UNIVERSITY STUDENTS’ VIEWS OF THE ROLE OF MATHEMATICS IN THEIR FUTURE

We report on an international study about mathematics students’ ideas of how they will use mathematics in their future study and careers. This builds on our previous research into students’ conceptions of mathematics. In this paper, we use data from two groups of students studying mathematics: those who participated in an in-depth interview and those who completed an open-ended questionnaire. We found that their responses could be grouped into four categories: don’t know; procedural skills; conceptual skills; and professional skills. Although some students held clear ideas about the role of mathematics, many were not able to articulate how it would be used in their future. This has implications for their approach to learning and our approach to teaching.     

ENHANCING MATHEMATICS TEACHERS’ KNOWLEDGE OF STUDENTS’ THINKING FROM ASSESSING AND ANALYZING MISCONCEPTIONS IN HOMEWORK

This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth?Ceighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of students?? thinking. By engaging in the inquiry process of the 4 steps of identifying errors, analyzing reasons for the errors, designing approaches for correction, and taking action for correction, the teachers made obvious progress in their knowledge of students?? thinking, understood the difficulties and challenges their students had in learning mathematics, and enhanced their pedagogical content knowledge.     

THE EFFECTS OF PRIOR KNOWLEDGE AND VOCABULARY KNOWLEDGE ON THE READING COMPREHENSION PROCESS AND SOME INSTRUCTIONAL IMPLICATIONS

现代心理语言学理论视阅读为一个十分复杂的心理语言处理过程。这个过程包含两个不同层次的信息处理模式:基于语言材料,处理句子层并列关系及从属关系信息的自下而上的微观信息处理模式;基于内容背景知识,处理篇章层中心信息的自上而下的宏观信息处理模式。这两个信息处理模式在阅读过程中相互作用,但起决定作用的是后者。图式论认为,词汇知识结构即语言图式主要作用于自下而上的微观信息处理过程,内容知识图式和篇章结构图式主要作用于自上而下的宏观信息处理过程。在阅读过程中,不具备、不能激发及错误使用任何一种图式都会导致阅读理解错误。     

FIRST COMES THE THEORY, THEN THE PRACTICE? ON THE ACQUISITION OF GENERAL PEDAGOGICAL KNOWLEDGE DURING INITIAL TEACHER EDUCATION

Teacher education systems worldwide are confronted with the essential question of how to foster both future teachers’ theoretical and practical knowledge and to adequately enable future teachers to connect their theoretical and practical knowledge for teaching. This article investigates how future teachers acquire general pedagogical knowledge (GPK) as a central component of teacher knowledge during initial teacher education, exemplified by pre-service teachers in Germany, where initial teacher education is divided into a first phase with a heavy focus on theoretical, academic study, and a second phase where future teachers learn how to apply their theoretical knowledge in the classroom. Data from teacher knowledge studies Teacher Education and Development Study in Mathematics and Längsschnittliche Erhebung pädagogischer Kompetenzen von Lehramtsstudierenden/Longitudinal Survey of Student Teachers’ Pedagogical Competencies are used to compare future teachers’ GPK at different teacher education stages (the beginning, after 2 years, and end of training). Findings show the more advanced future teachers are in the course of their initial teacher education, the better they perform in the test measuring GPK. When analyzing subscales of the test measuring cognitive dimensions of GPK, as would be expected declarative-conceptual knowledge (measured by cognitive dimensions “recall” and “understand/analyze”) was gained predominantly during the theoretical study (first phase), whereas future teachers who had additionally passed through the practical second phase performed much better on the practical knowledge test subscale (measured by the cognitive dimension “generate”). Research findings are discussed with regard to the development of teacher expertise during initial teacher education, and recommendations for future policy directions with respect to teacher education are given.     

THE ROLE OF TEACHER CHARACTERISTICS AND PRACTICES ON UPPER SECONDARY SCHOOL STUDENTS�� MATHEMATICS SELF-EFFICACY IN NYANZA PROVINCE OF KENYA: A MULTILEVEL ANALYSIS

The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy. Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy, reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional development opportunities should also be made available to in-service teachers to continually update their knowledge and skills and develop new strategies for teacher effectiveness.     

