初中数学教学案例分析 ——趣味课堂外文翻译资料

初中数学教学案例分析

——趣味课堂

原文作者：John A. Van de Walle

单位：Late of Virginia Commonwealth University

摘要：建立问题解决型课堂的步骤：确定数学内容和学习目标；考虑你的学生们的需要；选择，设计，或者采用一项任务；设计课程评估。计划课堂的前阶段。

关键词：目标； 需求； 设计；评估：计划

第一步：确定数学内容和学习目标。你如何确定你的学生要学什么数学知识？每个州有自己的教学标准。许多州采用了《共同核心州立标准》，由年级平均水平来确立数学内容。教师利用他们的教科书和其他资源来确定教学目标。一个单元的设计的每一堂课都是为了实现本单元更大的目标。事实上，在教学计划中，一直关注于更大的数学教学目标比学习到小技巧来得更加重要。从课程水平出发，“当一堂课结束时，我的学生们能学会什么”这是很重要的。牢记一节课能够花上几天去完成。当你回答这个问题的时候，请确保你的注意力放在数学上而不是你想做的活动上。

第二步：考虑你的学生们的需要。关于挑选好的数学教学内容，你的学生们已经了解或者理解多少？也许在你教学内容上，他们已有一些经验基础，但是课堂是为了扩大或精炼学生知识层面。确保你第一步当中确定的教学内容包含一些新知识或者至少对你的学生而言有些陌生的知识。同时要确定你给出的学习目标不是遥不可及的。考虑个别学生的需要，包括学习障碍和每个学生的优缺点。另外，语言和文化也必须考虑在内。关于这个话题，学生已经知道了什么？这可以作为一个发布点。对于某一范围的学生，什么难度的知识是适合他们的？有什么学习代沟或误区需要解决？拿些视觉效果或者模型可以帮助学生理解？需要哪些名词支持？

第三步：选择，设计，或者采用一项任务。根据设想好的教学目标和学生基础，你应该考虑好你将要主要使用哪种教学手段，可能是一项任务、活动或是可能在你练习册上的练习题。选择一个有价值的任务的重要性不能被夸大。看看数学教学专业标准三，这是在需要重要考虑的列表之内。回想第三章，以下几点使一项任务更加有价值：认知需要水平、多个出入点、学生的相关因素。因为任务的选择已经完成，这里只是简明的提及。你要问自己，“你正在考虑的任务(从课本或任何其他来源)能完成第一步中制定的预期目标内容和满足第二步中制定的我的学生们的需求吗？”和“这个任务有价值吗？”。如果答案是“是”，那么你可以计划着做小小的适应来提高课堂，比如使用不同的更加贴近学生的背景或者创建一座连接儿童文学的桥梁。如果你发现这个任务并不符合你的教学内容和学生的需求,那么你将要针对任务做出实质性修改或找到一个新的任务。

第四步：设计课程评估。你可能会疑惑，为什么在课堂开始前就要进行评估，但是思考你想让学生们去了解什么，还有他们将要怎么向你展示，这是评估的内容。你刚才所读的句子可能给你一种与部分教学目标相关的似曾相识的经历，当然这本该如此。你的评估就是来自你的教学目标。从众多角度评估是重要的，看第五章对评估策略的深一步讨论。形成性评价是信息收集的一种类型，让你知道在课堂之中，学生们在实现每一个目标的过程中是怎么做的。此信息可以用来调整中游或者第二天的改变。形成性评价也告知了你在任务讨论中提出的问题，为课堂的后期做铺垫。总结性评估描述了学生们是否达到你计划的这堂课（或本单元）的目标列表。

第五步：计划课堂的前阶段。正像在第三章中讨论的题为“在前阶段教师的行动”，课堂的开始应该唤起学生的已有经验知识，提供教学内容，并且建立期望。思考你所选择的任务还有你将怎么介绍它。问题引导你去思考这些：学生们需要为了任务准备什么术语和背景？你会问些什么问题来帮组学生回忆他们的旧知和相关经验？（你会读一本与任务有关以及构建学生兴趣的儿童读物吗？有实时或受欢迎的事件用来介绍主题吗？）有什么挑战任务可以呈现给学生，特别是针对鳗鱼或者残疾人？

