四川农村初中实施数学新课程的调查与思考

为了解农村初中数学新课程实施状况,采用问卷调查法对四川省21个地市州的农村初中数学省级骨干教师进行了调查．调查显示：教师普遍对新教材不满意,多数教师感到对新课程倡导的学习方式和教学方式运用得较差,在校本教研、运用信息技术、教学评价等方面存在一些问题,在课改实验中遇到的主要困难排在第一位的是“新课程资源少”,当前初中数学教师迫切需要解决的问题是“加强现代教育技术”．因此,应大力开发新课程资源,转变教学方式,改进教学评价,改革教师培训方法,发挥校本教研制度的作用,国家和地方财政应加大对西部农村初中学校教育的投入．     

Early childhood mathematics teaching: challenges,difficulties and priorities of teachers of young children in primary schools in Ireland

Issues of pedagogy are critical in all aspects of early childhood education. Early childhood mathematics is no exception. There is now a great deal of guidance available to teachers in terms of high‐quality early childhood mathematics teaching. Consequently, the characteristics of high‐quality early childhood mathematics education are clearly identifiable. Issues such as building on young children’s prior‐to‐school knowledge; engaging children in general mathematical processes; and assessing and documenting children’s learning are some of the key aspects of high‐quality early childhood mathematics education. The extent to which teachers of four‐ and five‐year‐old children in primary schools in Ireland incorporate current pedagogical guidance in early childhood mathematics education was explored in 2007 in a nationally representative questionnaire survey of teachers of four‐ and five‐year‐old children attending primary schools. This paper presents some of the findings of the study in relation to teachers’ self‐reported challenges, difficulties and priorities in teaching early childhood mathematics. Implications are drawn for professional development, curriculum guidance and educational policy.     

Professional Journals: do mathematics teachers read them?

Today, teachers are expected to be able to make informed decisions about curriculum, be aware of current teaching methodologies, and be conversant with the latest educational theory. Keeping up to date is not easy. Fortunately, professional journals do provide one avenue by which teachers can stay abreast of current developments. However, do teachers read professional journals? The study reported here surveyed 439 Australian mathematics teachers from 73 secondary schools to establish which mathematics teacher education journals they had heard of and to determine the extent to which they read these journals. The results indicate that the majority of mathematics teachers neither are regular readers of professional journals nor are they aware of them. Moreover, if journals are read, they are generally those obtained with membership of professional organisations.     

Double Visions: Educational Technology in Standards and Assessments for Science and Mathematics

For educational technology integration in content disciplines to succeed, teachers and teacher educators need clear standards delineating why, how, where, and how much educational technology they should include in their teaching. This paper examines the visions offered by current science, mathematics, and educational technology standards for educational technology integration in K-12 schools. Since national assessments exert a profound influence on what teachers and students choose to teach and learn, the vision of educational technology use supported by national assessments is also examined. The National Council of Teachers of Mathematics Standards (NCTM, 2000. Principles and Standards for School Mathematics. Retrieved April 6, 2002 from http://standards.nctm.org), the National Science Education Standards (National Research Council (NRC) 1996. National Science Education Standards. Available at http://books.nap.edu/catalog/4962.html), and the National Educational Technology Standards (International Society for Technology in Education (ISTE) 2000. National Educational Technology Standards for Students: Connecting Curriculum and Technology, ISTE, Eugene, Oregon) provide different visions of educational technology use in the classroom. In addition, the current technology use policies for national assessments in science and mathematics, in particular the college admission tests (ACT, SAT I and SAT II subject area tests), Advanced Placement (AP) course assessments, and the Praxis Series assessments indicate that while mathematics assessments often recommend or require the use of educational technology, few science assessments permit the use of educational technology by students. Recommendations are offered for science educators regarding teacher preparation for the technology-rich classrooms of the future.     

Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.     

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.     

Big Math for Little Kids: The Effectiveness of a Preschool and Kindergarten Mathematics Curriculum

Research Findings: Big Math for Little Kids (BMLK) is a mathematics curriculum developed for use with 4- and 5-year-old children. To investigate the BMLK curriculum's effect on children's mathematics knowledge, this cluster-randomized controlled trial randomly assigned child care centers to provide mathematics instruction to children, using either the BMLK mathematics curriculum or the centers’ business-as-usual curriculum, over a 2-year period when children were in prekindergarten and kindergarten. Participants in the study were 762 children and their teachers at 16 publicly subsidized child care centers. The study assessed children's mathematics knowledge using the Early Childhood Longitudinal Study, Birth Cohort (ECLS-B), Direct Mathematics Assessment, a measure of young children's mathematics knowledge that is not aligned with the curriculum. The ECLS-B scores of children in the BMLK group increased significantly more than did those of children in the comparison group. The study also included exploratory analyses to examine whether children in the BMLK group demonstrated evidence of improved mathematical language. Practice or Policy: These results indicate that the BMLK curriculum, which is designed to help teachers use play-based, developmentally appropriate mathematics instruction, has a positive impact on young children's mathematics knowledge as measured by a general mathematics assessment that is not aligned with the curriculum.     

