Научение и обучение КМ (тексты, видео, картинки)

When I was first learning basic math, I played a computer game at home called Math Rescue. The object of the game was to solve each problem that appeared on the screen whenever your avatar jumped into the air—from the ocean floor, the roof of a castle, a boardwalk in space, an icy underground cave, the side of an active volcano—to capture a floating box. I remember that some of the boxes contained word problems, which I dreaded because they slowed down the action of the game. Plus, there were Gruzzles—nefarious blobs with frowny faces—to stop from wreaking any more havoc in the pixelated world. Eventually, I figured out how to turn off the word problem setting so that only numeric problems appeared.

Looking back, I realize two things: first, I probably avoided the word problems because they were too hard (and Gruzzles would descend upon me from mid-air if I answered incorrectly); and second, they were too hard not because of the math but because of the language.

To illustrate my point, let me revisit a story you may be familiar with. In 2008, Fran Simmons, an English teacher at New Dorp High School in New York—at that time one of the lowest-performing secondary institutions in the nation— devised a simple test for her students in an effort to keep district officials from pulling the plug. First, she asked her freshman class to read Of Mice and Men. Then, using information from the novel, she asked them to answer the following prompt in a single sentence:

“Although George …”

She was looking for a sentence like: Although George worked very hard, he could not attain the American Dream.

What Simmons received was alarming in the truest sense of the word. Some students wrote passable sentences, but many could not manage to finish the line. More than a few wrote the following:

“Although George and Lenny were friends.”

At this point, Simmons said in an interview with Peg Tyre of The Atlantic Monthly, a light bulb went on in her head. These 14- and 15-year-olds didn’t know how to use some basic parts of speech. With such grammatical gaps, it was a wonder they learned as much as they did. “Yes, they could read simple sentences,” but works like the Gettysburg Address were beyond them—not because they were too lazy to look up words they didn’t know, but because “they were missing a crucial understanding of how language works. They didn’t understand that the key information in a sentence doesn’t always come at the beginning of that sentence.”

Similarly, when I saw a word problem like, “In the pet store, Lupe sees 9 snakes in one cage and 6 fewer snakes in another cage,” I may not have understood, at such a young age, that the word “fewer” signified a subtraction problem.

Of slightly greater concern, when a world history student is told to assess the economic success of the Cultural Revolution in China, and proceeds to write a poorly constructed essay, maybe it isn’t because she hasn’t studied—maybe it’s because she doesn’t understand that the word “assess” is asking her to do more than just cite evidence; it is asking her to take a side.

The Psycholinguistic Case For Writing Education

In many of today’s writing-intensive classrooms, instructors highlight the importance of thinking-to-write. Critical thinking skills are crucial in forming a clear argument and writing a cohesive essay. Even the controversial Common Core Standards Initiative states, regarding writing standards in grades 6-12, “Each year in their writing, students should demonstrate increasing sophistication in all aspects of language use, from vocabulary and syntax to the development and organization of ideas, and they should address increasingly demanding content and sources.” The Common Cores emphasize the importance of making and supporting claims, using valid reasoning, conveying complex ideas, and organizing component thoughts into a coherent whole.

If a student can’t write it, however, why should we assume that she can think it?

Many of us assume that thought influences language, in that order, because that is the order in which expression usually occurs— We have a thought, and then we use speech or writing to express it. One of the best courses I took in college was on the philosophy of language. I remember starting the class with a piece by German philosopher Gottlob Frege, who asserted that you can’t have thought without language: language influences thought, which results in more language. If you have a vocabulary of 100 words, you aren’t likely to be a good writer or speaker because you don’t have the necessary tools to express yourself. You can only express yourself with the tools you have.

If a student can’t write it, why should we assume that she can think it?

Take the Alaskan Eskimos, for example, who have, by some measures, over 50 different terms for “snow.” In the Inupiaq dialect of Wales, Alaska, there are a purported 70 different words for sea ice, including “utuqaq,” ice that lasts year after year; “siguliaksraq,” the patchwork layer of crystals that forms as the sea begins to freeze; and “auniq,” ice that is filled with holes, like Swiss cheese.

