幼儿园至8年级 Curriculum Framework
幼儿园课程(张婕老师)期末整理
2012-2013学年第一学期幼儿园课程期末整理补充：我国关于学前儿童的重要教育文件：《幼儿园教育指导纲要（试行）》、《3——6岁儿童学习与发展指南》五大学科领域：健康、语言、科学、艺术、社会上海学前教育四大板块：生活、运动、游戏、学习1.课程：curriculum来源于拉丁语,其含义是“跑道”或者是“奔跑”。
用名词形式解释该词的含义，“跑道”即“学程”，其含义是为儿童设计的学习轨道。
用动词形式解释该词的词义，“奔跑”即“学习的过程”，其含义是儿童对自己学习经验的认识。
2.课程定义的维度(1) 学科（领域）维度：将课程看作是教学的科目，包含以文化遗产和科学为基础组织教学的各种课程形态。
学科课程注重学科科学体系，并根据学习者的发展特征和认识水平编制教材，让学习者进行系统的学习。
(2) 经验维度：以儿童主体性活动的经验为中心组织的活动，也叫做生活课程、活动课程、儿童中心课程，起源于杜威的进步主义教育思想。
经验课程以开发与培养主体内在的、内发的价值为目标，突出地将生活现实和社会课题，或者说以社区、经验、活动、劳动等作为内容编成，旨在培养丰富的具有个性的主体。
其基本着眼点是儿童的兴趣和动机，以动机为教学组织的中心。
(3) 目标维度：将课程定义为“预期行为的结构化序列”，把预期的学习结果和目标看作为课程的观念。
目标维度起源于博比特、查特斯的课程工学，后经泰勒等人发展。
(4) 计划维度：将课程定义为“学习者在学校指导下所获得全部经验的计划和方案”，以计划的维度界定课程，反应的是一种综合的倾向，通常包括对目的和特定目标的阐述，对内容的选择和组织，或者是暗含着或者显示着一定的学与教的类型，还包括对结果的评价方案。
3.课程的价值取向（课程的核心问题）（1）一元化课程与多元文化课程一元化课程：是一种“主流中心”的课程，是一种以占主导地位的民族的文化、历史、立场和经验为中心设置的课程。
多元化课程：将多元文化的影响注入课程和活动设计，尊重因民族、地域、家庭背景导致的文化差异。
EF英孚青少儿英语南京学校 课程体系
EF英孚青少儿英语南京学校课程体系针对不同的学员年龄，英孚设置了以下课程：Small Stars幼儿英语培训探索课程（3-6岁）High Flyers儿童英语培训腾飞课程（7-9岁）EF Trailblazers英孚少儿英语全项突破课程（10-14岁）EF Frontrunner青少年英语领先课程（15-18岁）一、Small Stars幼儿英语培训探索课程（3-6岁）英孚3-6岁幼儿英语探索课程是一项专为幼儿设计的基础性英语课程。
课程旨在培养孩子良好的语感，提高社交能力、精细动作和认知能力。
我们根据中国孩子不同的特点因材施教，交际教学法、全身反应教学法、故事教学法、任务教学法等多元化的教学手法，将牢牢抓住3-6岁孩子的注意力，帮助孩子高效学英语。
课程特色：A.科学教学体系巩固学习效果课程根据小学课标新标准，涵盖500多个核心英语单词，帮助孩子们拓宽词汇量。
我们的教材被英国文化协会ELTons创新大奖提名，配合英孚自主研发Efekta™学习系统，致力于培养孩子听说读写各项基础，提高学习效果。
贯穿课程始终的自然拼读法学习，帮助孩子通过学习字母和发音的对应联系，准确发音，学习拼读单词。
自主研发的iLab学习系统同步课堂学习内容，包括配套音视频、在线英语练习和趣味英语游戏，让孩子在课后也能巩固课堂所学。
B.多元教学法提高英语学习兴趣外籍培训师主持的Life Club主题活动，为孩子创建英文浸入式环境，让孩子在真实语境中锻炼口语，培养表达的自信。
课程配套歌曲，童谣、视频，手偶，英语词卡及互动白板等工具的综合使用，将多方位调动孩子的视听动三大感官，提高英语学习兴趣。
通过课后作业本、配套CD、卡通动画视频、APP互动游戏等工具，将语言学习空间从教室延伸至家中，打造360度浸入式语言学习环境。
C.丰富活动培养综合软技能课程根据3-6岁孩子的认知特点和学习习惯，基于大量调研，系统研发而成。
丰富的课堂游戏和小组活动，旨在培养孩子动手能力、社交技能、解决问题的能力、团队协作能力等综合软技能。
新标准英语第八册知识框架图(完整版)
M3
Story
Unit 1 He shouted, “Wolf, wolf!”
Module
Theme
Topic Sentence
Function
Target Language
Words and phrases
M6
English Newspaper
Unit 1 I’ll draw the pictures.
Unit 2 Let’s have a class party this Saturday!
M4
Music
Unit 1 Dad played theerhu.
Unit 2 I was very nervous.
Consolidating simple past
What did they play? Dad played theerhu. And Mum played thepipa.
concert, Chinese, CD, nervous, before, end, clap, proud, when
Consolidating future tense and the usage of “let’s”
I’ll draw the pictures. I’ll write the reports. What will you do, Sam? I will cut the paper.
