest that one reason the students had difficulty applying their knowledge is that it was not sufficiently integrated. In addition, we found that varying the instruction for the categorization task elicited different mental representations. One instruction was particularly effective in revealing students’ partial understandings. This finding suggests that modifying the task format as we have done could be a useful diagnostic tool.     

PANSYSTEMS PHILOSOPHY,PANSYSTEMS MATHEMATICS(PPPM)AND APPLICATIONS TO APTMS:AFFAIROLOGY,PHYSICS,TECHNOLOGY,MEDICIEN AND STRATEGICS(Ⅱ)

A new type of philosophy and mathematics from the pansystems view is introduced here,including the7 philosophy theories(7PT)and related mathematizing researches.Many second/third philosophies are developed within pansystems framework and related applications to APTMS.     

An introduction to timetabling

A huge variety of timetabling models have been described in the OR literature; they range from the weekly timetable of a school to the scheduling of courses or exams in a university. Graphs and networks have proven to be useful in the formulation and solution of such problems. Various models will be described with an emphasis on graph theoretical models.     

Time allocated to mathematics in post-primary schools in Ireland: are we in double trouble?

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide calling for the inclusion of double class periods on the mathematics timetable. Research from the United States suggests that the introduction of double or block periods allow for the objectives of revised curricula to be realized. The aim of this study, which is set in the school context, is first to ascertain if schools in Ireland are scheduling double periods for mathematics at both lower post-primary level (Junior Cycle) and upper post-primary level (Senior Cycle). It also seeks to determine if there is a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods and to get insights from teachers in relation to their opinions on what can be achieved through the introduction of such classes. Questionnaires were sent to 400 post-primary schools (approximately 1600 teachers) which were selected using stratified sampling techniques. It was found that 8.7% of mathematics teachers reported the provision of double periods at Junior Cycle while 55% reported that double periods were included on their timetable at Senior Cycle. The study also identified a link between teachers’ levels of satisfaction with the time allocated to mathematics and the provision of double periods. Finally, teachers felt that double periods allowed for new teaching methodologies, which were promoted by the revised curricula, to be implemented and teaching for understanding was also more feasible. In essence, it was found that double periods have an influence on the mathematical experience of post-primary students as well as the teaching approaches employed.     

Examining the design features of a communication-rich,problem-centred mathematics professional development

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.     

A typological analysis: understanding pre-service teacher beliefs and how they are transformed

This article describes the beliefs and their transformations of members of a cohort of early-childhood, elementary and middle-level pre-service teachers (PSTs) as they professionally develop. A typological analysis of both quantitative and qualitative data collected between August 2011 and May 2013 was utilized to categorize how 40 PSTs’ beliefs transformed throughout their formal teacher preparation. Five typologies were identified, showing variation in how PST beliefs transform or remain static.

Among the findings, strong support related to the development of innovative beliefs during coursework coupled with at least one transformative experience where innovation was observed ‘working’ in the field were sufficient for the transformation to innovative beliefs, despite potential constraints by supervisors, cooperating teachers and/or mandated curricula (Typology 3). Another finding revealed disguised growth toward innovation among those in Typology 5, who reported being innovative and having productive beliefs but described extremely traditional practices. Implications call for improved connections between mathematics methods professors and field supervisors, particularly during clinical internships when PSTs are no longer enrolled in methods courses, to enhance PSTs’ productive struggle in their development of innovative beliefs (T3) and to increase opportunities for disconnects between innovative beliefs and traditional practices to be made explicit and negotiated (T5).     

Design thinking in integrated STEAM learning: Surveying the landscape and exploring exemplars in elementary grades

Complementing the aims of problem‐based inquiry, a pedagogical approach called design thinking (DT) has students grapple with issues that require a creative redefinition and reimagining of solutions akin to professional skills of designers, who consider conflicting priorities and complex negotiations to arrive at a solution to an ill‐defined problem. This article aims to synthesize the limited existing literature on the use of DT in the K–12 classroom, share two exemplars of DT in action in Grades 3–5 so that science, technology, engineering, arts, and mathematics (STEAM) educators, teacher educators, researchers, and other stakeholders can visualize how it can take shape in the elementary classroom, followed by concluding remarks on DT. The DT framework provides an exciting avenue for teaching more than simply the content areas of STEAM, it provides a vehicle through which a true transdisciplinary learning experience can occur—where students are passionately invested in solving problems as they strive to make the world a better place.     

Preservice mathematics teachers' conceptions and enactments of modeling standards

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics (CCSSM) included Model with Mathematics as one of the Standards for Mathematical Practices (SMP) and a modeling strand in the high school standards. This common aspect of standards across most states in the United States intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers (M‐PSTs) who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their attendance in the same course sections during a teacher preparation program. This result led us to investigate the ways the M‐PSTs understood modeling standards, which could provide insights into better preparing teachers to teach mathematical modeling. We present the contrasting ways in which M‐PSTs presented modeling related to their conceptions of mathematical modeling, choices of problems, and enactments over an academic year, connecting their practices to extant research. We consider this teaching and research experience as an opportunity to make significant changes in our instruction that may result in our students enhanced implementation of mathematical modeling.