教学辅助和中学数学
——监督和评价教师
原文作者：DANIEL J. BRAHIER
摘要：本外文翻译选自Daniel J. Brahier 的TEACHING SECONDARY AND MIDDLE SCHOOL MATHEMATICS 一书中的某一片段。主要讲述了如何监督和评价教师来提高教师的教学效果，根据多维度的评价指标，教师应从哪些方面来提高自身的教学素质，提高自身的教学能力，以提高教学效果。
关键词：监督；评价；标准；教学效果
正文：
在一个星期四的早上，你刚刚准备好最令人感到兴奋的数学课。学生将在学习中心活动，纺纺纱，交易卡片，拉球袋检查计数规则概率。更好的是，今天是参观日。在课堂上观察和阅读你的课程计划书。学生们来上课，面向的是学习的中心，但当他们开始流通房间，一切都错了。周末舞会迅速接近，在桌子边，比起从袋子中拿出红球，学生们对讨论乐队、礼服、裙子更有兴趣。一个学生扔下一袋子的大理石，石头溢出散落在教室的地板上。在你感受到挫折的时候，你试图阻止他们的行为，重新组织活动，但为时已晚。学生们都笑了，而且没有意识到他们在做什么。当门铃信号的周期结束，你深呼吸，看到校长皱着眉走出去了。不是以前没在课上遇到过像这样的一颗炸弹，但是校长并没有亲眼见到过。你意识到这学期你的评价取决于她对这节课的观察，你的恐惧，你的文件会因这场灾难受到不利的影响。你回想那一天，你的一个学生Francine，说你：“这太糟糕了，我们年级上学期三分之一是基于这样的考试；我知道的东西比这个测验测得的多很多，这真是糟糕的一天。”同样，你知道，你是一个比小组刚刚观察到的更好的老师，这也是你糟糕的一天。
如果你足够幸运，有一个管理员承认这次评估只看到了一部分，然后校长可能会使用更多的评判数据来进行评估，而不是只以一节课所观察到的信息为依据。正如我们所强调的，利用一系列重要评估策略来确定数学学习的进步学生，管理员应该使用多种证据来确定你作为一个老师的有效性。在教师的评价方面，以及从一个学校或地区到另一个往往有相差很大的用途。
以下列出的是一些可以收集得来的证据，用以确定你作为一个老师的有效性：
bull;从访问中得到的课堂观察记录；
bull;从暗访中得到的课堂观察记录；
bull;你的教学计划和学分表检查；
bull;你的自我陈述，你的年度目标，专业发展计划；
bull;正式的或非正式的输入来自同行的同事和部门，包括椅子，关于你的课堂表现，坚持标准，使用技术或教具，数学内容的理解等等；
bull;来自家长或学生的支持你的教学绩效的信息；
bull;学生在标准化地区或全州范围的测试获得得分成就的专业活动；
bull;当地的、国家的或者国际性数学组织的专业活动；
bull;在积极的课堂环境中建立的证据，包括公告板的照片和学生项目的其他样品，学生的成绩，包括项目的海报，课堂演示视频，和模型（如三维固体）；
虽然一些地区将使用在这里列出这些证据，或者组合使用其中的一些作为样本，作为教师工作绩效的评价标准。因此（幸运的是）一个对于文件的教学评价一般不单独在课堂观察中。作为一个结果，如果校长看见你的教学过程有问题，她也有一个文件，包括一系列证据支持，尽管在他观察到的那一天并不成功，你仍然是一个优秀的老师。事实上，许多管理者会通过一个正透镜来观察老师，和赞美老师至少尝试实践活动，参与学生的中心组织工作。他们还认识到教师在面对一周的教学难度时的困难和考虑到你的教学业绩报告。在最后，评估教学表现，评估学生的进步。对任何一个项目的评估，会在您的教学表现整个报告的不足的基础上，就如考试成绩都不是一个等级的唯一部件时，教师和学生都是值得用其他尺寸测量的，包括在最后的评价。
在许多地区，初任教师接受评估以使他们的能力得到许可或认证。许多国家已经联合起来组成一个财团开发和管理一个教师的绩效评价（TPA），目的是为了帮助教师进入这个行业。TPA通过课堂教学工作以及投资组合，并涉及组合的测量，评估教师在课堂教学中创造的材料，包括视频和各种伪影。另一个评估，由美国教育考试服务中心（ETS）开发的，是III绩效评估实践。使用这个工具，新的教师在四个领域中评价，包括（1）规划的经验教训，适合学生的需要；（2）创设积极的课堂环境；（3）证明有效的课堂教学实践；（4）作为一个教师所表现出的专业主义，从反思教训，与父母的交流，和同事一起工作等各方面。同样，新教师评价与支持联盟建立了一套10标准，可用于评估教师新的课堂表现。这些标准包括内容教学法，学生的发展，不同的学习者，多元教学策略，激励和管理，通信技术，规划，评价，反思性实践，专业成长，学校和社区参与。虽然每个国家有权特征它自己的许可的教师，TPA，实践流程，并会评估是常见的，要求测量教师的各种职业维度。同时，使用更多的证据评估，包括书面审查，以及观察和教师访谈。
在专业标准第二版数学教学中，现在有数学教学，作者提出的观察，标准监督，提高数学教学。第一个三标准是指教师的观察过程中，监督，改进（这个过程是如何进行的），后者是教师的观察，重点监管对象，改进（是什么可测量的）。让我们从这些标准看，他们圈定预期，当你阅读这些标准，注意他们如何进行最佳实践的有效的数学。这是在第7章所述的教师：
标准1：持续循环改进
观察，监督，和数学教学的改进应该是一个周期性的过程——
bull;定期收集和分析有关个人的信息的数学教学；
bull;基于教学分析的专业成；
bull;改进教学作为一种职业成长的后果。（NCTM，2007，p. 69）
像在第11节中描述的学生进步的评估周期，教师评价应遵循收集数据是一个连续的过程，分析它，并基于性能分析试图进行改善。在本书中，我们强调了在教学反思的重要性和学习过程中强调了教学提高时，我们认为我们试图在教室里做的活动，我们的计划是否确实起到了作用，和我们能做什么来改善我们的课后时间。原则和学校数学指出，美国有效的教师利用学生评价数据的评价以及数学任务，学生的话语，和课堂环境的相互影响培养学生的自主学习。然后他们使用这些评价适应他们的指令。”（19页）
标准2：教师参与观察，监督
完善过程对数学教学的改进应给教师提供持续的机会——
bull;分析自己的教学；
bull;和同事谈论他们的教学；
bull;赋予他们的教学主管权利和管理能力。
教学效果评价不应是“做老师”；相反，它应该是一个涉及本地管理员对实践的长期改善的教师工作。利用建构主义模式，例如，校长可能会问老师如何来描述观察到的课，以及学生如何反应，然后提出提高课堂教学效率的三个方面的教训——让校长来观察一节课，这可能是非常不同的方法，然后坐下来，告诉老师什么是应该发生的，为了提高教学效果老师应如何做。老师和学生在课堂中同时担任不同的角色，教师和导师有进行教学评价的作用。
标准3：对观察的数据源监督，数学教学的提高
在数学教学中的改进应基于从各种数据源中得到的数据，包括教师的信息——
bull;目标和为学生的学习和成绩的期望；
bull;应对学生的成就目标的计划；
