提高学生解决问题的能力
Josh Severin University of Nebraska-Lincoln
摘要： 本次研究的是我的八年级学生的数学课堂。我研究了如果学习了不同的解决问题的策略能更顺利地帮助学生解决问题。我还调查了如果学生参与了故事的话题，将对学生的成功率有影响。我发现学生在学习了不同的解决问题的策略和当他们对给定的问题有经验时，他们更能成功。我还发现当学生们对待问题时，当作一场游戏而不是当作一个数学问题去解决时，他们会更加地努力。令人意想不到的是学生努力的程度对他们的成功率有很大的影响。最后，我计划在我的班里继续关注学生的解决问题策略，我还打算改善能让学生在课堂上努力学习的方法。
关键词：数学问题； 能力
本研究的目的是提高学生解决问题的能力。我想让学生学习不同的解决问题策略，这样他们可以解决大多数他们在数学上遇到的问题。我还想看看当学生对遇到的问题有经验时是否能更容易解决问题。本研究的主要目的是为了帮助学生能在面对问题时能更加地轻松，能在面对他们遇到的问题的时候有一个更好的态度。
现在我的班里，学生在面对问题时他们的自信心非常低。他们在解决问题时的成功率相对于我的期望而言还是非常低的。在课堂上，他们有很多的任务就是去解决他们遇到的问题，这些问题大多数都涉及到怎么去分析问题和这些问题是在问什么。当学生对一类典型的问题做过训练时，他们对类似问题会很快理解题目的意思并且能够做得很好。
问题陈述
我希望在我做了这项研究调查之后，这些学生能够拥有更高的解决问题的能力。在忽略他们知识水平的情况下，我希望他们在解决数学问题时能够变得更加轻松。我还希望能够建立他们的自信，让他们在解决问题时能够更加自信。我认为在他们解决问题时，自信是一个很重要的因素，如果学生认为他们并不擅长解决某类问题或者他们认为自己没有能力解决这类问题，那么他们在解决问题时将会有很大的麻烦。如果我可以建立学生的自信心，这样他们就会开始相信自己，这将提高他们解决问题的能力。
本课题对所有的老师来说都很重要，有以下几个原因。我希望我交给学生策略以后，学生们能在其他的一些课程上运用这些策略，像科学和电脑课等等。我也希望他们能提高这项技能，这样他们在面对一些情况时能够处理得更加轻松，这些情况很有可能当他们长大成人之后会遭遇到。例如，我希望学生能够理解广告里的细则，而那些细则在2008年以前都没有利益可言。我也希望他们能够理解，如果一个人没有在期限以前还清全部的金额，他将要欠下所有的利息。我相信学生如果拥有了更好的解决问题的能力，他们就能成为更好的市民和消费者。
文献综述
我选择本课题作为研究的主要理由是因为我相信学生,在大多数情况下，只要他们记住常规的解题方法，知道了确切的要采取的步骤，就能解决实际中遇到的问题。洛夫 - 弗兰卡（1997）研究了6个班级，都是来自中产阶级收入较低的学校，他发现教师强调解决问题的过程，而不仅仅是教他们采取什么步骤能够获得更大的成功。在这类课堂里，学生能够证明并解释他们是如何获得答案，这就是这类课堂的价值。就如洛夫·弗兰克说：“孩子们通常把数学看作是一组规则，其中的问题是通过用老师明确地教过的计算机算法来解决的。” （第8页）当学生遇到了某些已经超出了用常规套路解决的问题时，他们很难找到思路去解决问题，因为他们很难把这些问题和已经掌握的知识所联系到一起。
我选择了提高学生的解决问题能力来研究的另一个原因是学生需要学习多种方式来处理问题。解决问题的时候时需要联系实际的，如果在解决问题的途中遇到了麻烦，就可以考虑能够用来迂回代替的解决方案。学生需要知道如何处理这个问题以及找到另一种方法。蒙塔古（2000）对54名中学生进行了研究，这些学生的范围很广：从有学习障碍的学生到有天赋的学生，均有涉及。蒙塔古研究的目的是为了发现，是否拥有不同策略知识能够帮助学生得到更多。蒙塔古发现所有的学生需要掌握多种策略去开始解决问题，以至于他们不会很快放弃。就像蒙塔古说的：当问题变得困难时，一个好的解决问题的人，会使用更多的策略以及特定的问题表征策略。因此，分化型的问题需要更多的、不同的策略。这体现了它们的结构效度（224页）。这就是为什么我选择把重点放在教学生用多种策略去解决问题的原因。我关注的策略是制作图形,制作一个表格,并用来猜测和检查。
我选择了这个题目作为我的行动研究项目的另外一个原因是我不认为数学教科书突出强调了解决问题。在我这边的地区要在一年的时间里学习很多的东西，没有很多时间去研究解决问题的策略。我希望我的研究可以表明问题解决是和学习一样重要，应该作为一个重要目标。布伦纳(1997)在加利福尼亚研究了在三个不同的初中生6节代数课，发现老师对学生解决问题的能力的影响。他发现了用词方面的教学表现技巧更能帮助学生成功。正如布伦纳状态：虽然问题表征能力在代数的领域对学生的成功是至关重要的，在问题表征能力的指令一般不强调初等代数课程。这项研究提供了清晰和一致的证据表明对问题表征能力的指导工作，那就是学生在建立和协调多个表示方面的能力在接受函数的问题比表象训练有更好的表现（682页）。当学生挑战较难的问题时，拥有多种解决问题策略的学生将会有更高的成功概率。
目标陈述
我的两个研究问题：通过教学和实践解决不同问题的策略对学生解决问题的能力有什么影响？学生的生活经验对正确解决应用问题有什么影响？我做这个研究项目的主要目的是提高学生解决问题的能力。许多学生只对课堂上提到的问题解决比较容易。然而，当问题是应用性问题时，学生似乎非常陌生和害怕，并不愿意去尝试自己解决问题。为了成为一个受过良好教育的公民，也能够成功完成高中数学课程，学生需要发展解决不同问题的策略。
