# on 13-Aug-2018 (Mon)

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 #AlanWatts #incrementalVideo #philosophy Incremental Video Test

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 Definition of the Difference of Two Squares Identity #identity #math #precalculus The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$

Difference Of Squares | Brilliant Math &amp; Science Wiki
Bhardwaj , 敬全 钟 , Sam Reeve , and 10 others Ashley Toh Lucerne O' Brannan Satyabrata Dash Ben Sidebotham Sandeep Bhardwaj Derek Guo Jongheun Lee Mahindra Jain Jimin Khim Tara Kappel contributed <span>The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$ We will also prove this identity by multiplying polynomials on the left side and getting equal to the right side. This identity is often used in algebra where it is useful in applicatio

#### Flashcard 3146181119244

Question

The [...] identity is a squared number subtracted from another squared number to get factorized in the form of

$a^2-b^2=(a+b)(a-b).$

difference of two squares

status measured difficulty not learned 37% [default] 0

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The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of a2−b2=(a+b)(a−b).

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
Bhardwaj , 敬全 钟 , Sam Reeve , and 10 others Ashley Toh Lucerne O' Brannan Satyabrata Dash Ben Sidebotham Sandeep Bhardwaj Derek Guo Jongheun Lee Mahindra Jain Jimin Khim Tara Kappel contributed <span>The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$ We will also prove this identity by multiplying polynomials on the left side and getting equal to the right side. This identity is often used in algebra where it is useful in applicatio

#### Flashcard 3146182692108

Question

The difference of two squares [...] is a squared number subtracted from another squared number to get factorized in the form of

$a^2-b^2=(a+b)(a-b).$

identity

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of a2−b2=(a+b)(a−b).

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
Bhardwaj , 敬全 钟 , Sam Reeve , and 10 others Ashley Toh Lucerne O' Brannan Satyabrata Dash Ben Sidebotham Sandeep Bhardwaj Derek Guo Jongheun Lee Mahindra Jain Jimin Khim Tara Kappel contributed <span>The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$ We will also prove this identity by multiplying polynomials on the left side and getting equal to the right side. This identity is often used in algebra where it is useful in applicatio

#### Flashcard 3146192391436

Question
[...] $$=(a+b)(a-b)$$
$$a^2-b^2=(a+b)(a-b)$$

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The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of a2−b2=(a+b)(a−b).

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
Bhardwaj , 敬全 钟 , Sam Reeve , and 10 others Ashley Toh Lucerne O' Brannan Satyabrata Dash Ben Sidebotham Sandeep Bhardwaj Derek Guo Jongheun Lee Mahindra Jain Jimin Khim Tara Kappel contributed <span>The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$ We will also prove this identity by multiplying polynomials on the left side and getting equal to the right side. This identity is often used in algebra where it is useful in applicatio

#### Flashcard 3146196323596

Question
$$a^2-b^2=$$ [...]
$$a^2-b^2=(a+b)(a-b)$$

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of a2−b2=(a+b)(a−b).

#### Original toplevel document

Difference Of Squares | Brilliant Math &amp; Science Wiki
Bhardwaj , 敬全 钟 , Sam Reeve , and 10 others Ashley Toh Lucerne O' Brannan Satyabrata Dash Ben Sidebotham Sandeep Bhardwaj Derek Guo Jongheun Lee Mahindra Jain Jimin Khim Tara Kappel contributed <span>The difference of two squares identity is a squared number subtracted from another squared number to get factorized in the form of $a^2-b^2=(a+b)(a-b).$ We will also prove this identity by multiplying polynomials on the left side and getting equal to the right side. This identity is often used in algebra where it is useful in applicatio

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 #mathematics #polynomials #precalculus Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7.$

Difference Of Squares | Brilliant Math &amp; Science Wiki
ction contains examples and problems to boost understanding in the usage of the difference of squares identity: $$a^2-b^2=(a+b)(a-b)$$. Here are the examples to learn the usage of the identity. <span>Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square$ Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At fir

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 #mathematics #polynomials #precalculus Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At first we may think about using the long multiplication method, but it wastes time and is, of course, boring. Notice that $$299=300-1$$ and $$301=300+1$$, so $$299\times 301=(300-1)(300+1)=300^2-1^2=89999$$.