report, stick, fantastic, meet
虫洞英语世界课程体系介绍
虫洞英语世界Amfa Kids课程体系介绍虫洞英语世界Amfa Kids课程体系专注于2-8岁儿童，包括拼读、单词、绘本阅读、数学、美德、艺术（戏剧、表演）、少儿编程、科学等八类课程，由京学教育研究院与美国西北大学、哈佛大学中外教育专家联合研发，配套开发了练习册、闪卡、教师指导手册、有声绘本、点读笔以及亲子指导手册等教学辅助资源，独家引进享誉北美的跨学科智能学习生态系统，让学生“穿梭世界，无边际”。
（一）全学科课程介绍拼读English Phonics拼读课程旨在帮助孩子识别和掌握26个大小写英文字母的发音以及在单词中的发音。
虫洞英语世界拼读课程英文字母进行拟人化，帮助孩子快速记忆；通过韵律诗、绕口令等形式，学习字母组合的识别和发音，掌握自然拼读的规律，做到见词即读；在朗读的过程中，培养整体语感和语言的灵活性。
征服拼读，英语发音不在话下。
单词English Vocabulary单词课程作为基本的英语启蒙，对帮助孩子建立和强化对英语语音、文字的认知和兴趣，培养对话意识，具有重要作用。
虫洞英语世界单词课程摒弃过去孤立、枯燥、乏味、低效的“死记硬背”模式，在各类情境主题中渗透敢于探索和尝试的概念，让孩子感受异国文化，灵活演练、学有所用、开拓眼界，自然掌握英语单词。
绘本阅读Picture Book Reading绘本阅读课程具有贴近儿童生活、图文并茂、生动有趣等特点。
虫洞英语世界精选众多适合中国儿童阅读的国外原版英文绘本，配备有声绘本、点读笔、外教讲绘本等增值产品及内容，让孩子察觉和掌握英语文字及其语音的特性，在阅读中得到智慧与心灵的启迪。
教师根据孩子测评结果及对应的Lexile蓝思值制定个性化阅读方案。
数学Mathematics数学是高符号化、高概括化的学科。
对于未达到抽象逻辑思维能力的幼儿来说，是一门深奥的课程。
虫洞英语世界数学课程注重让孩子在大量的操作活动中发现“数学”的规律，在此基础上举一反三，实现从被动学习变为主动学习，通过实物运算、到表象运算，最后达到抽象的符号运算。
剑桥少儿英语 幼儿园考级
剑桥少儿英语幼儿园考级Preschool Level Exams":The Cambridge Young Learners English exams are a series of fun and engaging English language assessments designed specifically for children aged 6-12. These exams, which include the Starters, Movers, and Flyers levels, provide a structured and supportive pathway for young learners to develop and demonstrate their English language skills. At the preschool level, the Starters exam is the perfect entry point, offering children aged 6-7 the opportunity to showcase their progress and build confidence in using English.The Starters exam is structured around three key papers – Listening, Reading and Writing, and Speaking. Each paper is carefully crafted to assess different aspects of a child's English language abilities, ensuring a comprehensive evaluation of their skills. The Listening paper, for example, tests a child's ability to understand simple instructions, identify key information, and follow basic conversations. The Reading and Writing paper, on the other hand, assesses their capacity to recognize familiar words, understand simple sentences, and engage in basic written communication.One of the standout features of the Starters exam is its focus on making the assessment process fun and engaging for young learners. The exam materials, including the question papers and accompanying audio, are designed with vibrant illustrations, colorful graphics, and relatable scenarios that capture the attention and imagination of the children. This approach not only helps to alleviate any potential anxiety or stress associated with the exam but also encourages the children to approach the assessment with a positive and enthusiastic mindset.Another key aspect of the Starters exam is its alignment with the Cambridge English Scale, a comprehensive framework that measures language proficiency on a continuous scale. This scale provides a clear and objective way to track a child's progress over time, allowing parents, teachers, and educational institutions to monitor their development and identify areas for further improvement. By achieving a specific score on the Cambridge English Scale, children can demonstrate their language abilities and potentially unlock new educational or career opportunities in the future.Preparing for the Starters exam is a collaborative effort between the child, their parents, and their teachers. At the preschool level, the focus is on creating a supportive and nurturing environment that encourages the child to explore and practice their English language skills. This may involve engaging in interactive activities, such as role-playing, storytelling, and singing, as well as regular practice with sample exam materials to familiarize the child with the format and expectations of the assessment.Parents play a crucial role in this process, providing encouragement, support, and opportunities for their child to use English in everyday situations. By incorporating English into the child's daily life, through activities like reading books, watching educational videos, or even having simple conversations, parents can help to reinforce the language skills being developed in the classroom.Teachers, on the other hand, are responsible for designing and implementing a comprehensive curriculum that aligns with the Starters exam syllabus. This may involve creating lesson plans that focus on the key language functions and skills assessed in the exam, as well as providing regular feedback and guidance to the children to help them progress. Additionally, teachers may organize mock exams or practice sessions to help the children become familiar with the exam format and build their confidence.The benefits