理解何谓理解 | Understanding Understanding

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Oct 12, 2021 2:00 PM
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了解 "理解 "的框架

The previous page discussed how information is processed in Working Memory and stored in Long-Term Memory. A four-level model of memory representations was suggested to describe the processes every "piece of knowledge" (ideally) progresses through: Know, Understand, Use, and Master. Here we dive into the relations between the first two: what is needed to progress from knowing something to understanding it.

上一页讨论了信息如何在工作记忆中被处理并储存在长期记忆中。有人提出了一个四级的记忆表征模型来描述每一个 "知识片断"(理想情况下)的进展过程。了解、理解、使用和掌握。在这里,我们深入研究前两个过程之间的关系:从知道某件事情到理解它需要什么。

To briefly summarize, when a learner knows a concept, it is represented in the mind and may be recognized shortly after learning. When it is explained in terms of already familiar concepts and their relationships, the concept is potentially understood. It is argued and demonstrated that any incoming information should be processed meaningfully in working memory, in order to become knowledge that is stored in long-term memory.

简而言之,当学习者知道一个概念时,它在头脑中的表现,可能在学习后不久就会被识别出来。当它被用已经熟悉的概念及其关系来解释时,这个概念就有可能被理解。有人认为并证明,任何传入的信息都应该在工作记忆中得到有意义的处理,以便成为储存在长期记忆中的知识。

Here I try to dive deeper into the 'making meaning' process that leads to the desired, yet elusive, state of 'Understanding'. By combining the simplified model of learning in the brain (introduced here) with the behavioral inputs and outputs, I explore the essential components and the processes that underlie 'Understanding'. The goal is to clarify the pedagogical discussion about the actions we can take to support learners in the process of making sense.

在这里,我试图更深入地探讨 "制造意义 "的过程,它导致了理想的,但难以捉摸的 "理解 "状态。通过将大脑中学习的简化模型(在此介绍)与行为的输入和输出相结合,我探索了 "理解 "的基本组成部分和过程。其目的是澄清关于我们可以采取什么行动来支持学习者理解的教学讨论。

记忆是如何被创造和表现的?

The framework of the discussion assumes, on the basis of current scientific understanding(1), that groups of synchronously active neurons in the brain underlie (among other processes) memory and behavior. Behavior and interactions in the environment, in turn, reshape these neuronal representations, which potentially influence future memory and behavior.

根据目前的科学理解(1),讨论的框架假设大脑中同步活动的神经元群是记忆和行为的基础(除其他过程外)。环境中的行为和互动反过来又重塑了这些神经元的表征,这可能会影响未来的记忆和行为。

When we experience something new, information enters the brain through processes of sensation and perception giving rise to certain patterns of neuronal activity. At the same time, already existing patterns are activated as one attempts to decipher the new experience in terms of the things that are already stored in the brain.

当我们体验新事物时,信息通过感觉和知觉过程进入大脑,引起某些神经元活动的模式。同时,已经存在的模式被激活,因为人们试图根据已经储存在大脑中的东西来破译新的经验。

Potentially, following the learning experience, a new representation of a new concept will be formed, as well as new connections to existing information.

在学习经历之后,将形成对新概念的新表述,以及与现有信息的新联系。

For example, in the (probably long) process of learning a new concept like "Multiplication":

例如,在学习 "乘法 "这样的新概念的过程中(可能很漫长)。

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巩固的要素

Using these terms it is possible to say that when teaching, the goal is to support deep or meaningful processing of the information that would potentially promote the consolidation of new information into the network of existing information. To do so we should consider three main components:

  • the new concept
  • The existing knowledge to be associated with the new concept
  • Meaningful associations between them (2)

使用这些术语可以说,在教学时,目标是支持对信息进行深入或有意义的处理,这将有可能促进新信息在现有信息网络中的巩固。要做到这一点,我们应该考虑三个主要部分。

  • 新概念
  • 要与新概念联系起来的现有知识
  • 它们之间有意义的关联 (2)

All three components should be ACTIVE at the time of learning in the brain of every learner. The process of consolidation is known to be dependent on activation: only active neurons or representations are candidates for consolidation and stabilization. (This idea goes back to the the theory by Donald Hebb from 1949 that brings together behavior and the brain and is summarized by the known phrase "Neurons that fire together wire together").