In Standard English, if we don’t have a word for something, we may just think about it as an abstract concept but not be able to express it clearly, or at least with a single term. This happens to people all the time, from both educated and uneducated walks of life. But there is also another phenomenon, and that is when, because we don’t have the language for it, we don’t think about it at all. I have never seen ice filled with holes like Swiss cheese, so how could I think about it, let alone have a word for it?

Considerable academic attention has been given to the way language influences one’s perception of reality, beginning with Yale anthropologist Benjamin Lee Whorf in the 1940s. The varying perceptions found among speakers of different languages has been especially instructive. I find these studies quite analogous to what’s going on in a student’s head when she doesn’t fully understand the structure of her own language before trying to speak the language of, say, government and economics. Insufficient writing skills may, in effect, alter her perception of government and economics as a graspable subject.

“When your language routinely obliges you to specify certain types of information,” writes author and researcher Guy Duetscher in a New York Times column from 2010, “it forces you to be attentive to certain details in the world and to certain aspects of experience that speakers of other languages may not be required to think about all the time. And since such habits of speech are cultivated from the earliest age, it is only natural that they can settle into habits of mindthat go beyond language itself, affecting your experiences, perceptions, associations, feelings, memories and orientation in the world.”

Similarly, when insufficient language skills limit you to citing only certain types of information, they simultaneously force you to be attentive only to a limited number of details in the world, thus limiting your understanding of other subjects as well.

In recent years, multiple experiments have shown that grammatical genders can shape the feelings and associations of speakers toward the objects around them. In the 1990s, for instance, psychologists compared associations between speakers of German and Spanish. When speakers were asked to grade various objects on a range of characteristics, Spanish speakers deemed bridges, clocks and violins to have more “manly properties” like strength, but Germans tended to think of them as more slender or elegant. With objects like mountains or chairs, which are “he” in German but “she” in Spanish, the effect was reversed.

“More recently,” Duetscher writes, “psychologists have even shown that ‘gendered languages’ imprint gender traits for objects so strongly in the mind that these associations obstruct speakers’ ability to commit information to memory.” Does this mean that there are emotional maps imposed by a gender system that may have behavioral consequences for everyday life? Do the opposite genders of “bridge” in German and Spanish have an effect on the design of bridges in Germany and Spain? Do they shape tastes, fashions, habits, and preferences in German and Spanish societies?

English speakers, in this case, are like the equivalent of illiterate students in the English classroom. Since we don’t have the advantage of considering words like “bridge” or “violin” in terms of gender, there is no chance of impaired or enhanced memory, emotional maps, or behavioral consequences due to gendered objects. We’re left out of the loop. Some may even call us mentally challenged…

Studies have shown that bilinguals change how they see the world depending on which language they are speaking. Two sets of findings published in 2010 demonstrate that even something as fundamental as who you like and do not like depends on the language in which you are asked. It has also been demonstrated in several experiments that we perceive colors through the lens of our mother tongue: If we have two different words for what is the same color in another language, then our brains exaggerate the nuance between these shades of color. As the author puts it, “Our experience of a Chagall painting actually depends to some extent on whether our language has a word for blue.”

Studies have shown that bilinguals change how they see the world depending on which language they are speaking.

Some cultures of the world—including parts of Polynesia, Mexico, Namibia, Bali, and Australia— use cardinal directions— north, south, east, and west— to express orientation in space. In most Western cultures, people use egocentric directions— behind you, in front of you, to your left, to your right. In the former cultures, in order to speak the language, you need to know where the cardinal directions are at each and every moment of your waking life. “Regardless of visibility conditions, regardless of whether you are in thick forest or on an open plain, whether outside or indoors or even in caves, whether stationary or moving,” Duetscher explains, “you have a spot-on sense of direction.” This language has actually led its people to perceive reality differently.