Difference Of Squares | Brilliant Math &amp; Science Wiki
es identity: $$a^2-b^2=(a+b)(a-b)$$. Here are the examples to learn the usage of the identity. Rewrite $$5^2-2^2$$ as a product. We have $5^2-2^2 = (5-2) \times (5+2) = 3\times 7. \ _\square$ <span>Calculate $$299\times 301$$. You can brute force the answer to this problem by using a calculator, but we have a sweeter way. We can apply the difference of two squares identity. At first we may think about using the long multiplication method, but it wastes time and is, of course, boring. Notice that $$299=300-1$$ and $$301=300+1$$, so \begin{align*}299\times 301&=(300-1)(300+1)\\&=300^2-1^2\\&=89999. \ _\square \end{align*} Show that any odd number can be written as the difference of two squares. Let the odd number be $$n = 2b + 1$$, where $$b$$ is a non-negative integer. Then we have $n = 2b+1 = [ (b+ #### Annotation 3146212314380  #mathematics #polynomials #precalculus Show that any odd number can be written as the difference of two squares. Let the odd number be $$n = 2b + 1$$, where $$b$$ is a non-negative integer. Then we have \[ n = 2b+1 = [ (b+1) + b ] [ (b+1) - b ] = (b+1)^2 - b^2. \ _\square$

Difference Of Squares | Brilliant Math &amp; Science Wiki
wastes time and is, of course, boring. Notice that $$299=300-1$$ and $$301=300+1$$, so \begin{align*}299\times 301&=(300-1)(300+1)\\&=300^2-1^2\\&=89999. \ _\square \end{align*} <span>Show that any odd number can be written as the difference of two squares. Let the odd number be $$n = 2b + 1$$, where $$b$$ is a non-negative integer. Then we have $n = 2b+1 = [ (b+1) + b ] [ (b+1) - b ] = (b+1)^2 - b^2. \ _\square$ What is $234567^2-234557\times 234577\ ?$ Using the same method as the example above, \begin{align*} 234567^2-234557\times 234577&=234567^2-\big(234567^2-10^2\big)\\ &=23456 #### Annotation 3146217819404  #mathematics #polynomials #precalculus What is \[234567^2-234557\times 234577\ ? Using the same method as the example above, \begin{align*} 234567^2-234557\times 234577&=234567^2-\big(234567^2-10^2\big)\\ &=234567^2-234567^2+10^2\\ &=100.\ _\square \end{align*}

Difference Of Squares | Brilliant Math &amp; Science Wiki
he difference of two squares. Let the odd number be $$n = 2b + 1$$, where $$b$$ is a non-negative integer. Then we have $n = 2b+1 = [ (b+1) + b ] [ (b+1) - b ] = (b+1)^2 - b^2. \ _\square$ <span>What is $234567^2-234557\times 234577\ ?$ Using the same method as the example above, \begin{align*} 234567^2-234557\times 234577&=234567^2-\big(234567^2-10^2\big)\\ &=234567^2-234567^2+10^2\\ &=100.\ _\square \end{align*} Solve the following problems: [emptylink] $b-a$ ${ a }^{ 2 }{ +b }^{ 2 }$ $a+b$ $a-b$ Which of the following equals $$\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b }$$ for $$a\neq b\ #### Annotation 3146224110860  #mathematics #polynomials #precalculus What is \(99^2 - 98^2 \, ?$$ Note: Try it without using a calculator.