在每个学习者的大脑中,这三个部分在学习时都应该是活跃的。众所周知,巩固的过程取决于激活:只有活跃的神经元或表征才是巩固和稳定的候选者。(这个想法可以追溯到1949年唐纳德-赫伯的理论,该理论将行为和大脑结合在一起,并由已知的观点「一起激发的神经元连在一起 」所概括)

We can think of the new and existing knowledge as representations, or unique neuronal patterns (as depicted above), and of meaningful connections as the connections that are formed between them, and will drive future associations. An important question would be - What drives the creation of connections? Why one connection is effective and another is not? Why do some connections last while others do not? What do we mean by :understanding" or by "making meaning" ?

我们可以把新的和现有的知识看作是表征,或独特的神经元模式(如上文所描述的),而把有意义的连接看作是它们之间形成的连接,并将推动未来的关联。一个重要的问题是--是什么驱动了连接的产生?为什么一个连接是有效的,而另一个是无效的?为什么有些联系能持续,而有些则不能?我们所说的:理解 "或 "创造意义 "是什么意思?

什么是 "意义"?

The answer suggested here is that a new concept becomes meaningful once it enables the brain (and hence the learner) to respond effectively. In other words, once the new concept was integrated within the existing network in a way that supports a potential action or a decision and their consequences. If the brain is responsible for the following chain of processes: perceive stimulus --> process stimulus --> generate a response --> receive feedback --> process feedback in relation to response, then a new concept becomes meaningful when it is effectively integrated in such a chain.

这里提出的答案是,一旦一个新的概念能够使大脑(也就是学习者)做出有效的反应,它就变得有意义。换句话说,一旦新概念以支持潜在行动或决定及其后果的方式被整合到现有网络中。如果大脑负责以下过程链:感知刺激-->处理刺激-->产生反应-->接收反馈-->处理与反应有关的反馈,那么当新概念在这样的过程链中被有效整合时,它就变得有意义。

For example, when a child first learns the word ‘Ball’ – it becomes useful once an effective association was made with the already familiar object. Only then she can understand the sentence “Kick the ball”, and respond to it. The new concept can now be used to successfully execute an action.

例如,当一个孩子第一次学习 "球 "这个词时,一旦与已经熟悉的物体建立了有效的联系,它就变得有用了。只有这样,她才能理解 "踢球 "这个句子,并对其作出反应。新的概念现在可以被用来成功地执行一个动作。

At the basic level of learning concrete meaning is attached to a meaningless concept (e.g. a word) – like the name of a person (Jess), an action (Play) or an object (Ball). The meaning relies on the ability to use the new concept to communicate or act effectively, which is usually accompanied by positive feedback (received from another person, or from the mere accomplishment ). A recurrent successful use reinforces the associations within the network, and the concept becomes more robust.

在学习的基本层面上,具体的意义被附加到一个无意义的概念(例如一个词)--像一个人的名字(Jess),一个动作(Play)或一个物体(Ball)。这种意义依赖于使用新概念进行有效沟通或行动的能力,这通常伴随着积极的反馈(从另一个人那里得到的,或仅仅是成就感)。反复的成功使用加强了网络中的关联,概念变得更加牢固。

We can conclude that low-level meaning relies on concrete experiences.

我们可以得出结论,低层次的意义依赖于具体的经验。

At higher levels of learning, well-established concrete concepts are used as examples for more abstract or more general concepts. For example, if we wish to teach what “equal” means we can say “If Jess has one ball and Danny has one ball, then they have an equal number of balls”. We establish the meaning of the new concept “equal” on the basis of already known concepts (“Ball”, “Jess”, “has”, "one" etc.) and the already known interactions between them (having one ball). Later, we can go further up the pyramid and give “equal” more abstract meaning as n “equality” or “equity”.

在更高的学习层次上,已确立的具体概念被用作更抽象或更一般的概念的例子。例如,如果我们希望教授 "平等 "的含义,我们可以说 "如果杰斯有一个球,丹尼有一个球,那么他们的球的数量是相等的"。我们在已经知道的概念("球"、"杰斯"、"有"、"一个 "等)和已经知道的它们之间的相互作用(有一个球)的基础上建立新概念 "平等 "的意义。后来,我们可以进一步上升到金字塔,赋予 "平等 "更抽象的含义,如n "平等 "或 "公平"。

Thus, higher or more abstract level of meaning critically depend on familiarity and experience with lower more concrete levels.

