An analysis of the competency-based secondary mathematics curriculum in Sri Lanka

In education, there is a growing interest in the concept of competency especially in vocational training and professional development. The concept is strongly associated with the ability to apply knowledge and skills in effective ways in unanticipated situations. In Sri Lanka, a new competency-based mathematics curriculum was introduced in 2007 for grade 6 and the implementation was completed in 2010 for grade 11 as part of a reform process. The main aim of this implementation was to eliminate previous transmission methods of teaching and to assign a transformational role to the teacher. In this study, I analyzed the suitability of this new curriculum as a competency-based curriculum and examined whether it has achieved its objectives. The results showed that the new curriculum was better in elaborating the subject content and teaching methods. However, in a broader sense, it has not fulfilled its objectives as a competency-based curriculum. The analysis led one to conclude that competency-based teaching and learning approaches were superficially introduced in mathematics education in Sri Lanka. The curriculum documents did not properly reflect their intended objectives.     

Influence of curriculum reform: An analysis of student mathematics achievement in Mainland China

This study investigated curriculum influences on student mathematics achievement by following two groups of students from fifth to sixth grade that were taught either the reformed curriculum or the conventional curriculum. Analyses with three-level modeling were conducted to examine learning outcomes of the students who were assessed three times over a period of 18 months. Achievement was measured with regard to computation, routine problem solving, and complex problem solving. Affective aspects included self-reported interest in learning mathematics, classroom participation, views of the nature of mathematics, and views of learning mathematics. The results showed overall improved performance among all the students over the time on computation, routine problem solving, and complex problem solving but not on the affective measures. There were differentiated patterns of performance between the groups. On the initial assessment, the reform group performed better than the non-reform group on calculation, complex problem solving, and indicated higher interest in learning mathematics. The two groups did not differ on the other achievement and affective measures at the first time of assessment. There was no significant difference in growth rate between the groups on the cognitive and affective measures except that the non-reform group progressed at a faster pace on calculation. Therefore, the non-reform group outperformed the reform group on computation at the third (last) assessment. These results are discussed with respect to the possible influence of the curriculum on student learning.     

Examining fourth-grade mathematics writing: features of organization,mathematics vocabulary,and mathematical representations

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and use writing features to convey mathematics knowledge. We collected mathematics-writing samples from 155 4th-grade students in 2 states. Each student wrote about a computation word problem and fraction representations. We compared mathematics-writing samples to a norm-referenced measure of essay writing to examine similarities in how students use writing features such as introductions, conclusions, paragraphs, and transition words. We also analyzed the mathematics vocabulary terms that students incorporated within their writing and whether mathematics computation skills were related to the mathematics vocabulary students used in writing. Finally, we coded and described how students used mathematics representations in their writing. Findings indicate that students use organizational features of writing differently across the norm-referenced measure of essay writing and their mathematics writing. Students also use mathematics vocabulary and representations with different levels of success. Implications for assessment, practice, and intervention development are discussed.     

Teachers' concerns regarding the adoption of a new mathematics curriculum: An application of CBAM

The main purpose of the present study was to identify and examine the concerns of primary school teachers in Cyprus in relation to the recent implementation of a new mathematics curriculum and the use of new mathematics textbooks. An adaptation of the Stages of Concern Questionnaire (SoCQ) based on the Concerns-Based Adoption Model (CBAM) was administered to a representative sample of teachers. According to the findings, the concerns of teachers largely focused on the task stage of the CBAM model. Furthermore, there were significant differences in the concerns of teachers across years of teaching experience but not across years of implementation. This revised version was published online in July 2006 with corrections to the Cover Date.     

History in the National Curriculum: a lesson in curriculum devolution

This article will focus on an event in the educational history of Wales in the 1980s which still impacts both on school practice and on thinking about concepts of Welsh identity. That event was the creation of the History Committee for Wales which was charged with devising a history curriculum for Welsh schools in the wake of the 1988 Education Act. The story will be told largely by using evidence gleaned in elite interviews with the ministers, senior inspectors and civil servants most closely associated with the decision to support or accept the creation of this committee.

The significance of the decision will be assessed by charting the progress of curriculum devolution in Wales from the beginnings of state education and the implications of this for ideas of Welshness. This background will be briefly sketched, as will the background to the 1988 Education Act on a wider canvas. General reaction to that act in the Welsh Office will be discussed before the detailed implications for the subject of history will be explored in detail.