Difference Of Squares | Brilliant Math &amp; Science Wiki
the following problems: [emptylink] $b-a$ ${ a }^{ 2 }{ +b }^{ 2 }$ $a+b$ $a-b$ Which of the following equals $$\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b }$$ for $$a\neq b$$? [emptylink] <span>199 187 197 198 What is $$99^2 - 98^2 \, ?$$ Note: Try it without using a calculator. [emptylink] Submit your answer $\large \color{blue}{2014}\color{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\ #### Annotation 3146226470156  #mathematics #polynomials #precalculus Which of the following equals $$\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b }$$ for $$a\neq b$$? \[a+b$

Difference Of Squares | Brilliant Math &amp; Science Wiki
[\begin{align*} 234567^2-234557\times 234577&=234567^2-\big(234567^2-10^2\big)\\ &=234567^2-234567^2+10^2\\ &=100.\ _\square \end{align*}\] Solve the following problems: [emptylink] <span>$b-a$ ${ a }^{ 2 }{ +b }^{ 2 }$ $a+b$ $a-b$ Which of the following equals $$\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b }$$ for $$a\neq b$$? [emptylink] 199 187 197 198 What is $$99^2 - 98^2 \, ?$$ Note: Try it without using a calculator. [emptylink] Submit your answer $\large \color{blue}{2014}\color{blue}{2014} \times \co #### Annotation 3146234858764  #mathematics #polynomials #precalculus \[\large \color{blue}{2014}\color{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator!

Difference Of Squares | Brilliant Math &amp; Science Wiki
he following equals $$\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b }$$ for $$a\neq b$$? [emptylink] 199 187 197 198 What is $$99^2 - 98^2 \, ?$$ Note: Try it without using a calculator. [emptylink] <span>Submit your answer $\large \color{blue}{2014}\color{blue}{2014} \times \color{blue}{2014}\color{blue}{2014} - \color{blue}{2014}\color{red}{2013} \times \color{blue}{2014}\color{fuchsia}{2015} = ?$ Don't use a calculator! Further Extension Since the two factors are different by $$2b$$, the factors will always have the same parity. That is, if $$a-b$$ is even then $$a+b$$ must also be even, so the product

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 Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material. This intense afterschool program, and others like it, is embraced by millions of parents in Japan and around the world who supplement their child’s participatory education with plenty of practice, repetition, and yes, intelligently designed rote learning, to allow them to gain hard-won fluency with the material.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
standing math through active discussion is the talisman of learning. If you can explain what you’ve learned to others, perhaps drawing them a picture, the thinking goes, you must understand it. <span>Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material. This intense afterschool program, and others like it, is embraced by millions of parents in Japan and around the world who supplement their child’s participatory education with plenty of practice, repetition, and yes, intelligently designed rote learning, to allow them to gain hard-won fluency with the material. Also in Psychology What Color Is This Song? By Stephen E. Palmer Suppose you’re at a concert with a friend who leans over and whispers in your ear, “What color was that music?” It may s

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 The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition. Worse, students often believe they understand something when, in fact, they don’t. By championing the importance of understanding, teachers can inadvertently set their students up for failure as those students blunder in illusions of competence. As one (failing) engineering student recently told me: “I just don’t see how I could have done so poorly. I understood it when you taught it in class.” My student may have thought he’d understood it at the time, and perhaps he did, but he’d never practiced using the concept to truly internalize it. He had not developed any kind of procedural fluency or ability to apply what he thought he understood.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
re supposed to be given equal emphasis with conceptual understanding, all too often it doesn’t happen. Imparting a conceptual understanding reigns supreme—especially during precious class time. <span>The problem with focusing relentlessly on understanding is that math and science students can often grasp essentials of an important idea, but this understanding can quickly slip away without consolidation through practice and repetition. Worse, students often believe they understand something when, in fact, they don’t. By championing the importance of understanding, teachers can inadvertently set their students up for failure as those students blunder in illusions of competence. As one (failing) engineering student recently told me: “I just don’t see how I could have done so poorly. I understood it when you taught it in class.” My student may have thought he’d understood it at the time, and perhaps he did, but he’d never practiced using the concept to truly internalize it. He had not developed any kind of procedural fluency or ability to apply what he thought he understood. There is an interesting connection between learning math and science, and learning a sport. When you learn how to swing a golf club, you perfect that swing from lots of repetition over