因此,更高或更抽象层次的意义关键取决于对较低的更具体层次的熟悉和经验。

背诵和理解

What are the implications of these explanations to what is commonly referred to as two distinct modes of learning: memorization (as in rote memorization) and understanding?

这些解释对通常所说的两种不同的学习模式有什么影响:记忆(如死记硬背)和理解?

Memorization usually means the ability to recite certain facts like “four times three equals twelve” – a student that is able to do that is not considered to demonstrate an understanding of multiplication. However, according to the formulation above, the student does understand “four times three” in a basic level that allows effective communication in a specific context (i.e. answering a question in a math quiz). To create a higher level of understanding additional concrete examples are required (e.g. “Jess has three baskets, four balls in each”) as well as explicit connection to the new concept (“so we can say Jess has four balls multiplied by three ”). By adding more familiar (concrete) examples to demonstrate the meaning of the concept we can establish a higher level of meaning for “Multiplication”. As a higher-level concept, it will be useful in an increasing number of contexts and situations (and as educators, we should supply these opportunities during the practice stage and beyond). Every time it is used effectively it is rewarded and strengthened.

背诵通常意味着能够背诵某些事实,如 "4乘以3等于12"--一个能够做到这一点的学生不被认为是对乘法的理解。然而,根据上面的表述,该学生确实理解了 "4乘以3 "的基本水平,可以在特定的环境中进行有效的交流(即回答数学测验中的问题)。为了建立更高层次的理解,需要更多的具体例子(例如 "杰斯有三个篮子,每个篮子里有四个球"),以及与新概念的明确联系("所以我们可以说杰斯有四个球乘以三")。通过增加更多熟悉的(具体的)例子来证明这个概念的意义,我们可以为 "乘法 "建立一个更高层次的意义。作为一个更高层次的概念,它将在越来越多的背景和情况下发挥作用(作为教育者,我们应该在练习阶段及以后提供这些机会)。每当它被有效地使用,就会得到奖励和加强。

The common terms “memorizing” and “understanding” may be mapped into lower and higher levels of understanding respectively. Understanding (at each level) is demonstrated by the possible actions that are achieved on the basis of the available background knowledge and on the meaningful connections that were explicitly learned and practiced. For a brilliant concrete example of these ideas, read the short story "Meaningful", by Scott Alexander (3).

常见的术语 "记忆 "和 "理解 "可以分别映射为较低和较高的理解水平。理解(在每个层次)表现为在现有背景知识的基础上以及在明确学习和实践的有意义的联系上实现的可能行动。关于这些观点的一个出色的具体例子,请阅读斯科特-亚历山大(Scott Alexander)的短篇小说《有意义》(Meaningful)(3)。

These levels have different consequences for long-term retention: additional, higher levels of meaning make the information more useful in an increasing number of situations, and every time it is used it is also practiced and reinforced. Hence, striving to achieve higher levels of meaning-making is unequivocally an important teaching goal, creating various opportunities for practice is another (see next page). At the same time, a lower level of understanding should not be dismissed but rather considered and treated as an important step on the way to reach the next level.

这些层次对长期保持有不同的后果:额外的、更高层次的意义使信息在越来越多的情况下更加有用,而且每次使用时也会得到练习和强化。因此,努力实现更高层次的意义生成无疑是一个重要的教学目标,创造各种实践机会是另一个目标(见下页)。同时,不应否定较低层次的理解,而应将其视为达到下一层次道路上的重要一步。

构建知识库

Hopefully, it becomes clear that knowledge and understanding can be viewed as components of the same thing: knowledge is the collection of concepts represented in the brain, and understanding is the connections that they form between them. Knowledge and understanding are interrelated and dependent on each other. This view highlights two important features of our learning system: New knowledge is built on the basis of the previous knowledge and they must be related by meaningful connections.

希望大家明白,知识和理解可以被看作是同一事物的组成部分:知识是大脑中代表的概念的集合,而理解是它们之间形成的联系。知识和理解是相互关联和相互依赖的。这种观点突出了我们学习系统的两个重要特征。新的知识是建立在以前的知识基础上的,而且它们必须通过有意义的联系联系起来。

Concrete Example | 具体例子

The process of constructing knowledge can be described as building a pyramid: a new piece of knowledge (orange triangle) is placed on top of the existing structure of knowledge (grey triangles), in a meaningful way (correctly aligned). The final structure is dependent on the existing layers and on the correct placement of the new one (or on all three components of understanding).

