Introduction to the Special Issue: Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses

Abstract

Mathematics for liberal arts courses are a staple of most mathematics departments and are often populated with students who have disengaged from mathematics. Inquiry-based learning is a student-centered pedagogical tool for re-engaging students in mathematics. In this paper, we introduce a Special Issue of PRIMUS on “Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses.”     

The Development of Metacognition in Primary School Learning Environments

Constructivist ideas have influenced recent major innovations in Dutch secondary education and new curricula for reading and math in primary education, for example, pay much more attention to metacognition than before. In our study, we compared the growth of student metacognition in varying learning environments, direct instruction, and cognitive apprenticeship in primary school. The study also included a control group of teachers. In order to measure metacognition we developed a questionnaire, with separate parts for metacognitive skills and metacognitive knowledge. In the item selection procedure we made use of item response modeling. It was found that in the direct instruction and the cognitive apprenticeship group the pupils had higher scores on metacognitive skills and metacognitive knowledge compared to the control group pupils. No clear differences were found between direct instruction and cognitive apprenticeship. Interactions of learning environment and student intelligence were non-significant for both output measures.     

数学元认知差异的相关研究及启示

本文通过回顾关于数学元认知的相关研究,对数学元认知的理论和学生数学元认知差异的主要表现进行了分析与梳理.相关研究发现,学生的数学元认知水平在数学学优生与学困生、性别、年龄等方面,差异较为明显.文章最后指出了相关研究对数学教学的启示.     

基于结构不良问题解决的数学学习环境设计

当前数学课堂教学主要关注解决结构良好的问题,较少涉及真实情景中结构不良的问题,从而常造成学校数学教育与社会生活的脱节。本研究在分析已有关于结构不良问题解决研究的基础上,借鉴乔纳森建构主义学习环境设计理论,从学习环境设计视角出发,构建基于结构不良问题解决的数学学习环境,以期对培养学生使用数学知识解决真实情景中结构不良问题能力有所启发。     

Representation and Process in Learning Environments for Mathematics: A Commentary on Three Systems

Three computer‐based systems for teaching arithmetic and algebra are discussed. The systems embody several pedagogical tactics: To provide students with augmented repre‐sentations that reveal the structure of problem solutions; to make mathematical symbols meaningful by giving students concrete referents for those symbols; to provide students with enriched feedback about the consequences of their mathematical operations; and to adapt instruction to the cognitive processes of the students. Weaknesses in the three systems are discussed and two general problems, called complexity trade‐off and scaffold removal, are put forward as possible explanations for why the systems are not more effective. The alternative view that mathematics is difficult because it requires abstract thinking is outlined and some of its implications discussed briefly.     

Shaping and Being Shaped by Environments for Learning Science

Environments of learning often remain unnoticed and unacknowledged. This study follows a student and myself as we became aware of our local environment at MIT and welcomed that environment as a vibrant contributor to our learning. We met this environment in part through its educational heritage in two centennial anniversaries: John Dewey’s 1916 work Democracy and Education and MIT’s 1916 move from Boston to the Cambridge campus designed by architect William Welles Bosworth. Dewey argued that for learning to arise through constructive, active engagement among students, the environment must be structured to accommodate investigation. In designing an environment conducive to practical and inventive studies, Bosworth created organic classical forms harboring the illusion of symmetry, while actually departing from it. Students and I are made open to the effects of this environment through the research pedagogy of “critical exploration in the classroom,” which informs my practice of listening and responding, and teaching while researching; it lays fertile grounds for the involvement of one student and myself with our environment. Through viewing the moon and sky by eye, telescope, airplane, and astrolabe, the student developed as an observer. She became connected with the larger universe, and critical of formalisms that encage mind and space. Applying Euclid’s geometry to the architecture outdoors, the student noticed and questioned classical features in Bosworth’s buildings. By encountering these buildings while accompanied by their current restorer, we came to see means by which their structure and design promote human interaction and environmental sustainability as intrinsic to education. The student responded creatively to Bosworth’s buildings through photography, learning view-camera, and darkroom techniques. In Dewey’s view, democracy entails rejecting dualisms endemic in academic culture since the Greek classical era. Dewey regarded experimental science, where learners are investigators, as a means of engaging the world without invoking dualism. Although Dewey’s theory is seldom practiced, our investigations cohered with Deweyan practice. We experienced the environment with its centennial philosophy and architecture as educational agency supportive of investigation that continues to evolve across personal and collective history.     

高校文科学生数学学习的元认知水平调查

研究以调查问卷为主,辅之以访谈、观察、比较、查阅资料等方法,对高校文科学生数学学习过程中的元认知水平进行调查研究,在分析所得结论的基础上提出相应的教学建议。     

Exploration and Authority in Science Learning Environments: an International Study

Summaries

English

Scales derived from student responses were used to describe the science learning environments of 14‐year‐old students in 14 different countries. It was found that the best science achievement occured in countries which combined exploratory and authoritarian teaching styles. Within countries, exploratory teaching styles were again associated with high science‐achievement, although the relationship was less strong. These results suggest that some science teachers might improve their pupils’ performance if they adopted more exploratory teaching styles. But no firm conclusions can be reached until the results have been replicated in an experimental study.     

Science Learning in Special Education: The Case for Constructed Versus Instructed Learning

Throughout the history of education, debate has existed between the relative merits of instructed versus constructed knowledge. In this article, we review our program of research in science education for students with disabilities in order to reveal some insights into this debate. We review research in science curriculum, mnemonic strategies, text-processing strategies, hands-on approaches, coached elaborations, “discovery” learning, correlates of effective inclusive science classrooms, and class-wide peer tutoring with differentiated curriculum enhancements. Overall, both instructed and constructed knowledge are important and can be facilitated with appropriate instructional strategies. Implications for practice and future research are provided.     

Introduction to the Special Issue: Multimodal Meaning-Making in Science

Research in Science Education -