of preparing for and taking the Starters exam extend far beyond the assessment itself. By engaging in the exam process, children develop a range of valuable skills and qualities that can support their overall academic and personal growth. These include improved communication abilities, enhanced problem-solving skills,increased self-confidence, and a greater appreciation for language learning.Furthermore, the Starters exam provides a tangible and recognized achievement that can be celebrated and shared with others. When a child successfully completes the Starters exam, they receive a certificate that acknowledges their accomplishment and can serve as a source of pride and motivation for further language learning. This recognition can also be valuable for parents and teachers, who can use it to demonstrate the child's progress and potentially open up new educational or extracurricular opportunities.In conclusion, the Cambridge Young Learners English: Starters exam is a comprehensive and engaging assessment that offers preschool-aged children the opportunity to showcase their English language skills in a supportive and fun-filled environment. By working collaboratively with parents and teachers, children can develop a strong foundation in English and unlock a world of educational and personal growth opportunities. As they progress through the various levels of the Young Learners exams, they will continue to build their language proficiency and confidence, preparing them for future success in their academic and professional pursuits.。
幼儿园教学大纲最新版
幼儿园教学大纲最新版1. 导言本教学大纲旨在对幼儿园教学内容进行规范和指导，确保教学活动的质量和效益。
该大纲适用于幼儿园各年级，包括幼儿园小班、中班和大班。
2. 教学目标本教学大纲的目标是帮助幼儿全面发展，培养他们的认知、语言、社会、情感和身体等方面的综合能力。
具体目标如下：- 发展幼儿的思维能力和创造力；- 培养幼儿良好的行为惯和社会交往能力；- 培养幼儿的听、说、读、写等语言表达能力；- 培养幼儿的运动技能和身体协调能力；- 培养幼儿的审美能力和艺术表达能力。
3. 教学内容幼儿园教学大纲的教学内容包括但不限于以下几个方面：- 身体素质与健康- 语言与文字- 数学与逻辑思维- 社会与人文- 科学与探究- 艺术与音乐4. 教学方法为了确保幼儿园教学活动的有效性和趣味性，我们采用多种教学方法，包括但不限于以下几种：- 游戏教学法- 动手实践教学法- 故事教学法- 观察与探究教学法- 合作研究法5. 教学评估为了对幼儿园教学效果进行评估，我们将采用多种评估方法，如观察记录、口头表达、作品展示等。
评估结果将帮助教师了解幼儿的研究情况，并对教学过程进行改进。
6. 教学资源为了支持幼儿园教学工作，我们将提供丰富的教学资源，包括教学用具、图书、音像资料等。
同时，教师应当根据幼儿的实际需要选择和利用相关教学资源。
7. 教学安全幼儿园教学活动应确保幼儿的安全和健康，教师应当制定相应的安全措施和应急预案，并加强对幼儿园教学环境的管理和监督。
8. 外文参考- Department of Education. Preschool Curriculum Guidelines. 2019.- Ministry of Education. Early Childhood Education Curriculum Framework. 2020.教学大纲的详细内容，请参考相关文件及政府教育部门发布的指导文件。
任何引用的内容必须经过确认。
ANZCA_Curriculum Framework
ANZCA Curriculum FrameworkDefinitionA curriculum framework is an organised set of learning outcomes which define the scope of content to be learned and what needs to be taught and assessed. The ANZCA Curriculum Framework aims to explicitly define, all aspects of contemporary practice of Fellows of the Australian and New Zealand College of Anaesthetists (FANZCAs) and will be used to plan and deliver all aspects of the ANZCA Training Programme (including its content, teaching, learning and assessment tools).Development ProcessTo develop this framework, the College adapted an internationally recognised and objectively researched framework used by many different medical specialties worldwide; the CanMEDS Curriculum Framework1. The ANZCA Curriculum Review Working Group (CRWG) coordinated the adaptation of this framework during the ANZCA Curriculum Review Project. During the review process consultation was sought regarding the ANZCA Curriculum Framework from all stakeholders, via an open submissions process, and from key stakeholders (i.e. ANZCA Fellows and Trainees), via a survey. Further amendments were also included following a review of other relevant curriculum frameworks, as well as input gathered from the ANZCA Trainee Committee and the ANZCA Regional/National Committees. Approval for the adoption of this framework was given by the ANZCA Education and Training Committee in February 2010, followed by ANZCA Council in April 2010.References1 Frank, JR. Ed. (2005). The CanMEDS 2005 physician competency framework. Better standards. Better physicians. Better car e Ottawa: The Royal College of Physicians and Surgeons of Canada.INTENTIONALLY BLANK PAGEMEDICAL EXPERTDefinition:As Medical Experts, FANZCAs integrate all of the ANZCA Roles, applying medical knowledge, clinical skills, and professional attitudes in their provision of patient-centred care. Medical Expert is the central Role in the ANZCA framework.Description:FANZCAs possess a defined body of knowledge, clinical skills, procedural skills and professional attitudes, which are directed to effective patient-centred care. They apply these competencies to collect and interpret information, make