新加坡中学数学教师教育课程设置的特点与启示

新加坡中学数学教师教育课程具有6个特点：中学数学教师培养模式的高层次化;课程设置系列化、综合化、专题化;突出与中学数学教育的接轨;强调理论和实践的整合;教育类课程比例高,教学实践课时足;重视现代教育技术的学习与应用。其先进的经验对于我们构建数学教育类课程体系的基本指导思想、基本原则以及基本的课程体系框架具有极大的启发意义。     

Elementary school teachers’ uses of mathematics curricular resources

With the adoption of new content standards, teachers are often left without adequate curriculum resources. This study examined how educators used their curricular resources to teach new mathematics standards in the USA. Analyses of open-ended survey responses from 257 teachers and teacher–leaders in Grades 3 through Grade 5 indicated that every educator reported supplementing their districts’ or schools’ primary curricular resources with other materials. These supplements primarily included resources found for free on websites and resources that claimed to be aligned to the new standards, but varied in terms of alignment to national standards for effective mathematics curriculum. Implications for this study include further research on how teachers make decisions regarding curriculum resources as well as increasing teachers’ access to quality curriculum materials that can support students’ mathematical learning.     

The growing gap between colombian education policy, official claims and classroom realities: insights from mathematics teachers' conceptions of beginning algebra and its teaching purpose

Since 1994 when the General Law of Education was issued, educational authorities have been claiming that Colombia has embarked on an educational revolution [‘La revolución educativa’ (n.d.). From the Colombian Ministry of Education website: . Retrieved 23 Nov 2004] where schools have curricular autonomy, and are to improve the quality of education by attending to the needs of the communities they serve. Teachers are urged to engage in a continuous process of constructing the curriculum which is to be anchored in the fundamental aim of educating critical citizens. The findings of this study carried out with the participation of 13 mathematics teachers with a range of teaching experiences and from different schools in Bogotá, show a totally different picture. Instead, for the teaching of school algebra, teachers emphasised the purpose of training pupils in the manipulation of symbolic expressions, as the prerequisite knowledge for the next school mathematics level and ultimately for the External Examination. I offer explanations for the identified gap and argue for the crucial need to create conditions for change at the education systemic level and for the actual empowerment of teachers.     

Investigating the Alignment of Bhutanese Mathematics Teachers’ Planned Approaches Within the Context of a Reformed Curriculum

Reform of mathematics education has been in focus in many countries including those in major economic transition. This paper reports a segment of a study which was conducted in Bhutan, where a reformed elementary mathematics curriculum has been recently introduced. The reformed curriculum is based on social constructivism and its design has been influenced by the USA’s National Council of Teachers of Mathematics (NCTM) standards. This paper reports upon the planned teaching of a sample of elementary (primary) teachers in their implementation of the reformed curriculum. The data for this part of the investigation were aggregated from a qualitative survey of randomly selected elementary school teachers (N = 72) from 40 schools across the country. A set of 3 analytical rubrics, based on intentions embedded in the curriculum, was developed to analyse the alignment of teachers’ planned sample learning activities with the intentions of the curriculum. Our conclusions are that while the curriculum’s intentions might be meaningfully stated in the curriculum documents, implementation remains problematic because there appears to be a mis-alignment between curriculum intentions and classroom practices. For instance, teachers by not adopting evidence-based approaches recommended in the curriculum document and are continuing to deny students opportunities to achieve deep understanding in achieving national priorities. This paper also argues that the proposed analytical rubrics may be of value for Bhutanese mathematics educators and, with minor modification, educators in other contexts, as they critique planned and actual practices.     

A Study of Early Childhood Mathematics Teaching in the United States and China

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts. Specifically, 27% of the U.S. participants did not set any goals for mathematics, and 20% did not use a curriculum or any resources. In contrast, 3% of the Chinese participants fell into each of these categories. Second, early childhood mathematics content in the United States appears to be broader and less differentiated by age group than in China. Lastly, emerging curriculum (mathematics learning that emerges from children's play, activities, and routines) is the prevailing approach for 3- and 4-year-olds in the United States. In comparison, mathematics-specific teaching is the primary, but not sole, form of instruction in China. Practice or Policy: These findings have important implications for implementing the Common Core mathematics standards in the early years.     

Pre-service versus in-service mathematics teachers’ opinions of mathematics reform in post-primary schools in Ireland

A new approach to the teaching and learning of mathematics has been introduced on a phased basis in post-primary education in Ireland. As part of the OECD PISA 2012, a survey was undertaken of in-service mathematics teachers in Ireland, with the aim of gathering data on the opinions of teachers about this reform. Here, a modified version of the survey was distributed to pre-service teachers immediately before and after a four-month teaching placement to ascertain if there were differences in the views expressed by pre-service and in-service teachers in relation to the teaching and learning of mathematics, and also if there were differences expressed by the pre-service teachers before and after their placement in post-primary schools. Analysis of the results showed considerable levels of agreement between all groups, with some exceptions in relation to confidence in teaching the reformed curriculum, emphasis on various teaching and learning activities, and usage of ICT in the classroom.     

