Moving Beyond Solving for “x”: Teaching Abstract Algebra in a Liberal Arts Mathematics Course

Abstract

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context, identifying patterns, and venturing conjectures. A sequence of open-ended instructional tasks that aim to capitalize on students’ prior experiences with equation solving is provided along with notes and sample student responses for prospective instructors.     

Teaching Line Balancing through Active and Blended Learning*

The design of balanced assembly lines, especially when considering workforce, material, and cycle time factors, is an important managerial decision‐making activity in manufacturing firms. Numerous active learning activities are available to assist instructors in teaching assembly line balancing to students. While effective in improving student engagement, they require considerable planning and expense on the part of instructors, and they may be difficult to implement in inflexible teaching spaces and lecture‐oriented curricula. We present a new approach to teaching line balancing using online videos depicting an assembly process. Students design an assembly line by determining themselves how to separate and time tasks, rather than by modifying an existing configuration. To save valuable classroom time, students complete a portion of the activity outside of class. This blended learning approach allows for all students to be engaged in the activity, both in and out of class. Furthermore, a controlled study showed that compared to the traditional lecture format, it better equips students to address less tangible aspects of line balancing, such as ergonomic and workforce factors, material handling considerations, and changing cycle time. With the online content for this activity completely developed and available, other instructors can easily implement this approach within their courses.     

Rolling: A new technique for the practical teaching in computer science university degree

In this paper we describe a new methodology for practical teaching in the Computer Science University Degree. The methodology is based on the Rolling technique. This technique consists in assign, in a rotary process, tasks, activities and responsibilities to students along an established calendar with the aim of developing a software product. Practical teaching is supported by a student-teacher contract that describes the goal, rules, plan with stages and activities, responsibilities and even the assessment method. Students are organized in groups and teams, emulating a company organization. They develop all the activities of the software engineering process in order to obtain a commercial product (the goal). In this process, students take different responsibilities over the software verification and validation, activities and tasks, and over groups and teams leadership. Along the teaching process, comprehensive information about the working team, time invested, deliverables in each stage, and work/students assessment is gathered. The methodology has been tested for 4 years at the University of Córdoba and the results, described in this paper, have shown an improvement in the students learning as well as in the acquisition of attitudes and skills mandatory for their professional development.     

Sharpening a tool for teaching: the zone of proximal development

Vygotsky's Zone of Proximal Development (ZPD) provides an important understanding of learning, but its implications for teachers are often unclear or limited and could be further explored. We use conceptual analysis to sharpen the ZPD as a teaching tool, illustrated with examples from teaching critical thinking in zoology. Our conclusions are the following: teachers should assign tasks that students cannot do on their own, but which they can do with assistance; they should provide just enough assistance so that students learn to complete the tasks independently and, finally, teachers can increase learning gains by providing learning environments that enable students to do harder tasks than would otherwise be possible and by assigning the hardest tasks students can do with assistance. This analysis provides a sharp and useful tool for supporting learning across all curriculum areas.     

高职高专英语口语交际法教学实践

探讨交际能力形成的因素和口语采用交际法教学的实践策略,主张通过构建交际环境,让学生自然感知、体验并使用英语进行情感交流,培养学生的英语交际能力,提出营造全英语环境是进行口语交际法教学的关键。     

Preliminary Evolutionary Explanations: A Basic Framework for Conceptual Change and Explanatory Coherence in Evolution

This study aimed to explore secondary students’ explanations of evolutionary processes, and to determine how consistent these were, after a specific evolution instruction. In a previous study it was found that before instruction students provided different explanations for similar processes to tasks with different content. Hence, it seemed that the structure and the content of the task may have had an effect on students’ explanations. The tasks given to students demanded evolutionary explanations, in particular explanations for the origin of homologies and adaptations. Based on the conclusions from the previous study, we developed a teaching sequence in order to overcome students’ preconceptions, as well as to achieve conceptual change and explanatory coherence. Students were taught about fundamental biological concepts and the several levels of biological organization, as well as about the mechanisms of heredity and of the origin of genetic variation. Then, all these concepts were used to teach about evolution, by relating micro-concepts (e.g. genotypes) to macro-concepts (e.g. phenotypes). Moreover, during instruction students were brought to a conceptual conflict situation, where their intuitive explanations were challenged as emphasis was put on two concepts entirely opposed to their preconceptions: chance and unpredictability. From the explanations that students provided in the post-test it is concluded that conceptual change and explanatory coherence in evolution can be achieved to a certain degree by lower secondary school students through the suggested teaching sequence and the explanatory framework, which may form a basis for teaching further about evolution.     