思考你将怎么呈现任务。选项包括把它写在纸上,用他们的语言,使用文档摄像机投影在设备上,或者写在互动白板、黑板、图表纸上。一定要告诉学生关于他们的责任。学生们需要知道：1、他们可能用到的资源或工具；2、学生们是否会独立作业或者团队合作，如果是团队合作，那么团队将怎么组织，包括角色分配；3、他们的作品将怎么呈现（比如完成讲义、写在日记里、准备一个团队的海报）

外文文献出处：《Elementary and Middle School Mathematics Teaching Developmentally》

附外文文献原文

Step 1: Determine the Mathematics Content and Learning Goals. How do you decide what mathematics your students need to learn? Every state has mathematics curriculum standards. Many have adopted the Common Core State Standards (CCSSO, 2010), which identifies mathematics content by grade level. Teachers within districts determine how they will teach objectives, making use of their textbook and other resources. Each lesson within a unit is directed toward supporting the larger goal of the unit. In fact, keeping focused on the bigger mathematical goals, rather than small skills, is very important in planning. At the lesson level, it is important to ask, “What is it that my students should be able to do when this lesson is over?” Keep in mind that a lesson can take several days to accomplish. As you respond to this question, be sure you are focused on the mathematics and not the activity you want to do.

Step 2: Consider Your Studentsrsquo; Needs. What do your students already know or understand about the selected mathematics concepts? Perhaps they already have some prior knowledge of the content you have been working on, which this lesson is aimed at expanding or refining. Be sure that the mathematics you identified in step 1 includes something new or at least slightly unfamiliar to your students. At the same time, be certain that your objectives are not out of reach. Consider individual student needs, including learning disabilities and each personrsquo;s strengths and weaknesses. In addition, language and culture must be a consideration. What might students already know about this topic that can serve as a launching point? What context might be engaging to this range of learners? What learning gaps or misconceptions might need to be addressed? What visuals or models might support student understanding? What vocabulary support might be needed?

Step 3: Select, Design, or Adapt a Task. With your goals and students in mind, you are ready to consider what focus method you will use, perhaps a task, activity, or exercises that may be in your textbook. The importance of selecting a worthwhile task cannot be overstated! See Standard 3 in

NCTMrsquo;s Professional Standards for Teaching Mathematics for a helpful list of what is important to consider. Also, recall from Chapter 3 that the following points were made regarding what makes a task worthwhile: level of cognitive demand, multiple entry and exit points, and relevance to students. Because task selection has already been addressed, it is only mentioned briefly here.

The questions to ask yourself are “Does the task you are considering (from the textbook or any other source) accomplish the content goals (step 1) and the needs of my students (step 2)?” and “Is the task worthwhile?” If the answers are yes, you can plan minor adaptations to enhance the lesson, like using a different context that better relates to your students or including a childrenrsquo;s literature connection. If you find the task does not fit your content and student needs, then you will need to either make substantial modifications to the task or find a new task.

Step 4: Design Lesson Assessments. You might wonder why you are thinking about assessment before you have even introduced the lesson, but thinking about what it is you want students to know and how they are going to show that to you is assessment. The sentence you just read may

give you a deacute;jagrave;-vu experience related to the section on objectives—and so it should. Your assessments are derived from your objectives. It is important to assess in a variety of ways—see Chapter 5 for extended discussions of assessment strategies. Formative assessment is the type of information gathering that lets you know how students are doing on each of the objectives during the lesson. This information can be used for adjusting midstream or making changes for the next day. Formative assessment also informs

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Step 1: Determine the Mathematics Content and Learning Goals. How do you decide what mathematics your students need to learn? Every state has mathematics curriculum standards. Many have adopted the Common Core State Standards (CCSSO, 2010), which identifies mathematics content by grade level. Teachers within districts determine how they will teach objectives, making use of their textbook and other resources. Each lesson within a unit is directed toward supporting the larger goal of the unit. In fact, keeping focused on the bigger mathematical goals, rather than small skills, is very important in planning. At the lesson level, it is important to ask, “What is it that my students should be able to do when this lesson is over?” Keep in mind that a lesson can take several days to accomplish. As you respond to this question, be sure you are focused on the mathematics and not the activity you want to do.

