Intentional Integration of Mathematics Content Instruction with Constructivist Pedagogy in Elementary Mathematics Education

The purpose of the research was to improve the effectiveness of instruction in constructivist pedagogy in a college elementary mathematics education course through intentional integration of instruction in mathematics content. Instructors of this course previously used examples involving mathematics content on an ad hoc basis in an attempt to illuminate desirable constructivist pedagogy but discovered that they were ineffective because students experienced difficulty with the mathematics content itself. An instrument was created to assess students' mathematics content knowledge required to understand these examples. Based on the outcome of the assessment, intentional instruction of mathematics content using anchoring examples was integrated with pedagogical instruction. Results showed significant improvement in mathematics content knowledge and confidence in that knowledge with a better understanding of constructivist pedagogy.     

模糊数学精品课程建设与实践

模糊数学课程是我校各专业研究生的一门重要的公共基础课,实施模糊数学核心课程建设,对于深化教学改革、提高教学质量以及培养研究生的实践能力和创新能力起着极其重要的作用,从模糊数学课程性质、目的和任务人手,较详细地阐述了模糊数学课程的教学内容、体系,教学模式和手段等系列改革以及模糊数学课程建设中取得的显著成效。     

Change in Preservice Teachers' Beliefs: An Evaluation of a Mathematics Methods Course

This study investigated and evaluated the potential impact of an elementary mathematics methods course in promoting teacher beliefs and attitudes that are consistent with the underlying philosophy of current reform efforts in mathematics education. Using the Mathematics Beliefs Instrument (MBI; Hart, 2002 ), data from 89 preservice teachers were used to evaluate the course. Findings from the study suggest a positive relationship between participating in the mathematics methods course and change in teacher beliefs and attitudes. This study also provided additional validation of the MBI.     

‘I Finally Get It!’: developing mathematical understanding during teacher education

A deep conceptual understanding of elementary mathematics as appropriate for teaching is increasingly thought to be an important aspect of elementary teacher capacity. This study explores preservice teachers’ initial mathematical understandings and how these understandings developed during a mathematics methods course for upper elementary teachers. The methods course was supplemented by a newly designed optional course in mathematics for teaching. Teacher candidates choosing the optional course were initially weaker in terms of mathematical understanding than their peers, yet showed stronger mathematical development after engaging in the extra hours the optional course provided.     

Pre- and in-service teachers’ perceived value of an experimental real analysis course for teachers

Prospective secondary mathematics teachers are usually required to complete several university advanced mathematics courses before being certified to teach secondary mathematics. However, teachers usually do not find these courses to be valuable for their teaching. We designed an experimental real analysis course with the goal of making real analysis content useful and relevant to teaching. Our approach was to ground the real analysis content in pedagogical situations that problematized a secondary mathematics topic, where the nuances of teaching secondary mathematics could be informed by the real analysis that was covered. The experimental course was implemented in a graduate teacher education programme with 32 pre- and in-service teachers (PISTs). After the course, we conducted focus group interviews with 20 of these PISTs to get feedback on how the course was valuable to their teaching practice. Many PISTs found the course to be valuable for teaching secondary mathematics, as well as for their understanding of secondary mathematics and real analysis.     

The Application of a Computer Algebra System as a Tool in College Algebra

This study compared a traditional lecture-based college algebra course to an experimental algebra course. The experimental course stressed active student involvement and the use of the computer as a tool to explore mathematics. One hundred thirty-seven subjects were divided into an experimental group and a control group. Subjects in the experimental group scored significantly higher than the control group on a final measure of inductive reasoning, visualization, and problem solving while maintaining an equivalent level of manipulation and computation skills. However, the attitude of subjects in the experimental group towards the use of the computer in learning mathematics declined significantly.     

Impacts of inquiry pedagogy on undergraduate students conceptions of the function of proof

Mathematicians and mathematics educators agree that proof is an important tool in mathematics, yet too often undergraduate students see proof as a superficial part of the discipline. While proof is often used by mathematicians to justify that a theorem is true, many times proof is used for another purpose entirely such as to explain why a particular statement is true or to show mathematics students a particular proof technique. This paper reports on a study that used a form of inquiry-based learning (IBL) in an introduction to proof course and measured the beliefs of students in this course about the different functions of proof in mathematics as compared to students in a non-IBL course. It was found that undergraduate students in an introduction to proof course had a more robust understanding of the functions of proof than previous studies would suggest. Additionally, students in the course taught using inquiry pedagogy were more likely to appreciate the communication, intellectual challenge, and providing autonomy functions of proof. It is hypothesized that these results are a response to the pedagogy of the course and the types of student activity that were emphasized.     

A metacognitive intervention in mathematics at university level

The paper reports the main results of an instructional study. The study was aimed at improving the performance in mathematics of a group of university students of biology who repeatedly failed the final examination of a compulsory course in mathematics. The main difficulties of these students seemed to be metacognitive and affective in nature. The training therefore worked on metacognitive and affective features: knowledge about cognition, monitoring, beliefs, emotions and attitudes. The intervention was successful: at the end of the course all students passed the examination that they had failed so often. The results also suggest that it may be possible (and necessary) to ‘teach learning to learn’ mathematics.     