谈高职英语专业“综合英语”课程的教与学

"综合英语"是高职商务英语专业的专业基础课,在整个课程设置及人才培养方案中处于核心地位。高职英语专业的教学现状与高职学生英语基础较差的客观事实,决定了高职"综英"课程的教与学中教师和学生的各自定位和任务,以及"综英"课程教学方法的改革应该秉承的原则。     

任务型教学六因素及在大学英语教学中的体现

任务型教学法是指以完成交际任务为教学目的的外语教学方法,其目标是提供机会让学生在各种各样的任务活动中接触真实语言,提高他们语言综合应用能力。本文阐述了任务型教学法的基本理念,具体分析了任务型教学法六因素及其在大学英语教学实例中的体现,并指出任务型教学法可激发学生的积极性和主动性,从而极大地提高大学英语的教学效率。     

探索任务型教学法在大学英语口语课堂教改中的应用

任务型教学以培养学生英语语言应用能力为宗旨,强调学生是学习过程的主体,任务真实性和互动合作性使他们不是被动地接受信息,而是主动地根据先前已有的认知结构,有选择地知觉外在信息,通过不断的语言实践,构建自己的新知识和新经验。因而,任务型教学极能体现学生的主体性,是有效实施教学改革,根本改变以往以教师讲授为主,学生极少有机会使用目标语进行交际的教学现状的途径之一。     

A Macro–Micro–Symbolic Teaching to Promote Relational Understanding of Chemical Reactions

The purpose of this research is threefold: (1) to identify the difficulties that Grade 10 students in a Lebanese school have that hinder their conceptual understanding at the micro–macro–symbolic interface in chemistry, (2) to investigate the effect of a macro–micro–symbolic teaching approach on students’ relational understanding of chemical reactions, and (3) to characterize students’ conceptual profiles regarding their understanding of chemical reactions in terms of macro, micro, symbolic levels and the relations among them, at the end of the teaching sequence. Forty six 10th graders from two sections participated in the study. A student-centered approach was followed in both sections based on constructivist pedagogy. Hence the teacher played the role of a facilitator who guided students in a meaning making inductive learning process, through questioning, monitoring, validating, and clarifying ideas. Instruction in the experimental group was characterized by macro–micro–symbolic teaching that focuses on the interplay between the levels, integrates various representations, and engages students in an epistemic discourse about the nature of knowing in chemistry. Data sources for the study included a pre-test and two post-intervention tasks: a post-test and a concept map task, in addition to interviews with selected students from both sections. Findings indicated that macro–micro–symbolic teaching enhanced students’ conceptual understanding and relational learning of chemical reactions. Besides, four assertions related to students’ conceptual and epistemological thinking in response to the different teaching approaches are presented. Implications for instruction and for teacher education programs, as well as recommendations for further research, are discussed in light of these findings.     

Facilitating preservice teachers’ development of mathematics knowledge for teaching arithmetic operations

Mathematical tasks, centered on arithmetic word problems, are discussed as the basis of an approach to facilitate preservice elementary teachers’ development of mathematical knowledge for teaching arithmetic operations. The approach consists of three groups of tasks that allow students to reflect on their initial knowledge, explore arithmetic word problem situations from multiple perspectives, and apply their resulting knowledge, respectively. Findings from the investigation of the approach indicate that the tasks can provide an effective and meaningful basis to help preservice teachers to develop deeper understandings of the arithmetic operations and their relationships and pedagogical-mathematical knowledge for teaching the arithmetic operations conceptually.     

Some reflections on learning from early school experience

This paper is a report of a study on early school experience as part of a Teacher Education programme in Turkey. The programme requires second-year students to act as students only, observing their mentors in classrooms rather than practising teaching so that they can gain a wider view of the teaching profession. The study analyses the experiences of these students, therefore, particularly focusing on the extent to which this scheme is conducive to making students learn from their experience. The findings from the qualitative data suggest that careful attention must be paid to major factors shaping this process, such as the school atmosphere as a whole, the nature of tasks for observation, the quality of interaction between student-mentor, and, more importantly, the opportunities for students to develop an inquiry-based approach to teaching.     

Assessment and teaching of science skills: whole of programme perceptions of graduating students

This study reports on science student perceptions of their skills (scientific knowledge, oral communication, scientific writing, quantitative skills, teamwork and ethical thinking) as they approach graduation. The focus is on which teaching activities and assessment tasks over the whole programme of study students thought utilised each of the six nominated skills. In this quantitative study involving two Australian research-intensive universities, the teaching activities identified by students as developing the broadest number of skills were laboratory classes and tutorials. Lectures were only effective for developing scientific knowledge and, to a limited extent, ethical thinking. Assessment tasks that students perceived to utilise the broadest range of skills were assignments and oral presentations. The findings of this study document the students’ perspective about their gains in skill sets, and the teaching activities and assessment tasks that require them to use and thus develop these skills. The findings provide an opportunity to evaluate the constructive alignment of skills development, teaching activities and assessment tasks from a student’s perspective. Further research is required to actually measure the skills that students gain over their whole programme of study.     