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 There is an interesting connection between learning math and science, and learning a sport. When you learn how to swing a golf club, you perfect that swing from lots of repetition over a period of years. Your body knows what to do from a single thought—one chunk—instead of having to recall all the complex steps involved in hitting a ball. In the same way, once you understand why you do something in math and science, you don’t have to keep re-explaining the how to yourself every time you do it. It’s not necessary to go around with 25 marbles in your pocket and lay out 5 rows of 5 marbles again and again so that you get that 5 x 5 = 25. At some point, you just know it fluently from memory. You memorize the idea that you simply add exponents—those little superscript numbers—when multiplying numbers that have the same base (104 x 105 = 109). If you use the procedure a lot, by doing many different types of problems, you will find that you understand both the why and the how behind the procedure very well indeed. The greater understanding results from the fact that your mind constructed the patterns of meaning. Continually focusing on understanding itself actually gets in the way.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
e, and perhaps he did, but he’d never practiced using the concept to truly internalize it. He had not developed any kind of procedural fluency or ability to apply what he thought he understood. <span>There is an interesting connection between learning math and science, and learning a sport. When you learn how to swing a golf club, you perfect that swing from lots of repetition over a period of years. Your body knows what to do from a single thought—one chunk—instead of having to recall all the complex steps involved in hitting a ball. In the same way, once you understand why you do something in math and science, you don’t have to keep re-explaining the how to yourself every time you do it. It’s not necessary to go around with 25 marbles in your pocket and lay out 5 rows of 5 marbles again and again so that you get that 5 x 5 = 25. At some point, you just know it fluently from memory. You memorize the idea that you simply add exponents—those little superscript numbers—when multiplying numbers that have the same base (104 x 105 = 109). If you use the procedure a lot, by doing many different types of problems, you will find that you understand both the why and the how behind the procedure very well indeed. The greater understanding results from the fact that your mind constructed the patterns of meaning. Continually focusing on understanding itself actually gets in the way. I learned these things about math and the process of learning not in the K-12 classroom but in the course of my life, as a kid who grew up reading Madeleine L’Engle and Dostoyevsky, who

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 What I had done in learning Russian was to emphasize not just understanding of the language, but fluency. Fluency of something whole like a language requires a kind of familiarity that only repeated and varied interaction with the parts can develop. Where my language classmates had often been content to concentrate on simply understanding Russian they heard or read, I instead tried to gain an internalized, deep-rooted fluency with the words and language structure. I wouldn’t just be satisfied to know that понимать meant “to understand.” I’d practice with the verb—putting it through its paces by conjugating it repeatedly with all sorts of tenses, and then moving on to putting it into sentences, and then finally to understanding not only when to use this form of the verb, but also when not to use it. I practiced recalling all these aspects and variations quickly. After all, through practice, you can understand and translate dozens—even thousands— of words in another language. But if you aren’t fluent, when someone throws a bunch of words at you quickly, as with normal speaking (which always sounds horrifically fast when you’re learning a new language), you have no idea what they’re actually saying, even though technically you understand all the component words and structure. And you certainly can’t speak quickly enough yourself for native speakers to find it enjoyable to listen to you.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
from my experience becoming fluent in Russian as an adult, I suspected—or maybe I just hoped—that there might be aspects to language learning that I might apply to learning in math and science. <span>What I had done in learning Russian was to emphasize not just understanding of the language, but fluency. Fluency of something whole like a language requires a kind of familiarity that only repeated and varied interaction with the parts can develop. Where my language classmates had often been content to concentrate on simply understanding Russian they heard or read, I instead tried to gain an internalized, deep-rooted fluency with the words and language structure. I wouldn’t just be satisfied to know that понимать meant “to understand.” I’d practice with the verb—putting it through its paces by conjugating it repeatedly with all sorts of tenses, and then moving on to putting it into sentences, and then finally to understanding not only when to use this form of the verb, but also when not to use it. I practiced recalling all these aspects and variations quickly. After all, through practice, you can understand and translate dozens—even thousands— of words in another language. But if you aren’t fluent, when someone throws a bunch of words at you quickly, as with normal speaking (which always sounds horrifically fast when you’re learning a new language), you have no idea what they’re actually saying, even though technically you understand all the component words and structure. And you certainly can’t speak quickly enough yourself for native speakers to find it enjoyable to listen to you. This approach—which focused on fluency instead of simple understanding—put me at the top of the class. And I didn’t realize it then, but this approach to learning language had given me