appropriate clinical decisions, and carry out diagnostic and therapeutic interventions. They do so within the boundaries of their discipline, individual expertise, the healthcare setting and the patient’s preferences and context. Their care is characterised by up-to-date, ethical, and resource-efficient clinical practice, as well as by effective communication in partnership with patients, other health care providers and the community. The Role of Medical Expert is central to the function of FANZCAs and draws on the competencies included in the Roles of Communicator, Collaborator, Manager, Health Advocate, Scholar and Professional.Key Competencies:FANZCAs are able to…1.Function effectively as specialists, integrating all of the ANZCA Roles to provide optimal, ethical and patient-centred medicalcare;2.Establish and maintain clinical knowledge, skills and attitudes appropriate to their practice;3.Perform a complete and appropriate assessment of a patient;e preventive and therapeutic interventions effectively;5.Demonstrate proficient and appropriate use of procedural skills, both diagnostic and therapeutic;6.Seek appropriate consultation from other health professionals, recognising the limits of their expertise.Enabling Competencies: FANZCAs are able to...1 Where anaesthesia encompasses perioperative/periprocedural care, including pre-, intra- and post- operative/procedural management.Enabling Competencies (continued): FANZCAs are able to...COMMUNICATORDefinition:As Communicators, FANZCAs effectively facilitate the doctor-patient relationship and the dynamic exchanges that occur before, during, and after the medical encounter.Description:FANZCAs enable patient-centred therapeutic communication through shared decision-making and effective dynamic interactions with patients, families, carers, other professionals and important other individuals. The competencies of this Role are essential for establishing rapport and trust, formulating a diagnosis, delivering information, striving for mutual understanding, and facilitating a shared plan of care. Poor communication can lead to undesired outcomes and effective communication is critical for optimal patient outcomes. The application of these communication competencies and the nature of the doctor-patient relationship vary for different specialties and forms of medical practice.Key Competencies:FANZCAs are able to…;1.Develop rapport, trust and ethical therapeutic relationships with patients and families22.Accurately elicit and synthesise relevant information and perspectives of patients and families2, colleagues and otherprofessionals;3.Accurately convey relevant information and explanations to patients and families2, colleagues and other professionals;4.Develop a common understanding on issues, problems and plans with patients and families3, colleagues and other professionalsto develop a shared plan of care;5.Convey effective oral and written information about a medical encounter.2 Where ‘families’ refers to the patients’ families, including significant others, carers and/or friends.Enabling Competencies: FANZCAs are able to...Enabling Competencies (continued): FANZCAs are able to...COLLABORATORDefinition:As Collaborators, FANZCAs effectively work within a healthcare team to achieve optimal patient care.Description:FANZCAs work in partnership with others who are appropriately involved in the care of individuals or specific groups of patients. This is increasingly important in a modern multiprofessional environment, where the goal of patient-centred care is widely shared. Modern healthcare teams not only include a group of professionals working closely together at one site, such as an operating theatre team, but also extended teams with a variety of perspectives and skills, in multiple locations. It is therefore essential for FANZCAs to be able to collaborate effectively with patients, families3, and an interprofessional team of expert health professionals for the provision of optimal care, education and scholarship.Key Competencies:FANZCAs are able to…1.Participate effectively and appropriately in an interprofessional healthcare team;2.Effectively work with other health professionals to prevent, negotiate, and resolve interprofessional conflict.3Where ‘families’ refers to the patients’ families, including significant others, carers and/or friends.Enabling Competencies: FANZCAs are able to...MANAGERDefinition:As Managers, FANZCAs are integral participants in healthcare organisations, organising sustainable practices, making decisions about allocating resources, and contributing to the