If you are not currently teaching students, there is a non-teaching format for this course. 请联系指导老师罗恩·克莱默 firstname.lastname@example.org 有关详细信息,.
分数可以是抽象的. 本课程努力使它们尽可能具体. 难度等级从简单地将形状切成两半, 第四项和第八项建立混合小数的三维模型. Students will engage in a variety of explorations using manipulatives to discover fractional relationships.
分数可以非常抽象和违反直觉. 分母越大，单位分数越小? 想象一下，两个数相乘，乘积比任何一个因子都小! 两个数除以后，商大于被除数! 帮助! (听起来像是《bet36365首页》里的情节.)
本课程努力使分数尽可能具体. 孩子们需要体验许多“真实世界”,通过动手练习来培养分数的数字意识. They need to divide things in half, measure liquids, weigh objects, play with toy clocks, etc.
The level of difficulty for the activities ranges from simply cutting paper shapes into halves, 四度, and eighths… to building three-dimensional models of mixed decimals using heavy grid paper, 剪刀, 和透明胶带.
As often as possible the student activities are presented as independent learning centers, 但可以很容易地作为整个班级的活动. 整个班级活动的一个缺点是需要足够的操纵. By working in a small group you only need enough manipulatives for five or six students at a time.
The course instructor is willing to work with you in modifying an activity to make it more appropriate to the needs of your students.
When children are taught abstract concepts without the conceptual development that comes from concrete interactions with manipulatives they often become confused. 困惑是沮丧和厌恶的根源. 在这种情况下，自尊会受到打击!
Working in small groups at learning centers has several important advantages that help ease the above problems:
- It encourages the interpersonal interactions of communication, sharing, teamwork, and responsibility.
This course is most appropriate for teachers of second grade through middle school, 特别是那些喜欢使用学习中心进行小组教学的学生. 喜欢集体授课的老师将能够教授这门课程, 但要想成功，他们需要有足够的操控能力.
This course may not be appropriate for teachers who prefer pencil, paper, and book-based activities.
“Teaching Elementary 数学 – Fractions” is designed to give abstract concepts a concrete, 经验背景, 在一个培养数学推理能力的小团体里. 即使是最简单的探索，学生们也被视为数学家, 收集数据, 比较和评价结果.
分数可以非常抽象. 本课程努力使它们尽可能具体. 难度等级从简单地将形状切成两半, 四度, and eighths… to building three-dimensional models of mixed decimals using heavy grid paper 和透明胶带. As often as possible the student activities are presented as independent learning centers, 但可以很容易地作为整个班级的活动.
- Collect/develop mathematical materials and manipulatives that engage students in interactive,探索性活动.
- 模型分数概念在各种各样的表示, 特别是, 初级水平的简单单位分数, 中等水平的等分和小数.
- Provide opportunities for students to engage in open-ended problem-solving using scientific method:
从探索中收集数据, 发布和评估数据, 寻找模式并组织数据，以找到缺失的解决方案.
This course aligns to the standards for: 2010 K-12 California’s Common Core Content Standards for 数学. Following are examples of some of the standards that are related to the activities in this course.
- Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- Add, subtract, multiply… decimals to hundredths, using concrete models or drawings.
罗恩·克雷默B.A., M.A. 在基础教育，小学数学和科学的重点
40岁:普通小学教师, 学区教职员培训师, 以及加州科学实施网络的开发人员.
作者和国家级数学会议的特邀演讲者. Recognized for exemplary work in the field of education by the Johns Hopkins Institute for the Academic Advancement of Youth.
My goal is to convince teachers of the importance of "discovery learning" using open-ended, 实践探索.
我喜欢和家人一起在家里做项目. I sing tenor in our church choir and volunteer tutor at Shriners Children's Hospital."