It will then be argued that wider discussions as to how schools should approach and reflect the history and culture of nations not only shed important light on devolutionary processes which were gathering pace at the time but also reflect the nature of Welshness as perceived by senior figures in the world of education policy-making.     

Characterising lesson planning: a case study with mathematics teachers

ABSTRACT

The quality of students’ learning experience depends on the learning activities that their teachers plan prior to classroom delivery. This article characterises the lesson planning practices of a group of 27 mathematics teachers. The questionnaire and the associated information coding and analysis procedures designed for that purpose may be applicable to lesson planning characterisation involving larger groups of teachers and of other disciplines. Some of the study group’s needs and difficulties are established. One of the observations discussed is that planning procedures and criteria tend to be generic rather than specific to the lesson at issue. Another is that these teachers’ vision of planning does not necessarily ensure a coordinated approach to all curricular dimensions.     

技工院校五年制数学课程改革的探究

从对技工院校五年制数学课程的现状分析以及面临的主要问题入手,围绕"全面提高教学质量"这一宗旨,对影响技工院校数学教学质量诸多因素进行了深入探索与研究,提出了改革五年制数学课程的原则、方法和教学内容。     

Time for curriculum reform: the case of mathematics

Mathematics education is rarely out of the policy spotlight in England. Over the last 10 years, considerable attention has been given to improving 14–19 mathematics curriculum pathways. In this paper we consider some of the challenges of enacting curriculum change by drawing upon evidence from our evaluation of the Mathematics Pathways Project (MPP). From 2004 to 2010 this project, which was directed by England's Qualifications and Curriculum Authority, aimed to improve the engagement, attainment and participation rates of 14- to 19-year-old learners of mathematics. Our particular focus is upon the temporal problems of piloting new curriculum and assessment and we draw on Lemke's discussion of timescales, heterochrony and the adiabatic principle to consider the interlocking and interference of various change processes.     

Procedural knowledge in mathematics: the role of the curriculum

Over the last few years, the information processing model of cognition has become increasingly prominent in the field. With this model, and other related research in cognitive science, there is a greater appreciation for the role of instruction in learning theory. One of the model's central tenets is that, as learners become more competent, they move from declarative to procedural states of knowledge. Researchers have concerned themselves with the efficiency of this transition, as well as with any systematic misconceptions that develop along the way. A carefully developed curriculum addresses both of these concerns. This article will focus on three principles of curriculum development: the nature of examples, explicitness, and parsimony. Recently conducted research that supports these principles will also be discussed. It is suggested that special educators strongly consider these principles when selecting or developing curricular material for students with learning disabilities.     

Developing a mathematics curriculum to improve learning behaviors and mathematics competency of children

The authors investigated the effect of a mathematical curriculum (CU) developed based on verbal and practical activities on the mathematical competency (MC) and learning behaviors (LB) of preschool children. In a quasi-experimental design, 60 children (5- to 6-year-old girls) were selected using the accessible sampling method. The children were randomly divided into an experimental group and a control group, and the relevant concepts were taught to the children in both groups. While the control group received the typical kindergarten education based on the usual textbooks and worksheets, the CU was taught to the experimental group. Structural equation modeling was used to model the data and statistical evaluation. The results demonstrated a significant difference between the two groups in MC and LB. The CU significantly improved MC directly, and indirectly through the improvement of LB (i.e., engagement and learning focus, verbal behaviors, and type of activity).     

Toward inclusive mathematics education: a metatheoretical reflection about countering ableism in mathematics standards and curriculum

This article documents efforts to advance inclusive mathematics education practices involving the introduction of equity-oriented resources in state-level mathematics standards guidance documents in a Midwestern United States jurisdiction. We adopt a critical stance by looking at ways to interrogate available metatheories for these kinds of change-making processes. The guiding resources documented in the present article center on issues of difference. These issues are related to dis/ability in mathematics education standards and curriculum to not only raise teachers' awareness of constructions of difference in order to foster inclusive education, but also to promote critical self-reflections around ableism. Guiding resources are a means to support recognition of dis/ability difference as a source of multiple mathematical knowledge bases from which to learn and advance mathematics thinking. Yet, we also recognize the need to be vigilant about the complex interpretative contours and the relational dynamics at work throughout their various layers of implementation, assessment, and anti-ableist realignment. Accordingly, we reflect metatheoretically about three questions: How might concepts of access, achievement, identity, and power support teachers of mathematics in advancing inclusive practices? How do word choices in mathematics standards, curriculum, and practices dis/able students in classroom practices? What may we learn from the mathematics education experiences of individuals with dis/abilities and their families in the broad configuration of change-making dynamics of educational policies and teaching practices?     