One report relates how a speaker of Tzeltal from southern Mexico was blindfolded and spun around more than 20 times in a darkened house. Still blindfolded and dizzy, he pointed without hesitation at the geographic directions. Psychological experiments have even gone as far as to show that under certain circumstances, these people remember “the same reality” differently from others. In twin hotel rooms across the corridor from each other, which naturally seem “mirrored” to egocentric speakers, geographic speakers see and remember the rooms not as “the same room twice” but as two different rooms, since everything is reversed north-side-south.

If the world changes depending on what language you’re speaking, then the world must also change according to the capacity with which you understand your native tongue.

Can You Better Teach Math and Science By Teaching Writing?

At New Dorp, instructors discovered that the only way to improve school performance was to highlight the importance of writing-to-learn, or, as I like to call it, writing-to-think.

By fall 2009, nearly every instructional hour except for math class was dedicated to teaching essay writing along with a particular subject. So in chemistry class in the winter of 2010, those same students who wrote “Although George and Lenny were friends” were required to complete worksheets describing the properties of hydrogen and oxygen with subordinating clauses like although.

Although … “hydrogen is explosive and oxygen supports combustion,” one student wrote, “a compound of them puts out fires.”

Unless … “hydrogen and oxygen form a compound, they are explosive and dangerous.”

If … “hydrogen and oxygen form a compound, they lose their original properties of being explosive and supporting combustion.”

The results of this “Writing Revolution” were extraordinary. By the time they were sophomores, the students who had begun receiving the writing instruction as freshmen were already scoring higher on exams than any previous New Dorp class. Pass rates for the English Regents, for example, bounced from 67 percent in June 2009 to 89 percent in 2011; for the global-­history exam, pass rates rose from 64 to 75 percent. The number of kids enrolling in college-prep courses shot up from 148 students in 2006 to 412 students last year.

Most important, although the makeup of the school has remained about the same—­roughly 40 percent of students are poor, a third are Hispanic, and 12 percent are black—a greater proportion of students who enter as freshmen leave wearing a cap and gown. This spring, the graduation rate is expected to hit 80 percent, a staggering improvement over the 63 percent figure that prevailed before the Writing Revolution began.

The results of this “Writing Revolution” were extraordinary. By the time they were sophomores, the students who had begun receiving the writing instruction as freshmen were already scoring higher on exams than any previous New Dorp class.

The reason for this change is simple: Students’ inability to write was contributing to their inability to think, severely impeding intellectual growth across many subjects. Once students began understanding the mechanics of the English language, they began understanding the language of chemistry, social studies, history, physics…

So the question is, why aren’t the rest of us giving language the spotlight it deserves in the classroom?

The following list highlights ten features of writing education that can be used to enhance student learning across all subject areas, ultimately resulting in higher academic performance. These are features that can be emphasized by instructors not just in English and writing departments, but in other academic departments as well, as they see fit. The goal is to promote the interdisciplinary power of writing, as instructors at New Dorp did.

I want to preface this by saying that these are not the tools that the teachers at New Dorp used to incorporate writing into their classrooms; these suggestions are my own. However, I do think that they probably resemble the ideas at play during New Dorp Writing Revolution. I also want to preface by saying that these points have more than a few things in common with the concept of writing-to-learn, which has been around for decades, but in light of the earlier emphasis on psycholinguistics, I’d like to delve a little deeper into the mechanics of language itself.

Writing To Think In The Classroom

1. Vocabulary Across The Disciplines: Emphasize that the concept of a word may change depending on the context in which it is used.

Consider the following excerpt from an Introductory Chemistry textbook. The Chapter is on Accuracy and Precision.

“Accuracy is the degree of closeness of measurements of a quantity to that quantity’s true value. Precision is the degree to which repeated measurements under unchanged conditions show the same results. The measurement of a system can be accurate but not precise, precise but not accurate or both or neither. It can be hard to discover a quantity’s true value, so the more the sample size is increased, the closer we can get to correctly getting a quantity’s true value.”