effectiveness of the healthcare system.Description:FANZCAs interact with their work environment as individuals, as members of teams or groups, and as participants in the health system locally, regionally or nationally. FANZCAs function as Managers in their everyday practice activities involving co-workers, resources and organisational tasks, such as care processes and policies as well as balancing their personal lives. Thus, FANZCAs require the ability to prioritise, effectively execute tasks collaboratively with colleagues, and make systematic choices when allocating finite healthcare resources. The ANZCA Manager Role describes the active engagement of all FANZCAs as integral participants in decision-making in the operation of the healthcare system.Key Competencies:FANZCAs are able to…1.Participate in activities that contribute to the effectiveness of their healthcare organisations and systems;2.Manage their practice and career effectively;3.Allocate finite healthcare resources appropriately;4.Serve in administration and leadership roles, as appropriate.Enabling Competencies: FANZCAs are able to...HEALTH ADVOCATEDefinition:As Health Advocates, FANZCAs responsibly use their expertise and influence to advance the health and well-being of individual patients, communities, and populations.Description:FANZCAs recognise their duty and ability to improve the overall health of their patients and the society they serve. They identify advocacy activities as important for the individual patient, for populations of patients and for communities. Individual patients need FANZCAs to assist them in navigating the healthcare system and accessing the appropriate health resources in a timely manner. Communities and societies need FANZCAs’ special expertise to identify and collaboratively address broad health issues and the determinants of health. At this level, health advocacy involves efforts to change specific practices or policies on behalf of those served. Framed in this multi-level way, health advocacy is an essential and fundamental component of health promotion. Health advocacy is appropriately expressed both by individual and collective actions of FANZCAs in influencing public health and policy.Key Competencies:FANZCAs are able to…1.Respond to individual patient health needs and issues as part of patient care;2.Respond to the health needs of the communities that they serve;3.Identify the determinants of health of the populations that they serve;4.Promote the health of individual patients, communities and populations.Enabling Competencies: FANZCAs are able to...SCHOLARDefinition:As Scholars, FANZCAs demonstrate a lifelong commitment to reflective learning, as well as the creation, dissemination, application and translation of medical knowledge into practice.Description:FANZCAs engage in a lifelong pursuit of excellence in the practice of anaesthesia. As learners, they recognise the need to be continually learning and modelling this for others. Through their scholarly activities, they contribute to the creation, dissemination, application and translation of medical knowledge. As teachers, they facilitate the education of their students, patients, colleagues, and others.Key Competencies:FANZCAs are able to…1.Maintain and enhance professional activities through ongoing learning;2.Critically evaluate information and its sources and apply this appropriately to practice decisions;3.Facilitate the learning of patients, families, students, trainees, other health professionals, the public, and others, as appropriate;4.Contribute to the creation, dissemination, application, and translation of new medical knowledge and practices.Enabling Competencies: FANZCAs are able to...PROFESSIONALDefinition:As Professionals, FANZCAs are committed to the health and well-being of individuals and society through ethical practice, profession-led regulation, and high personal standards of behaviour.Description:FANZCAs have a unique societal role as professionals who are dedicated to the health and caring of others. Their work requires the mastery of a complex body of knowledge and skills, as well as the art of medicine. As such, the Professional Role is guided by codes of ethics and a commitment to clinical competence, the embracing of appropriate attitudes and behaviours, integrity, altruism, personal well-being, and to the promotion of the public good within their domain. These commitments form the basis of a social contract between a FANZCA and society. Society, in return, grants FANZCAs the privilege of profession-led regulation with the understanding that they are accountable to those served.Key Competencies:FANZCAs are able to…1.Demonstrate a commitment to their patients, profession, and society through ethical practice;2.Demonstrate a commitment to their patients, profession, and society through participation in profession-led regulation;3.Demonstrate a commitment to their own health and sustainable practice.Enabling Competencies: FANZCAs are able to...。