试析使学生被动学习的教学原因

学生被动学习固然有诸多原因,但与之关系最直接的则是教师的教学。从教学的角度看,致使学生被动学习的原因主要有:过于强调知识学习过程中的认知因素,认识性任务成为课堂生活的中心目的;与之相应,学生所学的知识内容被赋予过高的确定性,学生的真实思想被标准化认识路线所遮蔽,师生共同沉沦于程式化的教学过程而不自知。     

任务型教学法在英语阅读教学中的应用研究

任务型语言教学是指以意义为中心,以完成交际任务为教学目标的外语教学方法。文章首先对任务进行界定,其次探讨了任务型教学模式的设计和结构,最后分析了笔者在泛读教学中对任务型教学模式的实验研究。研究结果表明任务型教学法增加了学生学习英语的兴趣,提高了学生的阅读能力。     

Biology Curricula at Universities in the European Community

In literature, several processes have been suggested to describe conceptual changes being undertaken. However, a few parts of studies analyse in great detail which students' learning processes are involved in physics classes during teaching, and how they are used. Following a socio-constructivist approach using tools coming from discourse analysis, we suggest studying three processes of students' learning: (1) establishing links between ideas, (2) increasing the domain of applicability of ideas, or (3) decreasing the domain of applicability of ideas. Our database consists of video data and written worksheets of two students at the upper-secondary school level (Grade 10 [15-year-old students]) during a one-month teaching sequence about gas. Based on semiotic resources contained in oral and written language, we reconstruct in great detail all the ideas about gas expressed by both students during the entire teaching sequence. Our analysis deals with (1) how learning processes are identified based on the ideas expressed by students, and (2) how the three learning processes are used by the two students during teaching. Our results show that during the teaching sequence: (1) the emergence of the networks of three ideas is supported by networks of two ideas expressed previously by students; (2) both students express more networks of two ideas than networks of three ideas; (3) the process ‘increasing the domain of applicability’ of an idea or a network of ideas is very often involved; and (4) the process ‘decreasing the domain of applicability’ of an idea or network of ideas is rarely used by them.     

任务驱动教学模式的构建及英语教学实践

以建构主义学习理论和认知理论为依据的任务驱动教学模式是指教师把教学内容设计成一个或多个具体的任务,让学生通过完成一个个具体的任务,掌握教学内容,并通过任务设计、任务呈现、任务实施和任务评价等4个环节的教学实现教学目标。教学实践表明,任务驱动教学模式有助于学生综合英语能力的提高。     

Examining the task and knowledge demands needed to teach with representations

Representations are often used in instruction to highlight key mathematical ideas and support student learning. Despite their centrality in scaffolding teaching and learning, most of our understanding about the tasks involved with using representations in instruction and the knowledge requirements imposed on teachers when using these aids is theoretical. In this study, we examine the task and knowledge demands for teaching integer operations with representations by analyzing teaching practice. Teaching integer operations is used as an intensity case, as integer operations are challenging for students, and teachers are often required to employ several representations to teach this topic. Following a practice-based approach while also taking prior literature into consideration, we first generate a list of tasks entailed in teaching with representations and then discuss the knowledge demands imposed on teachers to successfully undertake this work. We highlight these tasks and knowledge demands by analyzing and discussing an integer addition and an integer subtraction episode for each of two teachers, Bonita and Karen. Based on our analysis, we organize the generated knowledge components using the Mathematical Knowledge for Teaching framework. We conclude by drawing implications for teacher educators and curriculum developers.     

任务型语言教学法在英语泛读课中的运用

任务型语言教学法是近年来新兴的课堂教学手段,是一种以任务为核心来计划、组织语言教学的教学方法,旨在强调把语言运用的基本理念转化为具有实践意义的课堂教学模式,在课堂教学活动中让学生用英语完成各种真实生活、学习、工作等活动,从而培养学生运用英语的能力.目前,大多数高校英语泛读教学还是采用传统的方式授课,表现为过多地承担了词汇、语法等语言基础知识的任务,逐字逐句地讲解、翻译等.这种“满堂灌”的方法忽略了学生参与课堂教学的积极性,学生缺乏主动建构知识的动力,严重影响了阅读教学的效果.以英语泛读教学为突破点,依托任务型语言教学的核心理据,结合英语泛读课堂教学实际,对英语任务型泛读教学进行探析.     

视频资料在英语教学中的应用

视频以其丰富的语言信息承载优势,成为英语教学中普遍使用的教学资料和手段。教师如何在课堂上系统、合理、有效地运用视频资料,激发学生的学习兴趣,组织教学活动,成为值得思考的问题。视频资料在英语教学中的成败,从视频资料的选择,设计观影任务和活动以促进有效的语言学习,组织学生进行观看前、观看中、观看后各阶段的教学活动,激发学生语言意识,到将视频资料与英语教学有机结合起来,教师的作用至关重要。