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·克雷默 firstname.lastname@example.org 有关详细信息,.
Fractions can be abstract. 本课程努力使它们尽可能具体. 游戏的难度从简单地将形状切成两半不等, 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.
From the 教练
分数可能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，乘积小于任何一个因子! 除以两个数，商大于被除数! 帮助! (听起来像是《德甲联赛下注app》中的情节.)
本课程努力使分数尽可能的具体. 孩子们需要经历许多“真实的世界”,为了培养分数的数字感而进行的实践活动. 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全班活动讲授. 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:
- Less manipulatives are needed.
- It develops independent skills.
- It encourages the interpersonal interactions of communication, sharing, teamwork, and responsibility.
This course is most appropriate for teachers of second grade through middle school, 尤其是那些喜欢使用学习中心进行小组教学的人. 喜欢集体教学的老师可以教授这门课, 但要想成功，他们需要对整个班级有足够的操纵力.
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, experience-based context, 在一个培养数学推理的小组中. 即使是最简单的探索，学生们也被当作数学家看待, 收集数据, 比较并评价结果.
Fractions can be very abstract. 本课程努力使它们尽可能具体. 游戏的难度从简单地将形状切成两半不等, 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全班活动讲授.
- Collect/develop mathematical materials and manipulatives that engage students in interactive,exploratory activities.
- 在各种演示中建模分数概念, 特别是, 初级阶段的简单单位分数, 以及等效的普通分数和十进制分数.
- Provide opportunities for students to engage in open-ended problem-solving using scientific method:
从探索中收集数据, posting and evaluating the data, 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.
40岁:普通小学教师, school district staff trainer, 加州科学实施网络的开发人员.
作者和国家数学会议的客座发言人. 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, hands-on explorations.
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."