高等农林院校大学数学课程的改革与实践

介绍了目前我国高等农林院校大学数学课程的开设情况,分析了大学数学系列课程的教学改革成果、现状以及存在的一些问题,同时对在高等农林院校中如何进行大学数学课程改革提出了若干建议和措施.     

Seeking mathematics success for college students: a randomized field trial of an adapted approach

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students’ ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.     

Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes Toward Mathematics

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these expectations exist for both prospective teachers in a traditional undergraduate degree program and prospective teachers in an alternative licensure graduate degree program. We also found that these expectations do change with the completion of a mathematics methods course and classroom experiences.     

Development and Implementation of an Integrated Mathematics/Science Preservice Elementary Methods Course

If integration of mathematics and science is to occur, teacher preparation programs at colleges and universities must provide leadership in developing and modeling methods of teaching integrated content. This paper describes the development and implementation of an integrated mathematics/science preservice elementary methods course at the University of Connecticut. In planning the course several questions were addressed: (a) What does integration of mathematics and science mean? (b) What content should be taught in an integrated mathematics/science (IM/S) elementary methods course? and (c) How should an IM/S elementary methods course be taught? An important element of the course involved enlisting an exemplary elementary teacher who was released from her classroom one day per week to co-teach the methods class. Establishing a definition of integration proved to be one of the most challenging aspects of course development. The authors determined that most difficulties in integration of disciplines result from attempts to “force” the integration. As the team struggled with the philosophical, theoretical and logistical problems in the development of the course, it became apparent why integration has not been more widely implemented. It is believed this model can be adapted to allow for integration of all content areas. Plans are currently underway to incorporate social studies into the methods class for Fall of 1993.     

《数学物理方法》课程教改的探索与实践

随着我国科学技术的快速发展,对于理工科学生在数学基础和数学素养方面的要求越来越高.数学物理方法课程综合应用了各个数学分支的内容,是提升理工科本科学生应用数学能力的重要基础课程.本文以课程作用、课程安排以及教学内容的梳理改进为主线,介绍数学物理方法课程教改的思考与实践.     

专业大类教学模式下公共数学课程体系的改革与设计

高等数学课程对实现高校的人才培养目标起着十分重要的作用.在当前按照专业大类招生并组织教学的情况下,高等数学的课程教学遇到了前所未有的问题与挑战.总结近年来我校高等数学课程体系和教学内容改革的实践经验,重新设计了高等数学课程的体系(模块),提出了进行了相应教学内容改革的意见,形成了整体课改方案,并分析了本方案所具有的特色.     

A Special Topics Course in Perturbation Methods

A special topics course dealing with perturbation methods in applied mathematics which was recently taught at Stevens Institute of Technology is described. Since the course enrolment was comprised of undergraduate and graduate mathematics students as well as graduate students in engineering, an unusual course philosophy had to be developed and implemented. The approach taken to achieve this in both teaching techniques and selection of subject matter is discussed in detail. Finally, conclusions are drawn from the students’ and the instructor's experiences with the course which hopefully will be of value to those considering offering special topics courses in the future.     

高等数学教学中启发式教学意义的模糊分析

启发式教学是一种教学思想,应该贯穿于整个教学过程.本文通过实际统计数据用模糊数学理论分析高等数学教学中使用启发式教学的积极意义.     

Prospective Teachers' Perspectives on Mathematics Teaching and Learning: Lens for Interpreting Experiences in a Standards‐Based Mathematics Course

In a mathematics course for prospective elementary teachers, we strove to model standards‐based pedagogy. However, an end‐of‐class reflection revealed the prospective teachers were considering incorporating standards‐based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon, Tzur, Heinz, Kinzel, and Smith to examine the prospective teachers' perspectives on mathematics teaching and learning and to address two research questions. What perspectives on the learning and teaching of mathematics do prospective elementary teachers hold? How do their perspectives impact their perception of standards‐based instruction in a mathematics course and their future teaching plans? Qualitative analyses of reflections from 106 prospective teachers revealed that they viewed mathematics as a logical domain representative of an objective reality. Their instructional preferences included providing firsthand opportunities for elementary students to perceive mathematics. They did not take into account the impact of a student's conceptions upon what is learned. Thus, the prospective teachers plan to incorporate standards‐based strategies to provide active experiences for their future elementary students, but they fail to base such strategies upon students' current mathematical conceptions. Throughout, the need to address prospective teachers' underlying perspectives of mathematics teaching and learning is stressed.     

An Exploratory Study of College Students' Views of Mathematical Thinking in a Historical Approach Calculus Course

Heuristic training alone is not enough for developing one's mathematical thinking. One missing component is a mathematical point of view. This study reports findings regarding outcomes of a historical approach calculus course to foster Taiwanese college students' views of mathematical thinking. This study consisted of 3 stages. During the initial phase, 44 engineering majors' views on mathematical thinking were tabulated by an open-ended questionnaire, and 9 randomly selected students were invited to participate in follow-up interviews. Students then received an 18-week historical approach calculus course in which mathematical concepts were problematized to challenge their intuition-based empirical beliefs about doing mathematics. Near the end of the semester, all participants answered the identical questionnaire, and we interviewed the same students to pinpoint any shifts in their views on mathematical thinking. We found that participants were more likely to value logical sense, creativity, and imagination in doing mathematics. Further, students were leaning toward a conservative attitude toward certainty of mathematical knowledge. Participants' focus seemingly shifted from mathematics as a product to mathematics as a process.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.