高层次的思考是许多教师的目标。当学生深入思考时，他们就能记住知识。为了让我们的学生更深层次地进行思考，我们必须通过提问的方法，帮助学生记忆。
鼓励更高层次的思考与你的课堂文化、教学内容的严谨性、所提出问题的类型息息相关。另外一个挑战来了——提问学生时，他们是用口头还是用书面来回答？你能快速给出反馈吗？
如果教育的整体目标是引发思考，那么当然会有很多方面的教学与此相关。
本文作者：NOELLE
教育博客博主
初中数学教师
问题
在课堂上提问的目的：
- 问题给了我们反馈，让我们知道学生是如何处理和内化他们的学习的。
- 问题也可以用来引导学生思考。
- Questions give us feedback on what and how our students are processing and internalizing their learning.
- Questions also can be used to guide student thinking.
如果你在整个课堂上都在提问，而学生在评估中却表现得很吃力，那么你在课堂上提出的问题可能与学生在评估中做的事情并不一致。
If you are asking questions throughout class and then students are struggling on the assessment, it’s possible that your questions in class are not aligned to that which a student is expected to do on the assessment.
彼得·利耶达尔(Peter Lijedahl)在他的《建构思维课堂》(Building Thinking classroom)一书中提到了这一点，他谈到了“学生化”。做一些看起来很有成效的行为，“抄笔记或模仿老师”，但实际上他们并没有推理出问题的答案。
Peter Lijedahl touches on this a bit in his book Building Thinking Classrooms, where he talks about “studenting”. Doing behaviors that look productive, “filling in notes or mimicking the teacher” but they aren’t actually reasoning their way through the problem.
我们可以对课堂上的问题和互动做一些小的调整，来锻炼学生的思考能力。
We can make some small adjustments to the questions and interactions in our classroom to build those thinking muscles.
建立一个强大的班级文化
为了让学生在更高的层次上思考和回答问题，我们希望学生能够坦然面对错误。
For students to think and answer questions at a higher level, we want students to be comfortable with making mistakes.
Phil Daro (CCSS的合著者)说，老师们太强调答案了；答案是过程的一部分，但不是唯一的学习成果。错误的答案也是学习成果的一部分。
Phil Daro (co-author of the CCSS) says that teachers put too much emphasis on the answers; answers are part of the process, but they are not the only learning outcome. That wrong answers are part of the learning outcome.
如果你把错误的“答案”定为“发现”呢？
如果学生得出了一个错误的答案，你反而会更多地讨论为什么这种方法不起作用，而不是如何得到正确的答案。
What if you framed wrong “answers” as “discoveries”? If students reached a wrong answer, you instead talked more about why that approach doesn’t work instead of how to get the right answer.
你所提出的问题
如果我们用更高层次的问题进行更高层次的思考，我们必须关注我们所问的问题类型。
If we are focusing on higher level thinking using higher level questions, we have to focus on the types of questions we are asking.
为了做到这一点，我参考了布鲁姆分类法，这是一个教育目标的层次结构，从下往上，从低级思维技能到高级思维技能。
To do this, I am going to refer to Bloom’s Taxonomy which is a hierarchy of learning objectives that rank lower order thinking skills to higher order thinking skills.
这是一个金字塔，所以那些较低的层次有一个目的——提供基础。这些都是很容易脱口而出的问题，不需要太多的深思熟虑。
Now remember this is a pyramid, so those lower levels have a purpose and provide a foundation. These are the easy questions to ask, the ones that just roll off the tongue and don’t really require much forethought.
在数学中，它听起来像——“我们接下来做什么？”“解决办法是什么?”“我们要怎么操作？”
In math it sounds like – “What do we do next?” “What is the solution?” “What operation will we use?”
高层次的思考问题是那些需要更多思考和计划的问题。这些问题要求学生分析过程中的关系，或根据给定的信息对如何处理问题进行评估。
The higher level thinking questions are those that take a little more forethought and planning. These are the questions that require students to analyze the relationships in a process or make an evaluation on how to approach the problem based on given information.
激发高层次思维的最简单的方法之一，就是教给学生一个特定概念的多种方法，然后让学生根据给定的信息评估和论证——为什么一个过程可能比另一个更好。
One of the easiest ways to elicit higher level thinking is to teach students multiple approaches to a specific concept and then have students evaluate and justify why one process may be better than another based on given information.
如：
教师：4x-2=18 我们首先要做什么？
学生：在两边加上2。[教师在两边加上2] 。
教师：4x=20 那我们接下来要做什么呢？
这里有一种教同样问题的方法，混合使用高阶和低阶思维技能。
And here is a way to teach the same problem using a mix of higher and lower order thinking skills.
上面的图片可以来表达这个概念，学生们可以通过具体的模型来形象化和探索如何求解方程。当学生使用算法时，抽象内容变得具体了，他们的回答会更加丰富。
This is where I would make a plug to use algebra tiles for this concept because students can visualize and explore how solving equations actually works with concrete models. When students move to the algorithm, their responses will be richer because the abstract is now concrete.