LEARNERS’ AND TEACHERS’ CONCEPTUAL KNOWLEDGE OF SCIENCE PROCESSES: THE CASE OF BOTSWANA

The conceptual knowledge of science processes possessed by University of Botswana science students and senior secondary school science teachers was sought through a three-part questionnaire. One part requested demographic data of subjects, the second part asked them to select their level of familiarity with the processes, and the third part probed their conceptual definitions of the science processes. The definitions were scored as incorrect, partially correct and correct on an ordinal scale. Statistical analysis was done using Spearman rho correlation and one sample t test. The findings revealed that the science teachers did not have sufficient conceptual knowledge of science processes to help their students to understand in a meaningful way; both students’ and teachers’ views of their familiarity of science processes did not corroborate their demonstrated ability to provide acceptable conceptual definitions of the processes; there was no association between students’ and teachers’ conceptions of the science processes; and if conceptual knowledge of science processes was demanded, the entering students, who were the immediate graduates of the senior secondary schools, might not have enough to pursue tertiary level science courses. It is suggested that both conceptual and operational knowledge of science processes be required at secondary and tertiary levels of science education.     

PROSPECTIVE TEACHERS�� INITIAL CONCEPTIONS ABOUT PUPILS�� DIFFICULTIES IN SCIENCE AND MATHEMATICS: A POTENTIAL RESOURCE IN TEACHER EDUCATION

A crucial issue for prospective teachers (PTs) in their education is to develop pedagogical content knowledge (PCK; i.e. how to make a topic comprehensible to pupils). However, research has shown that PTs may have tacit ideas about teaching that act as filters preventing consideration of unfamiliar and discrepant ideas. These ideas must be elicited and taken into consideration in order to be modified. Therefore, PTs’ explicit conceptions may constitute a valuable resource in teacher education. The aim of this study was to investigate PTs’ ideas about pupils’ difficulties, at a topic-specific level, upon beginning the teacher education programme. The “Lesson Preparation Method” was used in four case studies to elicit the conceptions of 32 PTs regarding pupils’ difficulties in four specific science and mathematics topics: plant growth, gases, equations and heat and temperature. In all four topic groups (n = 5 – 11), there was a variety of initial conceptions about pupils’ difficulties, which were categorised into two to five topic-specific categories. Although, initially, PTs may not have expressed any notions about pupils’ difficulties, conceptions were elicited by using the Lesson Preparation Method. Furthermore, we found that the initial ideas corresponded with earlier research on pupils’ difficulties, which could provide a potential resource when creating a scaffolding context in teacher education programmes where PCK development is stimulated.     

SOCIETAL ISSUES AND THEIR IMPORTANCE FOR CONTEMPORARY SCIENCE EDUCATION��A PEDAGOGICAL JUSTIFICATION AND THE STATE-OF-THE-ART IN ISRAEL, GERMANY, AND THE USA

One common theme underlying recent reports on science education is that the content of school science and its related pedagogical approaches are not aligned with the interests and needs of both society and the majority of the students. Most students do not find their science classes interesting and motivating. These claims are especially valid regarding those students who, in the future, will probably not embark on a career in science or engineering but will need science and technology personally and functionally as literate citizens. One key problem seems to be that few science programs around the world teach how science is linked to those issues that are relevant to students’ life, environment, and role as a citizen. As a result, many students are unable to participate in societal discussions about science and its related technological applications. This paper discusses the need to incorporate socioscientific ideas into the science curricula more thoroughly. This recommendation is supported by a theoretical rationale from various sources leading to a reflection about common practices in science education in three countries: Israel, Germany, and the USA. The state-of-the-art, potentials, and barriers of effective implementation are discussed.     

THE EFFECTS OF COGNITIVE STYLES ON NAÏVE IMPETUS THEORY APPLICATION DEGREES OF PRE-SERVICE SCIENCE TEACHERS

The purpose of this study was to determine whether there is a relationship between pre-service science teachers’ Field Dependent or Field Independent (FD/FI) cognitive styles and the application of degrees of naive impetus theory. The sample consisted of 122 pre-service science teachers (97 females and 25 males) who were enrolled in the Introductory Physics course required by the Science Education program. Data were collected in two successive years, after the completion of the required Introductory Physics undergraduate courses, in 2008 and 2009. The Group Embedded Figure Test and Impetus Theory Application Test (a two-tier-type test) were administered to assess the FD/FI tendency of students and to determine the degree students applied the naïve impetus theory, respectively. Initial results showed that a majority of students had made use of the native impetus theory repeatedly. The results also indicated that the degree to which students applied the naïve impetus theory was statistically related to their FD/FI cognitive styles. The findings of this research showed that there existed a statistically significant difference between the FI and FD students’ degree of applying the naïve impetus theory in favor of FI students. However, the test score gap between FI and FD students remained almost constant regardless of the testing instruments utilized in this study.     