OECD_国家幼小衔接课程设计的经验与启示——基于幼、小课程纲要的分析
收稿日期:2023-02-28基金项目:中国基础教育质量监测协同创新中心课题项目‘科学幼小衔接背景下儿童入学准备评价研究“(项目编号:2022-02-009-BZPK01);华东师范大学学前教育学系第二届安乔科研基金项目‘幼小衔接课程设计的国际经验 基于学前课程纲要的分析“(项目编号:ECEAQFH203)㊂通讯作者:李召存,E-mail:zcli@OECD 国家幼小衔接课程设计的经验与启示 基于幼㊁小课程纲要的分析徐昭媛1,2,李召存1,2(1.华东师范大学教育学部,上海200062;2.中国基础教育质量监测协同创新中心华东师大分中心,上海200062)摘㊀要:2021年教育部发布了‘关于大力推进幼儿园与小学科学衔接的指导意见“,幼小衔接成为两个学段共同关注的问题㊂为了更好地落实基于儿童发展连续性的幼小双向衔接,本文以OECD 国家学前教育和小学教育的课程纲要文本为基础,从课程的角度探讨了幼小衔接课程设计的国际经验㊂通过对OECD 国家课程纲要政策文本的分析,梳理幼小衔接课程观㊁课程设置㊁课程目标㊁课程内容㊁课程实施和课程评价中的连续性课程设计逻辑㊂提出我国幼小衔接课程设计儿童为本的课程衔接观㊁儿童经验导向的课程实施㊁幼小协同合作的课程编制㊁连续性的课程评价机制四方面的建议㊂关键词:幼小衔接;课程设计;课程纲要;儿童发展连续性中图分类号:G61㊀㊀文献标识码:A㊀㊀doi :10.3969/j.issn.1005-2232.2023.04.007一㊁问题提出2020年中共中央‘关于制定国民经济和社会发展第十四个五年规划和二ʻ三五年远景目标的建议“中提出了 建设高质量教育体系 的目标㊂近年来,我国学前教育质量不断提升,义务教育质量在2022年发布的新课程标准推动下,也将迎来又一个质量提升的契机㊂在此基础上,如何加强两个学段之间的衔接,就成为建设高质量教育体系的重要一环㊂高质量幼小衔接对儿童早期发展及后续教育质量的重要作用也已成为国际共识,2017年,经济合作与发展组织(OECD)发布了‘强势开端Ⅴ:幼小衔接“(Starting StrongⅤ:Transitions From Early Childhood Education and Care to Primary Educa-tion)报告,聚焦OECD 国家在设计㊁实施㊁管理和监测幼小衔接中的过渡经验㊁挑战与应对,关注学前教育质量的延续,强调学段之间过渡的连续性(continuity)㊂该报告指出: 适当且一致的课程指导下的高质量过渡,将提高学前教育积极影响持续到小学和以后的可能性 [1]㊂课程是支持儿童持续性发展的重要载体,是学前教育质量监测的重要指标,课程质量的高低直接关系到儿童的学习和发展[2],幼儿园和小学在课程设置上的差异被认为是过渡时期最主要的差异之一[3]㊂连续一致的课程可以为儿童的学习与发展提供一致㊁渐进和全面的支持,是幼小衔接工作开展的保障,同时也可为后继29 第20卷㊀第4期2023年8月㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀Journal of Schooling Studies ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀Vol.20,No.4㊀㊀Aug.2023教育阶段奠定基础㊂2021年,教育部颁布‘关于大力推进幼儿园与小学科学衔接的指导意见“(以下简称‘指导意见“),首次提出幼儿园与小学 双向衔接 ,强调幼儿园与小学协同合作,科学做好入学准备和入学适应㊂但我国幼儿园和小学在学制上缺乏联系,缺少一体化的顶层设计,幼儿园以游戏为基本活动与小学分科教学的课程设计存在一定差异㊂在两个学段课程差异的现实背景下,幼小协同合作应以何为基础, 双向衔接 中幼小应分别承担什么任务,如何缩小两个学段的差异以增进教育的连续性,都将是学前教育工作者需要思考和回应的问题㊂课程纲要作为政府层面指导课程发展的政策文件,既体现着教育理论的指导性,同时也对课程设计与实施有一定规定性㊂通过顶层设计确保两个学段课程的连续性和一致性,有助于缩小两个学段间的差异,减缓学段间的衔接坡度,为开展幼小双向衔接提供抓手㊂OECD国家在幼小衔接连续性方面进行了积极探索,‘强势开端Ⅴ:幼小衔接“中课程与教学连续性是OECD国家成功过渡的重要经验领域㊂本研究在此基础上检索相关国家的幼小课程纲要政策文本,通过文本分析探索幼小衔接中的连续性经验㊂各国在指称 课程纲要 这一概念时有不同的表述,如 national curriculum guideline national curriculum framework national curriculum standards 等,但总体代表着全国(地区)范围内的一个共识性的课程愿景或课程发展框架[4]㊂通过对19个不同OECD国家(地区)的30余份学前和小学的课程纲要(见表1)的考察,从课程理念㊁课程设置㊁课程目标㊁课程内容㊁课程实施和课程评价六个方面分析其中幼小衔接课程设计的逻辑,为我国幼小衔接课程的设计及幼小衔接实践提供一定参考㊂表1㊀部分OECD国家幼儿园和小学课程纲要国家(地区)幼儿园课程纲要小学课程纲要澳大利亚‘早期学习框架“(BELONGING,BEING&BECOMING The EarlyYears Learning Framework for Australia)‘澳大利亚课程“(The Australian Curriculum)爱尔兰‘Aistear:幼儿教育课程框架“(Aistear:the Early Childhood Cur-riculum Framework)‘小学课程“(Primary School Curriculum)挪威‘幼儿园内容和任务框架计划“(Framework Plan for the Contentand Tasks of Kindergartens)‘国家中小学教育和培训知识促进课程“(The National Cur-riculum for Knowledge Promotion in Primary and Secondary Edu-cation and Training(Kunnskapsløftet))瑞典‘学前教育课程“(Curriculum for the Preschool)‘2011年义务教育学校㊁学前班和娱乐中心课程大纲“(Cur-riculum for the Compulsory School,the Preschool Class and the Out of School Centre2011)芬兰‘幼儿园教育与保育国家核心课程“(National Core Curriculumfor Early Childhood Education and Care)学前教育国家核心课程“(National Core Curriculum for Pre-primary Education)‘基础教育国家核心课程2014“(National Core Curriculum forBasic Education2014)新西兰‘编席子:学前课程“(Te Whāriki:Early Childhood Curriculum)‘新西兰课程“(The New Zealand Curriculum)毛利语学校课程“(the National Curriculum for Maōri medium Schooling)丹麦‘强化教学课程“(The Strengthened Pedagogical Curriculum)‘小学各年级(包括学前班)共同目标“Fælles Mål(Common Objectives)for Each Grade in Primary School,Including Preschool Class法国‘学前教育:一个独特的周期,所有人成功的基础“(Preschool:A Unique Cycle,Fundamental for the Success of All)‘基本学习周期,巩固周期和深化周期的教育方案“(Curricu-lum of the Fundamental Learning Cycle(cycle2,6to8yearsold),the Cycle of Consolidation(cycle3,9to11years old)andthe Cycle of Deepening(cycle4,since12years old))日本‘幼稚园教育要领“‘小学校学习指导要领“韩国‘努里课程“(Nuri Curriculum)‘中小学国家课程“(The National Curriculum for the Primary and Secondary Schools)39徐昭媛,等.OECD国家幼小衔接课程设计的经验与启示(续表1)国家(地区)幼儿园课程纲要小学课程纲要美国(新泽西州)‘新泽西州幼儿园实施指南“(New Jersey Kindergarten Implemen-tation Guidelines)‘新泽西州核心课程内容标准“(New Jersey s Core CurriculumContent Standards)英国(英格兰)‘学前基础阶段法定框架“(Statutory Framework for the Early Years Foundation Stage)英国(威尔士)‘基础阶段课程框架“(Curriculum for Wales-Foundation Phase Framework)德国‘各州关于儿童日托机构早期教育的共同框架“(National Framework for Early Education in Kindergarten)奥地利‘初等教育机构课程框架“(Framework Curriculum for ECEC In-stitutions