并不是每一种技能或概念都值得提出布鲁姆分类法中最高级的问题。当你为教学提供支架时，你在布鲁姆分类法中提出的问题类型会往上移。
Not every skill or concept warrants a question in the highest order of Bloom’s Taxonomy. As you scaffold instruction, the types of questions you ask in Bloom’s hierarchy will move up.
通过网站搜索，你可以找到许多数学问题的线索。
You can find many question stems for math with a simple google search, so I took a problem from a He Said, She Said Activity from our Proportional Relationships bundle.
等待时间和引出答案
在我教书的第五年，我们学校阅读了《Quality Questions》这本书，它帮助我了解了“等待时间”这个术语，也知道了不同的“等待时间”。
In my fifth year of teaching, our campus read the book Quality Questions which helped me to learn about the technical term of “wait time” and that there were different wait times.
“等待时间”是指在一个问题提出后，我们沉默的时间。实际上有第二个等待时间，即在学生回答后你反应的时间。
Wait time is the amount of time we sit in silence after a question has been posed. Then, there is actually a second wait timere which is the amount of time that you wait after a student responds.
“等待时间”背后的理念是，我们要给学生思考的时间，一旦我们接受一个答案或承认答案是正确的，那么其他人就会停止思考。
The idea behind wait time is that we are giving time for students to think and that as soon as we accept an answer or acknowledge that the answer is correct, then everyone else stops thinking.
以下是一些将其融入课堂的方法：
Here are a few ideas to incorporate this into your classroom:
- 学生写下东西，用手指做出多项选择题的回答，或者他们在传阅时间，与同学分享他们的答案。
- 如果我想让学生分享，我喜欢给他们一点提示，也就是所谓的“暖场”。你问一个问题，给一分钟的静默思考时间，请学生与他们的伙伴分享，然后再进行传阅。我听的是我希望全班都能听到的东西。如果我听到一个学生的精彩回答，我会让他们知道我希望他们分享，这样他们就不会措手不及了。接着，当我们作为一个班级一起回答时，我会让那个学生来回答。
- 你可以做一个拳头的动作。通常情况下，拳头对五指是在课程结束时，让学生衡量他们对这门课的感觉如何，从0（不理解）到5（完全理解）。在回答问题的情况下，你可以要求所有学生展示他们的拳头，评估他们认为自己能回答这个问题的程度。这实际上给了你一些信息——哪些学生完全不懂，哪些学生还可以，哪些学生认为自己回答会很标准。在0和1学生听课的情况下，会叫上4和5学生来回答。然后，我会回到0或1的学生身边，要求他们用自己的话来回答。
注意：我没有并没有对每一个问题都这样做。谁会有那么多时间？每堂课上，我会2-3次进行这种活动，用于那些需要更多时间和思考的问题。
- This can be that they have to write something down, show a finger for a multiple choice response, or they share their answer with a partner while you circulate.
- I like to give students a little bit of heads up if I want them to share, known as “warm calling”. You ask a question, give a minute of silent think time, ask students to share with their partner, and then circulate. I listen to things I want the whole class to hear. If I hear a great response from a student, I let them know that I would like for them to share, so they aren’t caught off guard. Then when we come back together as a class, I have that student respond.
- You can do a fist to five. Typically, fist to 5s are used at the end of the lesson for students to gauge how well they feel about the lesson on a scale from 0 (did not understand) to 5 (completely understand). In the case of answering a question, you can require all students to show their fist to five to assess how well they think they can answer the question. It actually gives you some information – which students are completely lost, which students are ok, and which students think they have exemplary responses. I would call on a mixture of 4 and 5s while making sure my fist and 1 students are listening in. Then I will go back to a fist or 1 student and ask for them to put the response in their own words.
两个想法
第一个想法来自于《Building Thinking Classrooms》。在你示范一项技能之前，首先给学生一个问题，要求他们自己尝试。给他们足够的背景知识，让他们做。
This first idea comes straight from Building Thinking Classrooms. Before you model a skill, first give students the problem and ask for them to try it on their own. Give them just enough background knowledge to get them started.
很多数学技能都可以这么做。这不一定要每天做，当这种方法对学生没有好处时，请自行决定。
You can do this for many math skills. Estimating square roots, operations with rational numbers, geometry skills, solving equations. It doesn’t have to be done daily, and use your discretion for when this approach may not benefit students.
第二个想法是我在一次培训中学到的，它对我的课程结束方式产生巨大影响。我把我的问题，从“还有什么问题吗？”到“对于我们今天学到的东西，你可能还有什么问题？”
My second quick hit is something that I picked up in a training that made a huge difference in how I ended my lessons. I adjusted my language from, “Are there any questions?” to “What questions might someone have about what we learned today?”
前者提问的结果是沉默。后者的结果是，学生们试图想出一些没有涉及的东西。此外，那些不愿意承认自己有问题或不明白的地方的学生，会更愿意提问。
The former resulted in silence.The latter resulted in students trying to think of something that wasn’t covered. In addition, students who may not want to admit that they have a question or don’t understand something, would be more willing to inquire.
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