THE SURVIVORS,THE EMERGENCE OF A NEW COMMUNITY AND A SYSTEM OF ZIONIST EDUCATION IN GERMANY 1945–1950

I — Reminiscences Deuteronomy 32:7

Back in 1925, upon graduation from the Teachers Institute of Yeshiva University, I started my career as teacher in the first and oldest Talmud Torah in the United States, the Machzikey TT on East Broadway in Manhattan. I recall with pleasure how boys and girls spent ten hours a week in Jewish studies: giving the 12-13 year olds intensive instruction in Torah, Neviim, Mishnah, Hebrew Grammar, Hebrew Literature and Yiddish. For many years the Machzikey TT had a school enrollment of one thousand students and more. When the '30s came and the enrollment fell considerably, it became necessary to consolidate the school with the National Hebrew School, especially when the Downtown TT closed it doors.     

SCIENTISTS’ PARTICIPATION IN TEACHER PROFESSIONAL DEVELOPMENT: THE IMPACT ON FOURTH TO EIGHTH GRADE TEACHERS’ UNDERSTANDING AND IMPLEMENTATION OF INQUIRY SCIENCE

The impact of a professional development experience involving scientists and fourth to eighth grade teachers of science was explored. Teachers attended a summer program at a research facility where they had various experiences such as job shadowing and interviewing scientists. They also participated in authentic inquiry investigations and planned inquiry units for their classrooms. Data on teachers’ understanding and implementation of inquiry were collected through surveys, questionnaires, and classroom observations. Findings show that the teachers’ understanding of inquiry improved and most participants were able to successfully implement inquiry science in their classrooms. Barriers to the implementation of inquiry practices and the impact of specific experiences with the scientists were explored.     

RECOMMENDATION ON THE RECOGNITION OF STUDIES AND QUALIFICATIONS IN HIGHER EDUCATION∗

The text reproduced below is that of an official Recommendation of the General Conference of UNESCO regarding the worldwide international recognition of higher education studies and qualifications. It suggests steps that the Member States should take to harmonize their policies with regard to mobility in higher education and the mutual recognition of diplomas, degrees, periods of study, and professional qualifications and practice. Evoking the six existing UNESCO Regional Conventions on the recognition of studies and qualifications in higher education, this Recommendation serves as a step toward the eventual creation and ratification of a Universal Convention on the recognition of studies and qualifications in higher education.

     

MATHEMATICS EDUCATORS’ VIEWS ON THE ROLE OF MATHEMATICS LEARNING IN DEVELOPING DEDUCTIVE REASONING

This study examines the views of people involved in mathematics education regarding the commonly stated goal of using mathematics learning to develop deductive reasoning that is usable outside of mathematical contexts. The data source includes 21 individual semi-structured interviews. The findings of the study show that the interviewees ascribed different meanings to the above-stated goal. Moreover, none of them said that it is possible to develop formal logic-based reasoning useful outside of mathematics, but for different reasons. Three distinct views were identified: the intervention–argumentation view, the reservation–deductive view, and the spontaneity–systematic view. Each interviewee’s view was interrelated with the interviewee’s approach to deductive reasoning and its nature in mathematics and outside it.     

EXPLORING TEACHERS’ KNOWLEDGE AND PERCEPTIONS ACROSS MATHEMATICS AND SCIENCE THROUGH CONTENT-RICH LEARNING EXPERIENCES IN A PROFESSIONAL DEVELOPMENT SETTING

This paper examines upper elementary and middle school teachers’ learning of mathematics and science content, how their perceptions of their disciplines and learning of that discipline developed through content-rich learning experiences, and the differences and commonalities of the teachers’ learning experiences relative to content domain. This work was situated within a larger professional development (PD) program that had multiple, long-term components. Participants’ growth occurred in 4 primary areas: knowledge of content, perceptions of the discipline, perceptions about the learning of the discipline, and perceptions regarding how students learn content. Findings suggest that when embedded within an effective professional development context, content can be a critical vehicle through which change can be made in teachers’ understandings and perceptions of mathematics and science. When participants in our study were able to move beyond their internal conflicts and misunderstandings, they could expand their knowledge and perceptions of content and finally bridge to re-conceptualize how to teach that content. These findings further indicate that although teachers involved in both mathematics and science can benefit from similar overall PD structures, there are some unique challenges that need to be addressed for each particular discipline group. This study contributes to what we understand about teacher learning and change, as well as commonalities and differences between teachers’ learning of mathematics and science.     