in Austria)卢森堡‘基础教育学习计划“(National Curriculum for Fundamental Education)意大利‘学前教育与第一周期教育课程的国家指导方针“(National Curriculum Guidelines for Preschool and First Cycle of Education)‘国家指标和新方案2018“(National Guidelines and New Scenarios(Indicazioni nazionali e nuovi scenari2018)英国(苏格兰)‘卓越课程“(Curriculum for Excellence)‘卓越课程:从学前到小学的过渡“(Curriculum for Excellence:Preschool into Primary Transition)波兰‘学前教育和单一结构小学核心课程“(Core Curriculum for Pre-school and General Education in Individual Types of Schools)二㊁OECD国家课程纲要中幼小衔接课程设计的经验(一)幼小衔接课程观连续性和一致性的课程是儿童学习与发展连续性的支持,是开展幼小衔接的载体;儿童学习与发展的连续性则是连续一致课程的基础,是实施幼小衔接的抓手㊂正如日本在‘幼儿园教育与小学教育的顺畅衔接(报告)“中所指出的, 为了促进幼儿园和小学的衔接,首先需要确定一个途径,即根据儿童发展和学习的连续性来理解学前教育和小学教育之间的关系 [5]㊂通过对国际幼小课程纲要的分析,可以看出其以儿童为本,坚持课程连续性与一致性的课程理念㊂儿童学习与发展的连续性本质是儿童经验的连续性㊂澳大利亚‘早期学习框架“指出要提供连续性经验确保儿童顺利过渡,新南威尔士州将儿童学习的连续性作为支持顺利过渡的关键,强调将儿童及其经验置于教育连续体,尤其是衔接实践的中心㊂爱尔兰‘小学课程“的课程原则强调儿童知识经验的重要性,认为儿童的现有经验是获得新理解的起点,使儿童能够从已知到未知,从简单到更复杂,从具体到抽象,形成有效的㊁连贯的和相关的学习经验㊂ 儿童之前的学习㊁自我价值和身份认同是建立在他们从家庭到学前班,再到小学阶段的过程中的,这为他们进入小学后的学习奠定了重要基础 [6]㊂ 了解儿童对其过渡过程经验的看法对于开展过渡实践至关重要 [7],以儿童为本的课程衔接观要以儿童的兴趣㊁需要让儿童积极参与到课程建设中㊂挪威‘幼儿园内容和任务框架计划“明确提到了儿童的参与权,鼓励儿童表达自己的想法和意见,尊重儿童的意图和经验, 儿童是最重要的行动者,发展和活动的起点必须是儿童的经历和观点 [8]㊂丹麦要求课程中必须包含儿童的观点,必须考虑到儿童的年龄和成熟程度,让儿童自然地参与到课程与评估中[9]㊂基于儿童观点㊁兴趣㊁动机和问题的过渡,有助于儿童从自身的角度理解其日常生活体验,也会促使儿童更加积极地参与到自身建设中,更有助于儿童的顺利过渡㊂在以儿童为本的理念导向下,许多国家(地区)关注幼小衔接中儿童学习与发展的连续性,在学49基础教育前课程纲要中明确规定了课程连续性的要求,在课程目标㊁内容㊁实施㊁评价等方面也均体现出儿童的连续性特点㊂挪威的课程纲要规定了幼儿园和小学课程的联系,强调两个学段要有一致的价值观与相似的学习领域㊂澳大利亚两个学段的课程中始终坚持整体主义的理念,强调儿童发展的整体性,‘早期学习框架“要求幼儿园教学要 采用整体主义的教学方式 ,‘澳大利亚课程“将课程分为学习领域㊁一般能力和跨课程优先事项三个维度,其中学习领域包含8个领域的多门学科,这些领域或学科都有共同的内容,领域㊁学科和其他维度相互联系,也体现了整体主义的课程理念㊂连续性课程框架不仅支持从幼儿园到小学的平稳过渡,还能确保学习方法聚焦于适合儿童的发展水平,而不是从一个阶段到另一个阶段的重复[10]㊂(二)幼小衔接课程设置OECD 对成员国的调查报告显示,78%的国家学前阶段和小学阶段的课程是具有连续性的;54%的国家明确将两个阶段的课程保持一致;而24%的国家则将两个学段的课程进行整合,形成了完全整合的课程设置㊂从课程整合的角度分析不同国家(地区)课程纲要,可以将其分为分段课程㊁衔接课程㊁一体化课程三种类型(如图1)㊂图1㊀幼小衔接课程设置的三种类型㊀分段课程是指幼儿园和小学遵循两份不同的课程纲要,教育实践中采用两种不同的课程框架㊂为了顺利从幼儿园过渡到小学,学前阶段根据‘幼稚园教育要领“制定了 接近课程 (Approach Cur-riculum),小学阶段根据‘小学校学习指导要领“制定了 开端课程 (Start Curriculum),以儿童学习与发展的连续性为基础,将连贯性和一致性的教育理念渗透两套课程中㊂幼小衔接课程以 教育目的和目标-课程-教育活动 的三层结构为基础,培养儿童学习的基本技能,使其在学前和小学低年级阶段形成学习独立㊁生活独立㊁精神独立的 三种独立 能力,并在此基础上通过小学及以后的教育形成终身学习的基础[11]㊂新西兰学前阶段的课程‘编席子“和基础教育阶段课程‘新西兰课程“有一致的愿景和原则,‘编席子“中的幸福健康㊁归属感㊁贡献㊁交流㊁探索五大发展线索与‘新西兰课程“中关键能力㊁价值观㊁学习领域三方面相连接,从儿童的学习品质出发制定相应的课程标准,从不同的角度考虑儿童的学习目标与学习成果,使学前阶段与基础教育阶段得以很好的衔接[12]㊂衔接课程是指在学前教育和小学教育之间设置的专门的衔接课程,这种课程一般在学前教育的后一两年和小学的前一至三年实施㊂美国强调在学前教育与小学之间建立更强联系的重要性,将0-8岁早期儿童的教育分为两个阶段,设置了称为 PK-3 或 0-8 的课程㊂第一阶段是学前教育学段(Preschool),面向0-5岁的儿童;第二阶段是K 学段到小学3年级(K-3),面向5-8岁的儿童,其中专门设有面向5-6岁儿童的K 学段(Kindergarten),从学制上聚焦幼小衔接阶段的特殊性㊂美国没有全国统一的课程标准,但每个州都有自己的课程框架,如新泽西州在‘新泽西州K 学段实施指南“中强调各年级之间适宜性发展课程的协调,提出在达到总体内容领域目标的同时,课程应有目的地将有意义的技能和概念从多个内容领域整合成每次的学习经验,为学龄前到三年级的儿童提供不间断的教学实践和概念发展,使之成为连续性课程的一部分㊂英国威尔士制定了面向3-7岁儿童的基础阶段(Foundation Phase,FP)课程,课程连接学前教育和小学教育,旨在支持两学段之间的顺利过渡㊂一体化课程是指儿童从学前(出生)到小学(中学)的课程设置,不同地区的一体化课程在儿童年龄方面有不同要求,但本质是无论儿童处于哪一教育阶段,使用的都是同一个课程框架㊂意大利‘学前教育与第一周期教育课程的国家指导方针“涵盖了儿童从幼儿园到小学再到初中的发展目标和59 徐昭媛,等.OECD 国家幼小衔接课程设计的经验与启示基础教育经验领域,为儿童在学科或经验领域的发展设定了总体目标㊁学习目标和相关目标,使学前教育课程小学课程的目标保持一致,由此发展与经验和学科领域相关的技能㊂英国苏格兰的‘卓越课程“则面向3-18岁的儿童设置了一套连贯课程,其中幼小衔接期从三岁到一年级,通过发展儿童的学习素养与各项能力来帮其顺利实现从学前教育到小学教育的过渡㊂(三)幼小衔接课程目标幼小衔接课程目标是幼小衔接课程的基本导向和遵循,是期望儿童达到的理想发展水平或状态㊂在对幼小课程纲要的分析中,主要有聚焦儿童入学准备的近景目标和指向儿童终身学习远景目标㊂聚焦儿童入学准备的课程目标主要目的是帮助儿童顺利地从学前阶段过渡到小学阶段,根本旨归是通过课程发展儿童进入小学所需的各项能力,关注儿童在下一学段的学习与发展,以期通过学前教育为儿童接受小学教育乃至后续阶段的教育打下坚实基础㊂卢森堡的学前教育和小学教育处于不同周期,每个周期的目标和发展成果之间环环相扣,学前期的不同领域要达到的核心能力是过渡到小学所需的技能㊂芬兰‘国家学前教育核心课程“的课程目标认为每个孩子从学前教育到基础教育的学习路径是一个基于儿童需求的灵活连续体,学前教育是为小学教育做准备的,学前阶段的课程主要聚焦儿童入学准备,发展儿童入学所需的各项要求㊂瑞典的学前班作为过渡阶段,其目标和核心内容则是朝着义务教育所提出的知识标准的方向发展,由此保证学生学习与发展的连续性[13]㊂学前教育是为义务教育和后续基础教育奠基的场所,学前教育的目标是培养基本的学习技能,让儿童为进入小学做好准备,要求学前和小学在适合发展的学习环境中为儿童做好准备㊂指向儿童终身学习的课程目标将幼小衔接阶段置于整体的教育体系中,主张整个教育体系中教育理念的贯通,强调课程目标的连贯性㊂在日本以连续性和连贯性为基础的教育哲学的影响下,学前教育被看作是为人的终身人格的形成奠定基础,‘幼稚园教育要领“的课程目标是 培养终身人格发展的基础 ,‘小学校学习指导要领“规定义务教育以 发展每个人的能力 培养在社会中独立生活的基础 培养符合国家和社会的基本素质,成为社会的合格成员 为目标[14],两个学段都是以个人和社会成员的理想状态为目标㊂意大利一体化的课程设置对儿童终身发展的目标要求更明确,课程纲要指出课程的核心是促进儿童的基本技能,如认知㊁情感㊁社交等方面的发展,这些技能是每个儿童成长的基础㊂奥地利课程框架强调了终身学习的原则以及教育过程连续性的重要性,其目的是使学前教育和小学教育在对教育的理解上达成共识,在此基础上实现教育过程的连接㊂新西兰和德国的课程目标是建立在对教育的共同理解的基础上的,新西兰注重教育连续性和终身学习,德国旨在通过教育促进儿童的整体人格的发展㊂(四)幼小衔接课程内容课程内容是整个课程设计的核心㊂学前教育阶段以游戏为主要活动,小学阶段以学科教学为主要内容,儿童在两个阶段的学习方式不同,从幼小衔接课程连续性的角度来分析,学科或领域导向的课程内容聚焦学科知识的交叉整合,儿童能力发展导向的课程内容侧重儿童学习结果的拓展延伸㊂学科或领域导向课程内容㊂以连续性为基础的分阶段的课程内容,这类课程内容遵循连续性的课程设计逻辑,虽在学前教育和小学教育中有不同科目,但其中的内容有交叉或涵盖㊂日本‘小学校学习指导要领“中也明确规定,特别是在小学一年级,生活㊁日语㊁音乐㊁图画工作四科在制定教学计划和教学内容时要结合幼儿园教育的相关内容㊂此外,为促进幼小衔接,日本专门设置了生活科课程, 扮演着从以游戏为中心的幼儿教育可以顺利衔接培育学力的小学教育的桥梁 [15]㊂挪威学前教育和小学教育在课程框架上是两个独立的体系,但学前教育的大多数学习领域与小学教授的科目一致,‘幼儿园内容和任务框架计划“以类似于小学课程的方式定义了学习领域,促成了两个学段在学习领域上的衔接㊂此外,框架还要求幼儿园和小学应相互提供有关活动的共同信息㊂韩国学前阶段的69徐昭媛,等.OECD国家幼小衔接课程设计的经验与启示Nuri课程是五大领域体验式的综合课程,小学阶段则调整了课程内容的组织方式,以一种系统的方式获得每个学科的基础和基本元素,形成科目或学科群以连接不同年级,还通过创造性的体验活动来帮助小学一年级的学生顺利过渡㊂如果说以上国家在两个学段课程内容衔接的要求主要体现在学科领域上,那么法国幼小课程内容的衔接则具体到了主题内容上, 