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 Chunking was originally conceptualized in the groundbreaking work of Herbert Simon in his analysis of chess—chunks were envisioned as the varying neural counterparts of different chess patterns. Gradually, neuroscientists came to realize that experts such as chess grand masters are experts because they have stored thousands of chunks of knowledge about their area of expertise in their long-term memory. Chess masters, for example, can recall tens of thousands of different chess patterns. Whatever the discipline, experts can call up to consciousness one or several of these well-knit-together, chunked neural subroutines to analyze and react to a new learning situation. This level of true understanding, and ability to use that understanding in new situations, comes only with the kind of rigor and familiarity that repetition, memorization, and practice can foster. As studies of chess masters, emergency room physicians, and fighter pilots have shown, in times of critical stress, conscious analysis of a situation is replaced by quick, subconscious processing as these experts rapidly draw on their deeply ingrained repertoire of neural subroutines—chunks. At some point, self-consciously “understanding” why you do what you do just slows you down and interrupts flow, resulting in worse decisions.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
class. And I didn’t realize it then, but this approach to learning language had given me an intuitive understanding of a fundamental core of learning and the development of expertise—chunking. <span>Chunking was originally conceptualized in the groundbreaking work of Herbert Simon in his analysis of chess—chunks were envisioned as the varying neural counterparts of different chess patterns. Gradually, neuroscientists came to realize that experts such as chess grand masters are experts because they have stored thousands of chunks of knowledge about their area of expertise in their long-term memory. Chess masters, for example, can recall tens of thousands of different chess patterns. Whatever the discipline, experts can call up to consciousness one or several of these well-knit-together, chunked neural subroutines to analyze and react to a new learning situation. This level of true understanding, and ability to use that understanding in new situations, comes only with the kind of rigor and familiarity that repetition, memorization, and practice can foster. As studies of chess masters, emergency room physicians, and fighter pilots have shown, in times of critical stress, conscious analysis of a situation is replaced by quick, subconscious processing as these experts rapidly draw on their deeply ingrained repertoire of neural subroutines—chunks. At some point, self-consciously “understanding” why you do what you do just slows you down and interrupts flow, resulting in worse decisions. When I felt intuitively that there might be a connection between learning a new language and learning mathematics, I was right. Day-by-day, sustained practice of Russian fired and wired

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 When learning math and engineering as an adult, I began by using the same strategy I’d used to learn language. I’d look at an equation, to take a very simple example, Newton’s second law of f = ma. I practiced feeling what each of the letters meant—f for force was a push, m for mass was a kind of weighty resistance to my push, and a was the exhilarating feeling of acceleration. (The equivalent in Russian was learning to physically sound out the letters of the Cyrillic alphabet.) I memorized the equation so I could carry it around with me in my head and play with it. If m and a were big numbers, what did that do to f when I pushed it through the equation? If f was big and a was small, what did that do to m? How did the units match on each side? Playing with the equation was like conjugating a verb. I was beginning to intuit that the sparse outlines of the equation were like a metaphorical poem, with all sorts of beautiful symbolic representations embedded within it. Although I wouldn’t have put it that way at the time, the truth was that to learn math and science well, I had to slowly, day by day, build solid neural “chunked” subroutines—such as surrounding the simple equation f = ma—that I could easily call to mind from long term memory, much as I’d done with Russian.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
not only when to use that word, but when not to use it, or to use a different variant of it—I was actually using the same approaches that expert practitioners use to learn in math and science. <span>When learning math and engineering as an adult, I began by using the same strategy I’d used to learn language. I’d look at an equation, to take a very simple example, Newton’s second law of f = ma. I practiced feeling what each of the letters meant—f for force was a push, m for mass was a kind of weighty resistance to my push, and a was the exhilarating feeling of acceleration. (The equivalent in Russian was learning to physically sound out the letters of the Cyrillic alphabet.) I memorized the equation so I could carry it around with me in my head and play with it. If m and a were big numbers, what did that do to f when I pushed it through the equation? If f was big and a was small, what did that do to m? How did the units match on each side? Playing with the equation was like conjugating a verb. I was beginning to intuit that the sparse outlines of the equation were like a metaphorical poem, with all sorts of beautiful symbolic representations embedded within it. Although I wouldn’t have put it that way at the time, the truth was that to learn math and science well, I had to slowly, day by day, build solid neural “chunked” subroutines—such as surrounding the simple equation f = ma—that I could easily call to mind from long term memory, much as I’d done with Russian. Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their s