bull;教案，学生活动和材料，并评估学生对数学的理解方式；
bull;课堂教学中复杂片段的分析；
bull;课堂教学的分析；
bull;学生对数学的理解的证据；
bull;参与同事的协作活动。
这听起来是不是很熟悉？我们认为在使用多种评估策略来确定学生的进步，并指出考试成绩不代表一个学生的成绩。同样地，评估教学的性能要求有各种信息来源，超出课堂观察之外，或着两个以上。我们现在把我们的注意力集中在目标标准的观察，监督，和数学教学的改进上。毫不奇怪的是，这三个教学标准是在第7节中描述的学习，包括有价值任务，学习环境，话语，和评估。
标准4：教师知识与实现
重要的数学对有价值的数学任务的有效教学评价应提供证据证明老师—
bull;演示数学概念和程序的良好知识；
bull;代表数学作为一个相互关联的概念网络程序；
bull;强调数学与其他学科之间的联系，与日常生活的联系；
bull;建立模型和强调解决问题方面，包括建立新的数学应用知识，适应各种适当的解决问题的策略，制造和研究数学猜想，选择和使用各种类型的证据推理方法；
bull;识别推理和证明数学的基本方面；
bull;模型强调数学交流，帮助学生组织和巩固学生的数学思维。
教师必须具备一个内容区域和课程的结构性，把握研究往往在追求学生的问题上是最好的，认识到教育时应帮助学生建立连接。虽然它是教师在教育心理学的一个强大的背景，对有效教学来说，深刻理解数学概念的学习是一个重要的组成部分。内容区域的知识可以帮助教师选择任务，这是学生探索的一个重要的数学问题。课程实施原则考虑几个相关的碎片对教师的数学概念的理解和研究，弗兰卡（1992）认为，“[数学]内容知识影响教师对课堂教学做出的决定”。因此，它是监视数学教师的学科领域知识的重要原则。同时，在第1章中，我们描述了数学作为一个组合的内容和过程（实践）——人们做的和人们知道的事。该标准强调，作为数学教师，我们必须认识过程技能和数学实践在我们的日常教学工作中的作用。理想情况下，主要管理人应该能够在促进数学过程和实践记录的证据的每一节课都进行观察。这是一个用于反思自己的有趣的思考标准：观看录像带的教训，并问自己，“在这本课的那个关键点上，我推进了过程中的技巧和数学实践？”
外文文献出处：Teaching secondary and Middle school mathematics
外文文献原文：
The Supervision and Evaluation of Teachers
It is Thursday morning, and you have just prepared the most exciting mathematics lesson of the year. Students will be rotating among learning centers, spinning spinners, dealing cards, and pulling marbles from bags to examin acounting rules and probability. Even better, today is the day that the principal has decided to visit your classroom to observe and read through your lesson planning book. The students come to class and are oriented to the learning centers, but as they begin to circulate about the room, everything goes wrong. Prom weekend is rapidly approaching, and at the tables, students are more interested in talking about the band, tuxedos, and dresses than the chances of pulling a red marble from the bag. The spinner falls apart at one table, and a student drops a bag of marbles, spilling
them all over the classroom fl oor. In your frustration, you try to stop the class and reorganize the activity, but itrsquo;s too late—the students are laughing about the marbles on the floor and do not understand the point of what they are doing at the stations. As the bell signals the end of the period, you take a deep breath and watch the principal walk out the classroom door with a frown on her face. Itrsquo;s not that you havenrsquo;t had a lesson bomb before, but the principal hasnrsquo;t been there to witness it. You realize that your evaluation for the semester depended on her observation of this lesson, and you fear that your fi le will be adversely affected by this disaster. You think back to the day that Francine, one of your students, said to you, “Itrsquo;s too bad that one-third of our semester grade is ba
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The Supervision and Evaluation of Teachers