Improving mathematics instruction through lesson study: a theoretical model and North American case

This article presents a theoretical model of lesson study, an approach to instructional improvement that originated in Japan. The theoretical model includes four lesson study features (investigation, planning, research lesson, and reflection) and three pathways through which lesson study improves instruction: changes in teachers’ knowledge and beliefs; changes in professional community; and changes in teaching–learning resources. The model thus suggests that development of teachers’ knowledge and professional community (not just improved lesson plans) are instructional improvement mechanisms within lesson study. The theoretical model is used to examine the “auditable trail” of data from a North American lesson study case, yielding evidence that the lesson study work affected each of the three pathways. We argue that the case provides an “existence proof” of the potential effectiveness of lesson study outside Japan. Limitations of the case are discussed, including (1) the nature of data available from the “auditable trail” and (2) generalizability to other lesson study efforts.

关于数学建模课程改革及其教学方法的探讨

数学建模教学和竞赛的开展,是培养学生创新能力的重要途径.对数学建模竞赛中出现的问题进行分析,找出问题产生的根源与必修课和专业课设置不合理有关,应对高校数学课程的设置、教学方式等进行改革,提出具体改革建议.     

Towards numeracy for the third millennium: A study of the future of mathematics and mathematics education

The research reported here has sought to identify target skills and abilities that will compose a future numeracy, so that new expertise can be incorporated and the exposed deficiencies remedied within a dynamic rather than static concept of competency. A nation-wide selection of panellists contributed to a three-round Delphi process, with the final data comprising both structured responses and qualitative comment. The scope of the items covered calculating activities, writing activities, reading activities, physical skills, supporting (mental) skills, applications, and problem solving. Responses to the structured items have provided priorities for numeracy for the turn of the century, in terms of both expected and desired characteristics. In general, expectations for numeracy fall short of the levels deemed desirable by panel consensus. The qualitative comments have been incorporated into three scenarios reflecting altermative visions for the future. A comparison of the scenarios uncovers wide differences between informed thinkers with respect to future visions of the ends, means, and mechanics of learning. These differences among individuals who are otherwise consistent in their views of future needs must be addressed if the identified priorities are not to be lost in a quagmire of conflicting interests, opinions, priorities, and values.     

Working toward a third space in the teaching of elementary mathematics

Building on work in the area of third space theory, this study documents one teacher’s efforts to create third spaces in an elementary mathematics classroom. In an attempt to link the worlds of theory and practice, I examine how the work of other theorists and researchers – inside and outside the field of education – can create new lenses for classroom practitioners. In addition, the article provides evidence that third spaces may be more difficult to realize than others have described. Rather than forcing a third space to emerge, what this study finds more important is creating an environment that will allow third spaces to surface more organically as students and teachers engage in the everyday life of the classroom.     

对大学数学与高中数学课程内容的衔接问题的思考

首先分析当前大学数学与高中数学缺乏衔接所造成的问题,然后回顾我国在基础教育领域开始了由应试教育向素质教育转变的新一轮的课程改革,对《高中数学新课程标准》要求的教学内容和大学数学的教学内容两者作了比较分析,最后提出了大学数学教学改革的几方面的建议。     

An interdisciplinary collaboration between computer engineering and mathematics/bilingual education to develop a curriculum for underrepresented middle school students

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.     

新课程理念下的一节绪论课

人教版高中《生物》必修教材,其独特的设计思路和崭新的教学内容呈现方式使人耳目一新。这套教科书的三个必修模块教材,在正式教学内容之前都安排了“科学家访谈”这一内容。为什么要这样安排？在课时很紧张的情况下,这部分内容有没有学习的必要？如何处理这些内容？学习这些内容的意义和价值何在？下面是我在教学中的思考和做法。