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 Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
lowly, day by day, build solid neural “chunked” subroutines—such as surrounding the simple equation f = ma—that I could easily call to mind from long term memory, much as I’d done with Russian. <span>Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency. In other words, in science and math education in particular, it’s easy to slip into teaching methods that emphasize understanding and that avoid the sometimes painful repetition and pra

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 Advantage of interruption in learning: improving attention: whenever attention declines, change of the subject is the simplest remedy other than taking a definite break from learning

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by a higher authority, student's own choices require prioritization, which in turn requires preview. Previewing is a form of interruption. Regular interruption allows of prioritizing on the go <span>improving attention: whenever attention declines, change of the subject is the simplest remedy other than taking a definite break from learning As for the disadvantages ... there are none! Simply put: interruption is optional! It is true that incremental learning may lead to "learning impatience" and "craving interruption", how

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Incremental learning - SuperMemo Help

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 #incremental_learning #learning you will quickly discover that multiple cloze deletions on a single paragraph are not a good idea

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s a bit about your memory and habits (1-3 weeks), you will oscillate around 95% recall as of the first repetition (if you do not delay , and if you stick to the rules of formulating knowledge ) <span>you will quickly discover that multiple cloze deletions on a single paragraph are not a good idea (e.g. compare the measured forgetting index with items that have the same cloze keywords separated, or just see how thus gained knowledge works in practice) you can look at learning par

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Incremental learning - SuperMemo Help

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 #incremental_learning #learning The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information. Some consequences of IFS listed by Dr. David Lewis, a British psychologist, include: anxiety, tension, procrastination, time-wasting, loss of job satisfaction, self-doubt, psychosomatic stress, breakdown of relationships, reduced analytical capacity, etc. The information era tends to overwhelm us with the amount of information we feel compelled to process. Incremental reading does not require all-or-nothing choices on articles to read. All-or-nothing choices are stressful!

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lation according to a number of studies, and is actually less likely in younger individuals, including students, who are shielded from stress by their less crystallized motivation for learning. <span>The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information. Some consequences of IFS listed by Dr. David Lewis, a British psychologist, include: anxiety, tension, procrastination, time-wasting, loss of job satisfaction, self-doubt, psychosomatic stress, breakdown of relationships, reduced analytical capacity, etc. The information era tends to overwhelm us with the amount of information we feel compelled to process. Incremental reading does not require all-or-nothing choices on articles to read. All-or-nothing choices are stressful! Can I afford to skip this article? For months I haven't had time to read this article! etc. SuperMemo helps you prioritize and skip articles partially (by decision) or automatically (i.

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Incremental learning - SuperMemo Help

#### Annotation 3146340240652

 #incremental_learning #learning The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information.

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The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information. Some consequences of IFS listed by Dr. David Lewis, a British psychologist, include: anxiety, tension, procrastination, time-wasting, loss of job satisfaction, self-doubt, psychosomatic

#### Original toplevel document

Incremental learning - SuperMemo Help

#### Flashcard 3146341813516

Tags
#incremental_learning #learning
Question
The term [...] has been coined recently to refer to stress coming from problems with managing overwhelming information.
Information Fatigue Syndrome

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The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information.

#### Original toplevel document

Incremental learning - SuperMemo Help

#### Flashcard 3146343386380

Tags
#incremental_learning #learning
Question
The term Information Fatigue Syndrome has been coined recently to refer to [...]
stress coming from problems with managing overwhelming information.

status measured difficulty not learned 37% [default] 0

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The term Information Fatigue Syndrome has been coined recently to refer to stress coming from problems with managing overwhelming information.