构建知识的过程可以被描述为建立一个金字塔:一个新的知识(橙色三角形)被放置在现有的知识结构(灰色三角形)之上,以一种有意义的方式(正确对齐)。最终的结构取决于现有的层次和新的层次的正确位置(或理解的所有三个组成部分)。

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Extending the Analogy | 延伸类比

As more and more information is acquired meaningfully, more pyramids and larger pyramids are created with an increasing number of opportunities for higher-order learning (where a whole pyramid becomes just a brick in a new one), and interdisciplinary learning (that is supported by several other pyramids; top panel). These types of higher-order learning are impossible to attain meaningfully without the supporting lower-level structures of knowledge (bottom panel).

随着越来越多的信息被有意义地获取,更多的金字塔和更大的金字塔被创造出来,有越来越多的机会进行高阶学习(整个金字塔成为新金字塔的一块砖),以及跨学科学习(得到其他几个金字塔的支持;顶板)。如果没有低层次的知识结构的支持,这些类型的高阶学习是不可能有意义地实现的(底板)。

Check out the "Building Pyramids" page, for more illustrations and explanations
Check out the "Building Pyramids" page, for more illustrations and explanations

To the classroom

Anyone who teaches may often feel discrepancy when aiming at a certain level of complexity, while some of the learners “still do not understand”. They may attain a lower level of understanding, but this is not enough, as this kind of knowledge will not be useful enough and will not last.

任何从事教学的人都可能经常感到差异,因为他们的目标是达到一定的复杂程度,而一些学习者 "仍然不明白"。他们可能会达到一个较低的理解水平,但这是不够的,因为这种知识将不够有用,也不会持久。

What can we do when learners "do not understand"?

当学习者 "不理解 "时,我们能做什么?

It may be helpful to approach the situation by breaking the process of understanding to its components and to consider potential problems in each. What is described here is naturally a theoretical, domain-general approach, which every teacher may apply to specific teaching materials, approaches and students. Some of the components described here are "straightforward" and unsurprisingly inline with the most existing lesson and topic plans. However, some of the processes are more subtle than others and are more often taken for granted, it might be fruitful to explicitly consider them in order to locate and target gaps in students' learning:

将理解的过程分解为各个组成部分,并考虑每个组成部分的潜在问题,可能会有所帮助。这里所描述的自然是一种理论性的、领域性的方法,每个教师都可以将其应用于具体的教学材料、方法和学生。这里所描述的一些组成部分是 "直接的",而且不出所料地与大多数现有的课程和主题计划相一致。然而,有些过程比其他的更微妙,更经常被认为是理所当然的,明确地考虑它们以定位和瞄准学生学习中的差距可能是富有成效的。

The route to understanding includes these three key components: new information, prior knowledge, and meaningful connections. Below are some key points to consider about each of them, with some examples.

通往理解的途径包括这三个关键部分:新信息、先前的知识和有意义的联系。下面是关于它们各自的一些关键点,以及一些例子,供大家参考。

Considering new information, prior knowledge, and meaningful connections | 考虑到新的信息、先前的知识和有意义的联系。

1. 新概念是明确的、独特的、清晰的。

It is helpful to present the new concept before learning - to establish familiarity, if possible even more than once. For example:

  • As a preview for the lesson - presenting just the new concepts without in-depth explanations.
  • Including no-stakes predictions questions about upcoming new concepts (may help frame the learning, familiarize learners with the new terms).
  • Light homework assignments, targeted at establishing familiarity, not deep understanding.

在学习之前介绍新的概念是很有帮助的--建立熟悉感,如果可能的话,甚至不止一次。例如。

  • 作为课程的预演--只介绍新概念,不做深入解释。
  • 包括关于即将到来的新概念的无风险预测问题(可能有助于确定学习框架,使学习者熟悉新术语)。
  • 轻微的家庭作业,目标是建立熟悉,而不是深入理解。

Present the new concept explicitly, clearly and distinctly to ensure processing

  • Give a straightforward explanation, rather than let students explore and discover. Making meaning by itself may be a demanding mental task (4)
  • Present a minimal possible number of new concepts in one session, if there is more than one, they should be clearly distinct (temporally and conceptually).