在幼儿园,儿童通过实际操作和体验建立了相关的知识体系,包括几种形状和大小㊁平面图形㊁空间数量等,这些知识构成了学习小学几何和测量的第一种方法 [16]㊂不仅指出了儿童在不同学段的学习方式,更是明晰了两个学段的相同主题但知识深度渐进的课程内容㊂儿童能力发展导向的课程内容㊂这类课程内容的组织以儿童能力发展为目标,幼儿园课程内容是儿童能力发展的奠基,小学课程内容则是儿童能力的深化拓展㊂如苏格兰‘卓越课程“将学前两年(3-4岁儿童)到小学一年级(5岁儿童)的儿童早期的保育和教育作为一个单元,聚焦于儿童的价值观㊁社交能力㊁规则意识等核心素养的发展与能力提升,建立了相同的课程组织㊁学习经验和相关标准㊂新西兰的学前阶段‘编席子“中课程内容以五大领域和发展目标的形式呈现,小学阶段‘新西兰课程“以关键能力和学习领域的形式呈现,但小学课程的关键能力和学习领域是建立在幼儿园课程学习结果的基础之上的,这也是两个学段课程联系的起点㊂卢森堡的基础教育分为四个周期,第一周期是学前教育,第二至第四周期为小学教育,‘基础教育学习计划“根据一致的教育原则确定了四个周期的学习领域,使四个周期在不同领域的学习是连贯的,如第一周期中有 用感官发现世界 的内容,在第二㊁第三周期则是 科学意识 ,到了第四周期则是 人文与自然科学 ,以此来确保课程内容的连续性[17]㊂爱尔兰在幼小衔接的课程内容上以关键知识和技能点为基础,两个学段在幼儿园向小学过渡的关键知识和技能方面达成一致,重点强调社交和情感技能,沟通和语言技能,积极的学习倾向等㊂由于这些能力在儿童的学习中发挥着核心作用,因而以学习成果的形式嵌入从幼儿园到小学的所有课程领域和科目中,使整个课程贯通且具相关性,这样各课程领域不仅有助于儿童关键能力的发展,也有助于儿童进入小学后学习的连续性和连贯性[18]㊂这两种不同取向的课程内容的设计是课程内容选择的基本取向,幼小衔接课程内容的设计既要考虑到知识的分类整合,也要考虑到儿童能力的发展,其根本是促使儿童在学习与发展中的经验的获得与延续㊂(五)幼小衔接课程实施由于学前阶段和小学阶段有着不同的教育目标和任务,学前教育主要是儿童的保育与教育,而小学教育则倾向于知识的学习,两个阶段不同的任务导致了其不同的教育方式,在课程实施上也有所不同㊂但通过对国前课程纲要的分析,OECD国家为了更好地推进幼小衔接,通常采取以游戏为基础的课程实施方式,采用符合儿童发展特点的实施策略㊂以游戏为基础的实施方式㊂基于幼小衔接课程中做好两个学段的衔接工作,就要采用灵活的实施方式㊂游戏是最适合学前儿童的活动方式,是一种让儿童积极参与并体验关系的活动方式,是培养儿童早期学习与发展课程的重要组成部分㊂在北爱尔兰,小学一年级和二年级(4-5岁儿童)采用以游戏为基础的发展适宜性课程,缓解了儿童从学前教育到小学的过渡㊂苏格兰‘卓越课程:从学前到小学的过渡“是对‘卓越课程“中幼小衔接理念与相关举措的强调,其中指出在小学教育低学段要延续学前教育课程实施中的方式方法,使儿童通过有目的㊁有计划的游戏来学习,将游戏教学的衔接理念渗透在两个学段的教育中[19]㊂奥地利为了实现教育过程的连接,非常重视学前和小学教育学习方法的连续性, 在游戏中学习 被定位在小学课程推荐的学习形式的首位,强调学习要建立在儿童已经获得的有一定差异性能力的基础上,实施开放的㊁以项目为导向的㊁以发现为基础的学习,儿童玩游戏的乐趣增加了他们学习的动力,这种对游戏的要求是教育机构之间成功过渡的重要组成部分[20]㊂79。
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The 2009 Mathematics Curriculum Framework can be found in PDF and Microsoft Word file formats on the Virginia Department of Education’s Web site at .
NOTICE
The Virginia Department of Education does not unlawfully discriminate on the basis of race, color, sex, national origin, age, or disability in employment or in its educational programs or services.
Virginia Mathematics Standards of Learning Curriculum Framework 2009 Introduction
The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students should learn. Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for each standard. The Curriculum Framework is divided into three columns: Understanding the Standard; Essential Understandings; and Essential Knowledge and Skills. The purpose of each column is explained below. Understanding the Standard This section includes background information for the teacher (K-8). It contains content that may extend the teachers’ knowledge of the standard beyond the current grade level. This section may also contain suggestions and resources that will help teachers plan lessons focusing on the standard. Essential Understandings This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the Standards of Learning. In Grades 6-8, these essential understandings are presented as questions to facilitate teacher planning. Essential Knowledge and Skills Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills that define the standard. The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.
Mathematics Standards of Learning Curriculum Framework 2009: Kindergarten
FOCUS K–3
STRAND: NUMBER AND NUMBER SENSE
GRADE LEVEL K
Students in grades K–3 have a natural curiosity about their world, which leads them to develop a sense of number. Young children are motivated to count everything around them and begin to develop an understanding of the size of numbers (magnitude), multiple ways of thinking about and representing numbers, strategies and words to compare numbers, and an understanding of the effects of simple operations on numbers. Building on their own intuitive mathematical knowledge, they also display a natural need to organize things by sorting, comparing, ordering, and labeling objects in a variety of collections. Consequently, the focus of instruction in the number and number sense strand is to promote an understanding of counting, classification, whole numbers, place value, fractions, number relationships (“more than,” “less than,” and “equal to”), and the effects of single-step and multistep computations. These learning experiences should allow students to engage actively in a variety of problem solving situations and to model numbers (compose and decompose), using a variety of manipulatives. Additionally, students at this level should have opportunities to observe, to develop an understanding of the relationship they see between numbers, and to develop the skills to communicate these relationships in precise, unambiguous terms.