Not only are accuracy and precision two different concepts in Chemistry; they are two different concepts in English. If a student already respects the fact that similar words in English can have slightly different meanings, she will be able to grasp this concept more readily when it occurs in another context. When her math instructor marks her down for forgetting to round to the nearest tenth, for example, she will  be able to appreciate the fact that her answer is still accurate, if not precise.

2. Syntax Across The Disciplines: Emphasize that every math problem and essay prompt has a hierarchical structure. 

It’s not all about vocabulary-building. Grasping the structure of language itself can also help students learn across various disciplines.

Although the New Dorp School ignored math as a subject that can be influenced by writing-to-think, I believe it is actually very closely related to language. Take the order of operations, or PEMDAS, for example. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (or Please Excuse My Dear Aunt Sally). The rule demands that, in solving any problem, you pay attention to the numbers inside the parentheses first, then to the exponents, if there are any, then multiplication/division, and finally addition/subtraction.

7 x 2 + ( 7 + 3 x ( 5 – 2 ) ) / 4 x 2 = ?

If you follow the order of operations, the answer is 22.

No matter what problem you’re trying to solve, question you’re trying to answer, or statement you’re trying to respond to— whether it’s in math, history, or English—you always regard it as a hierarchical structure: some things in the expression are more important than others, and you pay attention to those first.

Take the following essay prompt:

Analyze the extent to which the Byzantine Empire was a continuation of the old Roman Empire and in what ways it was a departure.

Here’s one way you could break it up, according to the hierarchy of the language, assuming that X stands for “the extent to which” and “Analyze” is asking you to solve for X:

X = (Byzantine Empire + old Roman Empire) – (Byzantine Empire – old Roman Empire)

How did I translate this?

First, I identified the most important characters (or factors) in the statement: Byzantine Empire and old Roman Empire. Then, I identified the action (subtraction, addition, etc.): continuation, a positive value, and departure, a negative value. Although it sounds like the action is directed toward old Roman Empire (“continuation of…”), you are actually being asked about the Byzantine Empire: To what extent is the Byzantine Empire…? “Continuation of old Roman Empire” may as well just be “+ old Roman Empire” and “departure” might as well be “- old Roman Empire.” When the statement asks for “the extent to which,” it is simply asking for the difference between value added and value negated. So you have two main concepts, separated by parentheses: the traits of the old Roman Empire added to those of the Byzantine Empire, and the traits of the old Roman Empire subtracted from those of the Byzantine Empire. You want to find the difference between these, as manifested by the Byzantine Empire. That difference is X.

I’m not suggesting that a history teacher should break down a statement like this into a math equation. I’m just trying to make a point about how much logic writing requires—as much logic as thought, if not more. Thus, in requiring such logic, writing becomes a terrific exercise in thinking.

Thus, in requiring such logic, writing becomes a terrific exercise in thinking.

When a student writes, “Although George and Lenny were friends” without a follow-up clause, it means she has an insufficient concept of the hierarchy (or “order of operations”) of language. This phrase is like a numeric expression begging to be an equation.

3. Concision Across The Disciplines: Emphasize that concise writing skills lead to efficiency of thought in all subject areas. 

Not only do languages influence what we remember, but the structures of languages can make it easier or harder for us to learn new things. For instance, because the number words in some languages reveal the underlying base-10 structure more transparently than do the number words in English (there are no troublesome teens like 11 or 13 in Mandarin, for instance), kids learning those languages are able to learn the base-10 insight sooner. And depending on how many syllables the number words have, it will be easier or harder to keep a phone number in mind or to do mental calculation. This is hard evidence that language does, in fact, shape the way we think, even the efficiency with which we think, which is often associated with intelligence. If a student can’t think of the word “analyze,” she will write something like, “Think very hard,” spending more time than necessary searching for the right combination of words when she could have used one and moved on.