Chinese primary school mathematics teachers working in a centralised curriculum system: a case study of two primary schools in North‐East China

Mainland China has a highly centralised curriculum development system. A study of two schools in northeast China, one in a rural area and the other in an urban area, indicates that the primary mathematics curriculum has been widely adopted by teachers at the classroom level. Feeling the intense pressure generated by the national mathematics Olympiad,1 1. The mathematics Olympiad is a type of ‘extracurricular’ activity that aims to promote students' interest and improve their ability in mathematics. Students participating in the competition are required to complete some challenging and non‐routine mathematical operations. The international mathematics Olympiad is held every year. In Mainland China, this competition is commonly organised at city, provincial and national level. Students who perform exceptionally well are exempted from the highly competitive national university entrance examinations for entry to universities View all notes teachers in the urban school tended to give more difficult mathematics problems to their students in the hope that above‐average students would perform well in the competition. In the rural school, the ability of students was more varied and generally lower. Teachers there worked very hard to push their students to meet the national requirements. The driving force behind this was the county‐wide public examination in which students' performance was taken as an indicator of teachers' competence. Teachers in both schools also have not taken effective steps to adapt the curriculum for students' individual differences. A comparison of the practices between the teachers in the two schools suggests that teachers' beliefs, their professional knowledge and skills shape their inclination and ability in curriculum adaptation and differentiation.     

高中数学教师专业知识研究--基于吉林省数学教师的调查

教师专业发展必然需要教师专业知识的有力支撑。对高中数学教师专业知识进行的问卷调查和访谈发现：目前高中数学教师基本上较好地掌握了常用的教师专业知识,但也存在一些问题：对数学学科知识的关注范围过于狭窄;运用数学教学知识进行教学时偏向于被动;对数学课程标准的理解存在偏差。另外,研究还发现：数学教学知识的增长并非是持续的;不同层级的教师之间、不同类别学校中的教师之间,其差异主要体现在数学学科知识与数学教学知识。进而对数学教师教育提出相应建议：数学教师应适当拓展数学学科知识的关注范围;应依据调查数据加强数学教师教育培养计划的针对性;关于教师一般教育学知识的评价方式亟需改进等。     

配备专职科学教师是开齐开好科学课程最基本的保证——小学科学教育现状调研报告

小学科学课程承担着培养小学生科学素质的重任,早期科学教育对每个人科学素质的形成具有十分重要的影响。然而在调研中发现,小学科学课程实施情况不尽人意：专职科学教师数量极其缺乏;科学课程开设严重不齐不足,兼职教师挪课现象相当严重;设施设备投入不足,科学专用教室和设备严重缺乏。这些问题严重影响小学科学教育正常开展。因此,必须提高对科学课程开设重要性认识,配备专职科学教师,保证开齐开好科学课程,促进学生创新意识和实践能力的提高。     

教师视域中的课程改革与数字教育资源——对烟台市部分中小学教师的调查

为了了解中小学教师对基础教育课程改革的认识,明确教师对数字教育资源的需求,作者对烟台市芝罘区10所中小学校中的全部任课教师进行了调查。调查从定量的角度对基础教育工作中某些观点给予了支持或否定,如学科与资源的关系、教师与资源的关系、支持改革的资源类型等等。     

数学课堂教学中师生交往的有效化

数学课堂教学改革是数学课程改革的一项重要工作。数学课堂教学改革就是要用新课程理念改革过去被动式的课堂教学模式,使课堂教学成为“师生之间、学生之间交往互动与共同发展的过程”。要实现这一目标,建构课堂教学中真实的师生交往是关键。当前,在中小学数学课堂教学的师生交往中存在一些不真实的现象,这已对数学新课程的教学实施造成了一些不利的影响。因此,要正确认识数学课堂教学中师生交往的涵义,分析不真实交往的成因,明确师生之间真实交往的特征,建构数学课堂教学中有效的师生交往,从而推动数学课堂教学改革的健康发展。     

高师计算机课与中学数学新课程整合的探究

在高师数学系计算机课中整合中学数学新课程,以在职和职前教师能胜任中学数学新课程的教学为研究出发点,选用中学数学新课程充实深化重组计算机课程内容,实施计算机支持的协作学习的六个步骤：教师创设情境和提出问题、教师分析问题和明确方法、学生自主探索和寻求解答、小组协作学习和解决问题、师生总结和评价成果及教学反思,培养学生基于信息技术平台更有效地学数学与教数学的能力,提升他们的信息素养和数学素养．