方法
在2007年上班学期，本研究是在八年级数据课堂上进行。我使用的方法如下。在开始研究的时候，我给学生一些预先的测试以评估他们解决问题的能力。我采用标题来给这些成绩预测试分级评分，这种标题指出了学生提出正确解决方案的努力和能力。我也给学生一个调查以确定他们对数学和解决问题的感受。预测试之后，开始这个星期，我收集了六周有关学生解决问题的数据。我根据正确性来对这些问题评分。在本研究的结束时，学生接受课程后测试，该测试与预测试类似，但只有一个问题不同。我认为这个特性问题太模糊，所以我提出了另外一个问题，涉及同样的范围的数学题目，这样的话更容易理解。测试之后，我让学生填写同样的调查表，这些调查表是他们在项目开始之前就已经完成了的。我收集我数据的一个困难是周五缺席上课学生的数量是非常多，这天就是我让他们解决这周、预测试、事后测试和调查的时候。
本研究项目的第一周，我给学生一个调查以评估他们对数学和解题的感受（见附录A）。
在这个调查中，我发现最积极的回应是学生在对问题束手无策之前尝试去解决问题。这鼓励了我，因为我在这一年中跟学生们说不要放弃，一定要尽他们最大的努力去做事。平均分最低的问题是有关学生是否敢于挑战数学难题。这对我来说并不感到奇怪，因为，大多数学生喜欢对其目标有一个清晰的思路，而不喜欢太多的波折。让我惊讶的是所有者6个问题的平均分数都在3和4之间，满分为5分，其他四个问题如下：“我喜欢数学”，“我擅长数学”，“善于解决应用问题对未来非常重要”，“我更加能够解决应用问题，如果我理解并且具有类似情况的经验的话”。
在第一周的星期五，我给每个学生一个预测试。见附件B的预测试，学生对预测试的不同反应，和测试分数结果。在我开始进行研究之前，我想要确定解决他们问题的技能。我也想要知道在我教他们其他解决问题的策略之前，他们具备什么样的解决问题的策略和方法。我使用一个标题，没有解决或错误解决为0分，多个错误为1分，有一个错误为2分，判断正确并且正确解决为3分。
关于预测试，学生对如下的问题反应最好：一个健身俱乐部的会员资格收费50美元，并且每个月花费30美元来使用俱乐部。你拥有260美元来花费在健身俱乐部的设备器材上。你能成为会员的时间多久？另外一个学生反应良好的问题如下：在巴顿中学，45名学生在学习日语。这个数字正以每年3个的数字在增长。学习德语的学生数量为108位，而在以每年减少4个的速度在减少。在这样的速度下，什么时候学习日语的学生人数和学习德语的人数相等？
我相信学生对这两个问题最成功，因为他们非常熟悉这些问题，并且他们能够画出表格来得到正确答案。我们制作了许多图表来寻找答案，在我2月份开始研究之前。这表明学生越具有解决某类问题的经验，他们越可能获得正确的解决方法。这使我希望这个研究项目对学生产生非常正面的作用。其他两个有关预测试的问题都是有关在商店能预定多少个不同锥形冰激凌和在矩形区域能布置多少草地。
The purpose of my research is to improve students abilities solving story problems. I wanted the students to learn different strategies by which they can solve most story problems they encounter in mathematics. I also wanted to discover whether students who had experiences with the topic of the story problem were more likely to solve the problem correctly. The main purpose of my research is to help students become more comfortable with story problems and to have a better attitude about their capabilities of solving story problems.
In my classes right now, the students confidence in solving story problems is very low. Their success rate on solving story problems is very low compared to where I would like to see it. In class, there were far too many questions about the story problems that were on their assignments. The majority of the questions dealt with how to set the problem up and what the question was asking. The students appeared to understand the concepts that were in the lesson because they did fine with the typical drill problems that were on their assignments.