Step 2: Consider Your Studentsrsquo; Needs. What do your students already know or understand about the selected mathematics concepts? Perhaps they already have some prior knowledge of the content you have been working on, which this lesson is aimed at expanding or refining. Be sure that the mathematics you identified in step 1 includes something new or at least slightly unfamiliar to your students. At the same time, be certain that your objectives are not out of reach. Consider individual student needs, including learning disabilities and each personrsquo;s strengths and weaknesses. In addition, language and culture must be a consideration. What might students already know about this topic that can serve as a launching point? What context might be engaging to this range of learners? What learning gaps or misconceptions might need to be addressed? What visuals or models might support student understanding? What vocabulary support might be needed?

Step 3: Select, Design, or Adapt a Task. With your goals and students in mind, you are ready to consider what focus method you will use, perhaps a task, activity, or exercises that may be in your textbook. The importance of selecting a worthwhile task cannot be overstated! See Standard 3 in

NCTMrsquo;s Professional Standards for Teaching Mathematics for a helpful list of what is important to consider. Also, recall from Chapter 3 that the following points were made regarding what makes a task worthwhile: level of cognitive demand, multiple entry and exit points, and relevance to students. Because task selection has already been addressed, it is only mentioned briefly here.

The questions to ask yourself are “Does the task you are considering (from the textbook or any other source) accomplish the content goals (step 1) and the needs of my students (step 2)?” and “Is the task worthwhile?” If the answers are yes, you can plan minor adaptations to enhance the lesson, like using a different context that better relates to your students or including a childrenrsquo;s literature connection. If you find the task does not fit your content and student needs, then you will need to either make substantial modifications to the task or find a new task.

Step 4: Design Lesson Assessments. You might wonder why you are thinking about assessment before you have even introduced the lesson, but thinking about what it is you want students to know and how they are going to show that to you is assessment. The sentence you just read may

give you a deacute;jagrave;-vu experience related to the section on objectives—and so it should. Your assessments are derived from your objectives. It is important to assess in a variety of ways—see Chapter 5 for extended discussions of assessment strategies. Formative assessment is the type of information gathering that lets you know how students are doing on each of the objectives during the lesson. This information can be used for adjusting midstream or making changes for the next day. Formative assessment also informs the questions you pose in the discussion of the task for the after phase of the lesson. Summative assessment captures whether students have learned the objectives you have listed for the lesson (or unit).

Step 5: Plan the Before Phase of the Lesson. As discussed in Chapter 3 in the section titled “Teacher Actions in the Before Phase,” the beginning of the lesson should elicit studentsrsquo; prior knowledge, provide context, and establish expectations. Think about the task you have selected and how you will introduce it. Questions to guide your thinking include:

● What terminology and background might students need to be ready for the task?

● What questions will you ask to help students access their prior knowledge and relevant experiences? (Will you read a childrenrsquo;s book that connects to the task and builds student interest? Is there a current or popular event that could be used to introduce the topic?)

● What challenges might the task present to students, in particular to ELLs and/or students who have disabilities?

Consider how you will present the task. Options include having it written on paper; using their texts; using the document camera on a projection device; or having it written on the interactive whiteboard, chalkboard, or on chart paper. Be sure to tell students about their responsibilities. Students need to know (1) the resources or tools they might use; (2) whether students will work independently or in groups and, if in groups, how groups will be organized, including assigned roles; and (3) how their work will be presented (e.g., completing a handout, writing in a journal, preparing a team poster)

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