It is Thursday morning, and you have just prepared the most exciting mathematics lesson of the year. Students will be rotating among learning centers, spinning spinners, dealing cards, and pulling marbles from bags to examin acounting rules and probability. Even better, today is the day that the principal has decided to visit your classroom to observe and read through your lesson planning book. The students come to class and are oriented to the learning centers, but as they begin to circulate about the room, everything goes wrong. Prom weekend is rapidly approaching, and at the tables, students are more interested in talking about the band, tuxedos, and dresses than the chances of pulling a red marble from the bag. The spinner falls apart at one table, and a student drops a bag of marbles, spilling
them all over the classroom fl oor. In your frustration, you try to stop the class and reorganize the activity, but itrsquo;s too late—the students are laughing about the marbles on the floor and do not understand the point of what they are doing at the stations. As the bell signals the end of the period, you take a deep breath and watch the principal walk out the classroom door with a frown on her face. Itrsquo;s not that you havenrsquo;t had a lesson bomb before, but the principal hasnrsquo;t been there to witness it. You realize that your evaluation for the semester depended on her observation of this lesson, and you fear that your fi le will be adversely affected by this disaster. You think back to the day that Francine, one of your students, said to you, “Itrsquo;s too bad that one-third of our semester grade is based on this exam; I know so much more than the test measured, and I just had a bad day.” Similarly, you are aware that you are a much better teacher than the one that the principal just observed, but you also had a bad day. If you are fortunate enough to have an administrator who acknowledges that assessments are merely snapshots of the whole, then that person probably is going to use more data in an evaluation than observation notes from one classroom visit. Just as we emphasized throughout Unit 4 that it is important to use a diverse array of assessment strategies to determine student progress in mathematics, administrators should use several pieces of evidence to determine your effectiveness as a teacher. The ways in which teachers are assessed and evaluated often vary greatly Chapter 13 The Teacher of Mathematics in the School Community 377 from one school or district to another. The following is a list of some of the pieces of evidence that can be collected to determine your effectiveness as a teacher: Classroom observation notes from announced visits Classroom observation notes from unannounced visits An examination of your lesson plan and gradebooks Preobservation and postobservation interview notes Degree to which you have addressed your self-stated goals on your annual professional development plan (which we discuss later in the chapter) Formal or informal input from peers, including colleagues and a