INDIGENOUS STUDENTS’ EXPERIENCES OF THE HIDDEN CURRICULUM IN SCIENCE EDUCATION: A CROSS-NATIONAL STUDY IN NEW ZEALAND AND TAIWAN

The tacit messages transmitted to indigenous learners in the science classroom provide a lens through which indigenous disengagement with school science can be better understood. In this paper, the findings of a cross-national comparative study conducted with indigenous Maori students in New Zealand and Seediq/Atayal students in Taiwan are discussed from a sociological perspective. The purposes of the present study were to explore the ways in which indigenous elementary school students in two industrialized nations experience the science curriculum and to identify the socialization processes through which patterns of indigenous under-achievement in science are maintained and reproduced. The findings suggest that the peripheral positioning of indigenous culture and knowledge within the science curriculum in developed nations underpins a series of tacit pedagogical codes that contribute to indigenous student disengagement with the subject.     

MEETING THE EDUCATIONAL NEEDS OF SERVICE PROVIDERS: EFFECTS OF A CONTINUING EDUCATION PROGRAM ON SELF‐REPORTED KNOWLEDGE AND ATTITUDES ABOUT AGING

A variety of approaches are available for meeting the educational needs of professionals currently providing services to older adults. This article focuses on the development of the Professional Development Program in Gerontology offered through Continuing Education at the University of North Carolina at Charlotte and examines the effectiveness of this program in educating regional service providers. The discussion is based on participants’ self‐reported before‐and‐after data on their knowledge and attitudes about aging and the aged. The importance of changing employers’ attitudes about the importance of gerontology education as a qualification for service providers is also discussed.     

BELIEFS ABOUT CHEMISTRY TEACHING AND LEARNING—A COMPARISON OF TEACHERS’ AND STUDENT TEACHERS’ BELIEFS FROM JORDAN,TURKEY AND GERMANY

This paper discusses beliefs about teaching and learning chemistry. The sample includes chemistry student teachers and in-service teachers from Jordan, Turkey, and Germany. Two test instruments were used to investigate (student) teachers’ beliefs. A qualitative instrument was used to explore Beliefs about Classroom Organization, Beliefs about Teaching Objectives, and Epistemological Beliefs. A quantitative instrument was added to evaluate participants’ beliefs concerning the Nature of Good Education. The results show that Jordanian chemistry teachers and teacher trainees held the most traditional, teacher-centered, and transmission-oriented beliefs, while the German sample showed the most modern beliefs toward teaching and learning. Turkish (student) teachers evidenced more moderate beliefs, which tended to be between the two extremes, but that could still be positioned more closely to the traditional way of thinking. The results are discussed in the context of chemistry teacher education in the three respective countries.     

TEACHERS’ MISCONCEPTIONS ABOUT THE EFFECTS OF ADDITION OF MORE REACTANTS OR PRODUCTS ON CHEMICAL EQUILIBRIUM

The importance of research on misconceptions about chemical equilibrium is well recognized by educators, but in the past, researchers’ interest has centered on student misconceptions and has neglected teacher misconceptions. Focusing on the effects of adding more reactants or products on chemical equilibrium, this article discusses the various misconceptions held by high school teachers. A misconception test was administered to two samples of chemistry teachers in Nanjing, China. Of the 109 teachers who participated in the test, only one understood that adding more CS₂ gas to the equilibrium system CS₂(g) + 4H₂(g) ⇌ CH₄(g) + 2H₂S(g) at constant pressure and temperature can shift the equilibrium to the reactant or product side, depending upon the amount of CS₂ in the initial equilibrium system. Most of the teachers relied on Le Chatelier’s principle and thus made erroneous predictions. The misconception test also revealed that those teachers who managed to compute equilibrium constants had a limited conceptual understanding of chemical equilibrium. Implications of these findings for teacher education and chemistry curriculum development are discussed.