In Style: Ten Lessons in Clarity and Grace, grammarist Joseph Williams offers some brilliant insight into the relationship between writing and cognitive efficiency, especially in his chapter on “Concision.” In particular, he advises replacing phrases with words. “Nominalizations,” referenced below, are abstract nouns that could be replaced by active verbs for greater efficiency, as in “My suggestion is that our discussion of the issue be done with care” versus “I suggest that we discuss the issue with care.”

As an extreme example, he writes:

“As you carefully read what you have written to improve wording and catch errors of spelling and punctuation, the thing to do before anything else is to see whether you could use sequences of subjects and verbs instead of the same ideas expressed in nouns.”

Then he makes the sentence more concise:

“As you edit, first replace nominalizations with clauses.”

Not only does this kind of attention to concision make reading our students’ essays a more pleasurable experience; it also influences our students’ capacity to think.

 Take the old history prompt again, which is full of nominalizations:

Analyze the extent to which the Byzantine Empire was a continuation of the old Roman Empire and in what ways it was a departure.

Now try this on for size:

How closely did the Byzantine Empire resemble the old Roman Empire?

If a student can economize the first statement into the second, she obviously understands what the prompt is asking.

4. Coherence Across The Disciplines: Emphasize the importance of considering each part in terms of the whole.

Coherence is arguably the most important feature of an effective essay, simply because it reflects the organization of one’s thoughts. If we can think coherently, then we can write coherently; if we can write coherently, then we can think coherently. The two go hand-in-hand.

But we expect our students to be able to think about the parts in terms of the whole in any classroom, regarding any subject, because this skill— perhaps more than any other— fosters sound logic and reasoning.

This is one huge reason the New Dorp School reform was so successful. Writing forced students to organize their thoughts on every lesson, in every discipline. And as soon as they learned to write coherently, they had already trained their brains to think coherently in the future, whether they’d be wielding a pen or not.

5. Attention Across The Disciplines: Emphasize that since writing forces you to highlight the important things, it also teaches you to pay attention to the important things when you’re reading, listening, etc.

Along the same lines as the point about hierarchy in syntax, but on a larger scale, writing teaches you to pay attention to the important things and discard the unimportant things when you are learning. This skill has been tied to intelligence by more than a few researchers.

Writing teaches you to pay attention to the important things and discard the unimportant things when you are learning. This skill has been tied to intelligence by more than a few researchers.

Considering the sheer volume of information students are exposed to every day at school, it is a wonder their brains don’t implode. The human brain filters out some peripheral information automatically, but it takes a special effort to sort out the rest. When a student is listening to a lecture in class or reading a text at home, it will save her time and mental effort if she thinks about details in terms of how she might write about them. A student who knows how to chip away at the irrelevant details until a succinct thesis statement is left framing a logical progression of paragraphs also knows how to navigate her thoughts through a lesson to maximize learning.

6. Memory Across The Disciplines: Writing helps you remember facts better.

Students take notes in class not only to use as study material before a test, but also to reinforce learning. Psychologists have found that the number of modes in which you learn something— auditory, written, digital, oral, etc— correlates positively with the strength with which you recall that information later.

There’s a reason writing isn’t easy. It requires more mental effort than competing in an expert chess tournament, learning to type, and mastering a musical instrument. The more effort you put into writing about a topic, the more effort you put into thinking about it, thus making it harder to forget.

As New Dorp instructors saw during the Writing Revolution, essay writing — even more than note-taking— enhances this effect. You interact with your topic at every level, from sea of information to individual word. In the 1970s, Flower and Hayes defined the writing process in terms of three main stages: planning, translating, and reviewing. Because thought processes are hierarchical, not linear, composition often involves the embedding of one stage within another. Since writing is a complex process involving complex thought, it is only natural that, each time you explore a topic in writing, you create strong neural pathways—like a network of breadcrumbs— leading you back to the important details whenever you need them.