Problem Statement
I wanted the students to become better problem solvers after doing this research project. I wanted them to be more comfortable with solving problems in mathematics regardless of their level of knowledge. I also wanted to build their confidence in their ability to solve story problems. I think confidence is the largest factor because if students do not believe they are good at something or cannot do it at all, they usually will have a very difficult time. If I can build the studentsrsquo; confidence, then they will start to believe in themselves, and this will improve their problem solving ability.
This topic is important to all teachers for a couple of different reasons. I wanted the students to take the strategies that I taught them and use these strategies in other classes like science, computers, etc. I also wanted them to develop this skill so they can be more comfortable dealing with situations they will encounter as they become adults. For example, I wa
剩余内容已隐藏，支付完成后下载完整资料
The purpose of my research is to improve students abilities solving story problems. I wanted the students to learn different strategies by which they can solve most story problems they encounter in mathematics. I also wanted to discover whether students who had experiences with the topic of the story problem were more likely to solve the problem correctly. The main purpose of my research is to help students become more comfortable with story problems and to have a better attitude about their capabilities of solving story problems.
In my classes right now, the students confidence in solving story problems is very low. Their success rate on solving story problems is very low compared to where I would like to see it. In class, there were far too many questions about the story problems that were on their assignments. The majority of the questions dealt with how to set the problem up and what the question was asking. The students appeared to understand the concepts that were in the lesson because they did fine with the typical drill problems that were on their assignments.
Problem Statement
I wanted the students to become better problem solvers after doing this research project. I wanted them to be more comfortable with solving problems in mathematics regardless of their level of knowledge. I also wanted to build their confidence in their ability to solve story problems. I think confidence is the largest factor because if students do not believe they are good at something or cannot do it at all, they usually will have a very difficult time. If I can build the studentsrsquo; confidence, then they will start to believe in themselves, and this will improve their problem solving ability.
This topic is important to all teachers for a couple of different reasons. I wanted the students to take the strategies that I taught them and use these strategies in other classes like science, computers, etc. I also wanted them to develop this skill so they can be more comfortable dealing with situations they will encounter as they become adults. For example, I wanted the students to be able to understand the fine print on advertisements that says no interest until 2008 and understand that if a person did not pay the entire amount by the date he would owe all of the back interest. I believe students are better citizens and consumers if they have better problem solving skills.
Literature Review
The main reason I chose this research topic is that I believe that students, for the
most part, are good at drill and practice problems because they memorize the routine and know the exact steps to take. Loef-Franke (1997) researched 6 classrooms from both middle class and lower income schools and found that teachers who stress the process of story problems instead of just teaching what steps to take have more success. Students in these classes valued being able to justify and explain how they obtained their answers. As Loef-Franke states: 'Children have typically viewed mathematics as a set of rules and procedures in which problems are solved by applying computational algorithms that have been explicitly taught by the teacher' (p. 8). When students come across problems that are out of the regular routine, they have a hard time with starting the problem or relating it to the knowledge they already possess.
Another reason I chose to improve students problem solving abilities is that
students need to learn multiple ways to approach problems. Problem solving is needed in real life, such as in being able to determine an alternative route if there is a detour on the way to a destination. The student will need to know how to deal with this and find another route. Montague (2000) studied 54 middle school students ranging from learning disabled to gifted to see if the knowledge of different strategies helped students achieve more. Montague found that all students need to have multiple strategies to get a story problem started so that they do not give up so quickly. As Montague states:
The good problem solvers used more strategies overall and more problem representation strategies specifically as problems became more difficult. Thus, the problems were differentiated with respect to a need for more and different strategies, which is evidence of their construct validity (p. 224).
This is why I chose to focus on teaching students multiple strategies to solve story problems. The strategies that I focused on were drawing a picture, making a table, and using guess and check.
Another reason I chose this topic as my action research project is that I do not think that problem solving is emphasized enough in mathematics textbooks. In my district there are so many objectives to get through in a year that there is not a lot of time to study strategies for solving story problems. I hope that my research shows that problem solving is just as important as learning the drill problems of the objectives.
Brenner (1997) studied six pre-Algebra classes at three different junior highs in California to find the teachersrsquo; impact on students problem solving abilities. It was found that teaching representation skills helped students be more successful with word problems. As Brenner states:
Although problem representation skills are crucial for student success in algebra, instruction in problem representation skills is not generally emphasized in pre-algebra courses. This study provides clear and consistent evidence that instruction on problem representation skills can work; that is, students who receive representation training for function problems perform better than comparison students in creating and coordinating multiple representations of functions (p. 682).
The more strategies a student has the better the probability the student will be successful when challenged with a difficult problem.
Purpose Statement 剩余内容已隐藏，支付完成后下载完整资料
资料编号：[287082]，资料为PDF文档或Word文档，PDF文档可免费转换为Word
以上是毕业论文外文翻译，课题毕业论文、任务书、文献综述、开题报告、程序设计、图纸设计等资料可联系客服协助查找。