department chair, regarding your classroom performance, adherence to standards, use of technology or manipulative, understanding of mathematics content, and so forth Letters from parents or students in support of your teaching performance Scores earned by students on standardized district- or statewide tests of achievement Professional activity within local, state, or national mathematics organizations Evidence of the establishment of positive classroom environments, including photographs of bulletin boards and student projects Other samples of student accomplishments, including project posters, videoclips of classroom presentations, and models (such as three-dimensional solids) constructed by students Although few districts would use all of the pieces of evidence listed here, many use a combination of some of them to serve as a sample of your work in the process of evaluating teaching performance. Consequently (and luckily) a teaching evaluation for the fi le generally does not hinge on one classroom observation alone. As a result, if the principal saw your probability lesson going awry, she would also have a fi le that included a host of evidence to support that, despite the lack of success on that particular day, you are still an excellent teacher. In fact, many administrators would look at the probability lesson through a positive lens and compliment the teacher for at least attempting a hands-on activity that involved groups of students working in centers. They would also recognize the difficulty of teaching during the week of the prom and take that into consideration when reporting on your teaching performance. In the end, the analogy of assessing teaching performance to that of assessing student progress in mathematics is powerful. Any one of the assessment items on its own would be an insufficient base for an entire report on your teaching performance, just as test scores are not the only components of a grade when both teachers and students have other dimensions that are worth measuring and including in a final evaluation. In many areas, beginning teachers are assessed to determine their abilities for licensing or certification. Many states have joined together into a consortium to develop and administer a Teacher Performance Assessment (TPA) for teachers entering the profession. The TPA involves the measurement of a combination of materials created through coursework and through a portfolio assessment of classroom teaching that includes videos and a variety of artifacts ( AACTE, 2011). Another assessment, developed by the Educational Testing Service (ETS), is the Praxis III performance assessment. Using this tool, new teachers are evaluated in four “domains” of the profession, including (1) planning lessons that are appropriate to student needs; (2) creating a positive classroom environment; 378 Unit 5 Meeting Indi
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