7. Revision Across The Disciplines: Emphasize that the revision process applies to all subject areas.

The term “revise” is usually used to describe a stage of the writing process, but if you break it down into its barest meaning, you’ll see that it shares its definition with “re-envision.” Revise, rethink, re-conceptualize, re-envision— whatever you want to call it, it’s a healthy habit of mind to cultivate in any classroom.

Granted, few disciplines teach you to “kill your darlings” like writing. The writing process requires heavy revision and re-conceptualization. The most successful pieces I’ve written were the result of merciless revision. But students should be ready to translate revision in the English classroom to adaptability and open-mindedness across other disciplines. They should know not only how to revise their writing, but their thoughts as well.

Our society places significant emphasis on getting things right the first time around, but in certain disciplines this attitude can be detrimental to academic progress. Take science, for example, which relies on proving itself wrong in order to prove itself right. Scientists are constantly revising their theories to reflect their findings; if they called the first “draft” of their findings fact, human civilization would never have advanced as it has.

8. Discourse Across The Disciplines: Emphasize that Standard English is but one tool in a box of varying discourses.

When I was in high school, English class only became “English class” my junior year. Before that, it was “Communications.” I have no idea why administrators opted for this devolution; “Communications” was a much better descriptor of what the course should have entailed. It’s a wonder that English class is ever still called “English class.” Unless the course only teaches Shakespeare, it’s a gross oversimplification of a curriculum that should cover dialects, accents, colloquialisms, varieties of slang, formal and informal written English, theories of grammar… 

If students are taught to view Standard English as a tool, and not just a skill, they will realize and appreciate its use in other subjects as well.

My point is that writing in Standard Anglo-Saxon English should be taught as one of countless forms of communication, one that can be used as a powerful tool to help students apply for jobs, conduct successful interviews, and network in society. But it is not the only discourse there is. At home, students may not use Standard English— and that doesn’t make what they use improper. Formal Standard English just happens to be the primary language students need to pocket in order to be college-bound and career-ready in our society.

If students are taught to view Standard English as a tool, and not just a skill, they will realize and appreciate its use in other subjects as well. For example, in scientific discourse, it is acceptable to litter your prose with nominalizations, just as in The Color Purple it is acceptable for Alice Walker to disregard the rules of grammar. Teachers in each content area can help students understand what it means to communicate in that discipline by framing language as a tool.

9. Fast Talking Across The Disciplines: Emphasize that writing skills are communication skills, first and foremost.

I’m not kidding about this one; it may be the most important and relevant point of all. I can guarantee you that the “B+” I got in my Buddhism class in college— I had taken on too many credits and didn’t have time for it— came not from hours of diligent study but from my writing skills.

I’m not endorsing that students coast through school without engaging in their courses. My point is simply that communication skills can save you when you are in a tight situation. They can save you on the AP History exam, they can save you on your college admissions essay, they can save you on your cover letter, they can save you in your job interviews.

I promise, you will be the coolest English teacher your students have ever had if you preface a lesson by saying, “I’m going to teach you how to cheat in your classes” and then proceed to teach them how to write.

10. Language Across Disciplines: Emphasize that everything with which we engage in an intellectual environment is a form of language.

From the publishing industry to the IT industry, language is everywhere. Math is a language, computer programming is a language, Swahili is a language. Language shouldn’t be intimidating or foreign or misunderstood: It’s an exciting, ever-expanding landscape that welcomes us all. Students who struggle with writing should learn to be empowered by it; students who excel at it should come to understand its full range of potential as an educational tool.

Our students deserve to be let in on every learning secret in the book, and the interdisciplinary power of writing is no exception. The decisions students make and the thoughts they generate in any classroom, at any point in their educational careers, are motivated and defined by the language they possess. At New Dorp, instructors realized this and used it to save an entire school from failing out.

Now it’s your turn.

About Saga Briggs

Saga Briggs is Managing Editor of InformED. You can follow her on Google+ or @sagamilena