明确、清晰、鲜明地介绍新概念,以确保加工

  • 给予直接的解释,而不是让学生探索和发现。创造意义本身可能是一项艰巨的脑力劳动(4)
  • 在一节课中提出尽可能少的新概念,如果有一个以上的新概念,它们应该是明显不同的(时间上和概念上)。

2. 相关的先前知识是可用的和活跃的。

If prior knowledge is not available there is no other way but to teach it.

Time is better spent at teaching the basics than trying to teach the new without it (we cannot build the top of the pyramid without the basis) (5)

如果没有先前的知识,除了教它,没有其他办法。

把时间花在教授基础知识上比试图在没有基础的情况下教授新知识要好得多(没有基础我们就无法建造金字塔的顶端)(5)

The relevant prior information should be ACTIVE at the time of learning

  • Teacher reviewing relevant material is often creating an illusion of active prior knowledge, the same is true when one or two students volunteer to review. It is tempting to assume that students intuitively relate to their prior knowledge, but it is better not to, especially when they are novices.
  • A Short questionnaire on the required knowledge would serve as effective retrieval practice, and as preparation for the new learning,

相关的先前信息在学习的时候应该是活跃的

  • 教师复习相关材料时,往往会产生一种**的幻觉,即主动的先前知识,当一两个学生自愿复习时也是如此。假设学生直观地与他们的先前知识有关是很诱人的,但最好不要这样做,特别是当他们是新手时。
  • 一份关于所需知识的简短问卷将作为有效的检索练习,并作为新学习的准备。

3. 在原有知识和新概念之间建立明确和有意义的联系

Connections are understood on the basis of already familiar connections: use familiar and well-grounded concrete examples that represent well the type of connection we are teaching (5,6) some examples:

  • The pyramids illustration above is a concrete example of the relations between the abstract concepts 'knowledge' and 'understanding'.
  • Real objects (e.g. fingers, blocks) are examples of number concepts.
  • Matrices of real objects are examples of the multiplication concept.
  • Visual or physical models help explain scientific concepts like DNA, chemical bonds, forces, currents etc..

连接是在已经熟悉的连接的基础上理解的。使用熟悉的、有根基的具体例子,这些例子很好地代表了我们所教的联系类型(5,6)一些例子。

  • 上面的金字塔图示是抽象概念 "知识 "和 "理解 "之间关系的一个具体例子。
  • 真实物体(如手指、积木)是数字概念的例子。
  • 真实物体的矩阵是乘法概念的例子。
  • 视觉或物理模型有助于解释科学概念,如DNA、化学键、力、电流等。

The nature of the connections in the example is discussed explicitly and distinctly to ensure making the appropriate association with the concept and to prevent misattributions of other characteristics of the model. A demonstration may be attention-grabbing by nature, but it is important to ensure explicit focus on the nature of the connection, on making the intended meaning (can be achieved by asking questions after the demonstration).

对例子中的联系的性质进行明确和清晰的讨论,以确保对概念进行适当的联想,并防止对模型的其他特征的错误归属。示范在本质上可能是吸引人的,但重要的是要确保明确地关注联系的性质,使其具有预期的意义(可以通过在示范后提出问题来实现)。

参考资料和补充阅读

1. Tonegawa, S., Liu, X., Ramirez, S., & Redondo, R. (2015). Memory engram cells have come of age. Neuron, 87(5), 918-931.‏

3. Meaningful, by Scott Alexander, a fiction story via Slate Star Codex blog - Thank you Adam Boxer for sharing!

4. Clark, R., Kirschner, P. A., & Sweller, J. (2012). Putting students on the path to learning: The case for fully guided instruction.

5. Willingham, D. T. (2009). Why don't students like school?: A cognitive scientist answers questions about how the mind works and what it means for the classroom. John Wiley & Sons.‏

  • Chapter 2: “Factual knowledge must precede skill” on the importance of knowledge as building blocks.
  • Chapter 4: “We understand new things in the context of things we already know, and most of what we know is concrete”. On the importance of familiar concrete examples, deep knowledge and transfer.

Further reading:

Hirsch, E. D. (2003). Reading comprehension requires knowledge—of words and the world. American Educator, 27(1), 10-13.‏

No “far transfer” – chess, memory training and music just make you better at chess, memory training and music. By Alex Fradera via The British Psychology Society, Research Digest.