VISUAL IMAGES AS EDUCATIONAL MATERIALS IN MATHEMATICS

In general, students in school learn mathematical concepts by words. Some mathematical concepts, however, are difficult to understand by words. This is especially true of some of the more complicated concepts in mathematics taught in higher education. For students who are studying to become engineers, it is very important to understand mathematics intuitively. Ways must be found for them to learn mathematics that will promote intuitive understanding. We often find that a figure helps us understand mathematical concepts and provides important clues for solving problems. A figure may serve as a concrete expression of an abstract mathematical concept; it is a visual image of the mathematical concept. A visual image is a figure with no words but its title. The aim of this article is to introduce some visual images that are effective in mathematical education.     

Attending to Precision: Mathematical Definitions in Courses for Pre-Service and Practicing Teachers

In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers’ understanding of mathematical definitions. We discuss teachers’ work in developing definitions for students at various levels of mathematics, in generalizing a definition in order to extend the domain to which it may be applied, and in correcting teachers’ misconceptions. The work discussed in this article is consistent with the recommendations of the Conference Board of the Mathematical Sciences for the mathematics education of teachers. In explicit response to contemporary mathematics education research, the author presents constructive assessment prompts which lend themselves to formal study by mathematics education researchers.     

Activity theory: A framework for design and reporting on research projects based on ICT

We propose using activity theory as a basis for designing and reporting on research projects that focus on information and communication technology (ICT) as a means to support educational processes. Adopting the theory, we describe teaching/learning activities mediated by ICT using a three level analysis: epistemological, methodological, social assistance. The analysis has been applied to the design and reporting of projects in both mathematics education at primary school level and training in technical innovation in commercial enterprises.     

Black Mathematics Educators: Researching Toward Racial Emancipation of Black Students

This article focuses on the scholarship of Black mathematics education researchers whose work focuses on Black students in P–20 mathematics spaces. We conducted a metasynthesis literature review of empirical studies by Black mathematics education researchers. The authors utilized critical theories of race and racism to aid in the synthesis of the literature. The Black researchers we reviewed challenged the perspective that failure and limited persistence in Black students who are learning and participating in mathematics is normative. As a critical defense, these scholars offer research that problematizes test score data, race and racism, opportunities to learn mathematics, identity considerations, and other constructs that produce unequal effects in mathematics learning. We found that Black mathematics education researchers strategically disrupt the deficit narrative about Black students. Black scholars select theoretical frameworks that allow them to focus on race and how racism operates in mathematics education. We present this research to incite dialogue among all mathematics educators about improving the mathematical context for Black students.     

The Value of Principled Eclecticism in Education Reform: 1965–2005

At Harvard in the early 1960s, when Ruth Wong received her doctorate in mathematics education, behaviourist B. F. Skinner and cognitivist Jerome Bruner were both teaching psychology, and their ideas continued to influence her work when she returned to educational research and administration in Malaysia and Singapore. Today, whereas exemplary models of math teaching in the United States include an emphasis on communication within a community of learners, Singapore students in more traditional classrooms lead the world in solving complex problems. Through a historical glimpse of math programmes in 1965 and 2005, this article suggests that students in both countries might benefit from more eclectic teaching repertoires.     

Assessing Mathematics Skills Through Portfolios: Validating the Claims From Existing Literature

The purpose of this article is to document the current practice of using portfolios as a tool for assessing students' mathematics learning. Literature related to the assessment of mathematics through portfolios is limited to information generated from a few large-scale and a scattered number of Classroom assessment projects. These reports provide weak support for claims that mathematics portfolio assessments enhance student learning and promote effective communication among teachers, students, and parents. There is a need to establish a strong rationale for selecting a portfolio as a means to assess mathematics. This article offers practitioners and researchers an opportunity to explore the validity of claims and identify factors that confound existing research activities.     

中国近现代数学教育的文化价值观研究

中国近现代数学和数学教育发展的史学研究越来越受到广大学者的重视.从文化传统的视角看待中国近现代数学和数学教育发展,可以得出如下思考:(1)数学史的教育中应突出中西数学的文化差异以及这种差异对数学家成长造成的影响.(2)数学教育应当加强数学哲学方面的研究和教学.(3)数学教育应当加强数学文化方面的研究与教学.     

寓视觉于体育教学之中

根据运动生理学、心理学原理,结合体育技能形成的特点,从5个方面论述了教师在体育技能教学中开发学生视觉的途径,从而能够加快学生获取视觉信息和利用多种感官的能力,更加有效地完成技术动作.     

Student–adult mentoring relationships: experiences from a Scottish school-based programme

Background:?This article reports on a mentoring programme which was implemented in selected Scottish secondary schools with the view to supporting students with school work, transition to further education/higher education, careers, and interpersonal skills. Mentoring students can enhance their academic, social, career and other outcomes. Mentoring relationships, when properly implemented, have been found also to yield positive results for mentors.

Purpose:?This paper is an investigation into a school-based mentoring programme which was implemented in 6 selected Scottish secondary schools. In so doing, we hope to contribute to an evolving framework for designing and implementing successful school-based mentoring.

Sample:?The sample for this study included 10 students aged between 16 and 17 years old in the second year of a broader 2-year business/education project, which aimed to promote student uptake of science, technology, engineering and mathematics (STEM) careers after secondary school. There were 11 mentors, who were drawn mainly from the science, health and the education sectors.

Design and method:?Methodologically, this study was qualitative interpretivist in nature. Data collection involved focus group discussion and individual semi-structured interviews.

Results:?The findings show mentee and mentor preparation, clarity of expectations, mentee–mentor matching, mentee motivation, appropriateness of meeting spaces and power relations, modes of communication including the use of social media, and the role of schools as essential conditions which influenced the quality of mentoring relationships.

Conclusion:?The findings suggest that mentoring programmes involving students in school and ‘external’ adult mentors need to consider a range of factors to achieve success when designing and implementing mentoring. This paper raises important issues for example, communication using social media, which have implications for practice in business sector and school partnerships involved in school-based mentoring.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

Preservice Teachers’ Perceptions of Mathematics Education in Urban Schools

This article reports findings from a study of preservice mathematics teacher education students and their beliefs about and experiences with students in an urban high school. The preservice teacher education students participated as mentors to a group of peer tutors in a mathematics tutoring program. Data collected from questionnaires and interviews reveal that the mentors had varied perceptions of tutoring program participants’ motivation, interest, and knowledge of mathematics. Mentors held varied perceptions of urban schools and what teaching mathematics in urban settings entails. Further, mentors reported that their work in the tutoring program had an impact on their strategies and plans for future mathematics teaching. Erica N. Walker is Assistant Professor of Mathematics Education in the Department of Mathematics, Science, and Technology and Research Fellow at the Institute for Urban and Minority Education at Teachers College, Columbia University.     

Peer Assessment of Student Constructed Posters: Assessment Alternatives in Preservice Mathematics Education

In this article I discuss a four-year action research project that involved the development of effective assessment tools for preservice mathematics teachers. The focus of the article is on peer assessment in which students reviewed posters created by their peers. The article discusses the strategies that were used and the implications that arose from the project. I argue that peer assessment is an effective tool for assessment in preservice mathematics teacher education but must not be seen as an alternative to teacher-based assessment due to the variability in marks between and within student cohorts. The value of peer assessment is its potential as a learning tool. This revised version was published online in August 2006 with corrections to the Cover Date.     

THE MATHEMATICS SYLLABUS AND ADULT LEARNERS IN COMMUNITY COLLEGES: INTEGRATING TECHNIQUE WITH CONTENT

This article presents a brief discussion of the challenges presented to mathematics education by change, in social dependence on mathematics, in professional response to the needs of students of mathematics, in institutional expectations of students and teachers, and in student demographics and expectations. Faculty in community colleges, where these changes might be most apparent, need new teaching tools. When constructed, presented, and enforced as a contract between adult student and teacher, the course syllabus can be a powerful teaching tool; an extension of its traditional role as administrative communication. The syllabus provides the venue to clearly communicate expectations to students. An extended outline for such a syllabus is given and discussed in terms of construction and presentation, and benefits to students and instructor. Nested within is an example of a grading rubric useful to a reform-minded instructor and acceptable to traditional institutions.     

Using Information and Communication Technologies to teach and learn mathematics in South African schools: A snapshot view of its impact

Information and communication technologies (ICTs) have become ubiquitous in most people’s lives. Yet, within the developing and emerging regions, there are still many who have not fully benefitted from ICTs. This article reports on a research project that focused on investigating the barriers, opportunities and impact that ICTs have on the teaching and learning of mathematics in South African schools. A quantitative research methodology in the form of a survey was used to assess South African mathematics teachers’ access to and use of ICTs and mobile technologies. A literature study revealed that there were universal barriers (i.e. lack of access to resources, time, effective training, confidence; resistance to change and negative attitudes; and no perception of benefits) and numerous opportunities for using ICTs in teaching and learning in general, and in subjects such as mathematics and science, in particular. The survey findings suggested increased deployment of ICT resources; introduction of more ICT training opportunities for teachers and students; and the firm adoption of ICT policies and directives within the education domain.     

“Moving quietly through the door of opportunity”: Perspectives of College Students who Type to Communicate

Colleges and universities across the United States are becoming increasingly diverse. That increased diversity includes students who do not use speech as their primary means of expression. This qualitative study focuses on the experiences and challenges of higher education for individuals with autism who type to communicate using a method known as facilitated communication. This article focuses on the perspectives of these individuals as they make sense of their inclusion in and, at times, exclusion from higher education, particularly their academic and social access. In addition, the findings of this research indicate that while there are structural and classroom supports that are helpful for individuals who type to communicate, their participation and meaningful inclusion is also incumbent on attitudinal factors and how receptive faculty and staff are to the students’ method of communication. While there is still much work to be done in the area of higher education for individuals with more complex needs, this study highlights the promise of higher education for this new population of students.     

指导数学教育硕士生学位论文答辩之我见

数学教育硕士学位论文答辩的目的要求是：检查研究生的学术水平，基本能力和独立工作；把握研究生的培养和质量．专家提问的着眼点是：质疑、考察、交流与指导．研究生答辩的要领是：强调独立工作，突出创新成果：点面结合，运用数据和案例说明观点，展示成果：阐明研究工作方法、特色和优势．教师的指导工作要领是：在论文指导中——掌握标准，严格要求；在答辩前——督促准备，指点要领；在答辩中——尊重同行，退居次席：在答辩后——指导反思，寄予厚望．     

The learning benefits of using eye trackers to enhance the geospatial abilities of elementary school students

In this study, we examined the spatial abilities of students using eye‐movement tracking devices to identify and analyze their characteristics. For this research, 12 students aged 11–12 years participated as novices and 4 mathematics students participated as experts. A comparison of the visual‐spatial abilities of each group showed key factors of superior spatial ability, and a spatial ability instructional strategy was developed. After training, the same spatial ability test was conducted again, and eye‐tracking records were used to compare the participants' line‐of‐sight and answer rate results with those of the previous test. Specific references and recommendations are provided for spatial ability training education and assessment.     

Conditions for the Effectiveness of Multiple Visual Representations in Enhancing STEM Learning

Visual representations play a critical role in enhancing science, technology, engineering, and mathematics (STEM) learning. Educational psychology research shows that adding visual representations to text can enhance students’ learning of content knowledge, compared to text-only. But should students learn with a single type of visual representation or with multiple different types of visual representations? This article addresses this question from the perspective of the representation dilemma, namely that students often learn content they do not yet understand from representations they do not yet understand. To benefit from visual representations, students therefore need representational competencies, that is, knowledge about how visual representations depict information about the content. This article reviews literature on representational competencies involved in students’ learning of content knowledge. Building on this review, this article analyzes how the number of visual representations affects the role these representational competencies play during students’ learning of content knowledge. To this end, the article compares two common scenarios: text plus a single type of visual representations (T+SV) and text plus multiple types of visual representations (T+MV). The comparison yields seven hypotheses that describe under which conditions T+MV scenarios are more effective than T+SV scenarios. Finally, the article reviews empirical evidence for each hypothesis and discusses open questions about the representation dilemma.