#### Original toplevel document

Incremental learning - SuperMemo Help

#### Annotation 3146346007820

 Incremental reading is best suited for articles written in hypertext or in an encyclopedic manner. Ideally, each sentence you read has a contribution to your knowledge and is not useless without the sentences that follow.

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s not a problem In learning, choosing the right learning sources is the first step to success. A well-written article will get you to the basic idea from its first paragraph or even a sentence. <span>Incremental reading is best suited for articles written in hypertext or in an encyclopedic manner. Ideally, each sentence you read has a contribution to your knowledge and is not useless without the sentences that follow. Imagine that you would like to learn a few things about Gamal Abdel Nasser . You will, for example, import to SuperMemo an article about Nasser from Wikipedia . In the first sentence yo

#### Original toplevel document

Incremental learning - SuperMemo Help

#### Annotation 3146347580684

 The hardest texts may not be suitable to reading in increments. For example, a piece of software code may need to be analyzed in its entirety before it reveals any useful meaning. In such cases, when the text (here the code) comes up in the incremental reading process, analyze it and verbalize your conclusions. The conclusions can then be processed incrementally. You will generate individual questions depending on which pieces of knowledge you consider important and which become volatile.

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ll not read the methods depending on the conclusions of the article). You can schedule the results and the discussion into a less remote point in time, and proceed with reading the conclusions. <span>The hardest texts may not be suitable to reading in increments. For example, a piece of software code may need to be analyzed in its entirety before it reveals any useful meaning. In such cases, when the text (here the code) comes up in the incremental reading process, analyze it and verbalize your conclusions. The conclusions can then be processed incrementally. You will generate individual questions depending on which pieces of knowledge you consider important and which become volatile. The original computer code can be still retained in your collection as reference only. When learning at the university, you do many courses in parallel. That's a macro version of increm

#### Original toplevel document

Incremental learning - SuperMemo Help

#### Annotation 3146350202124

 Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material.

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Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: <span>Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material. This intense afterschool program, and others like it, is embraced by millions of parents in Japan and around the world who supplement their child’s participatory education with plenty o

#### Original toplevel document

How I Rewired My Brain to Become Fluent in Math - Issue 17: Big Bangs - Nautilus
standing math through active discussion is the talisman of learning. If you can explain what you’ve learned to others, perhaps drawing them a picture, the thinking goes, you must understand it. <span>Japan has become seen as a much-admired and emulated exemplar of these active, “understanding-centered” teaching methods. But what’s often missing from the discussion is the rest of the story: Japan is also home of the Kumon method of teaching mathematics, which emphasizes memorization, repetition, and rote learning hand-in-hand with developing the child’s mastery over the material. This intense afterschool program, and others like it, is embraced by millions of parents in Japan and around the world who supplement their child’s participatory education with plenty of practice, repetition, and yes, intelligently designed rote learning, to allow them to gain hard-won fluency with the material. Also in Psychology What Color Is This Song? By Stephen E. Palmer Suppose you’re at a concert with a friend who leans over and whispers in your ear, “What color was that music?” It may s

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#kkhosravi #linux #topics
Question
True/False: Linux is a subset/direct derivitive of Unix
FALSE.
Linux (created in 1990s) was created from scratch but inspired by Unix (created in 70s) and sharing many of same commands.

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In Linux, a [...] is a process running in the background that is not associated with any terminal
Daemon

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In Linux, [...] is done to get access to content of hard drives / usb flash drives / cd roms / etc
mounting

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Before you mount a new hard drive, you must first create/make a new [...]
directory

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To get the name of drive to mount, command is [...]
fdisk -l

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Command to create new directory for new mount point is:
mkdir /mnt/SOMENAME

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Tags

Question
What formula is it?
market value accrued asset swap

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#### pdf

cannot see any pdfs

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Question
Command to mount a new drive (once mount point directory is created is: [...]
sudo mount /dev/NAME_OF_DRIVE /mnt/NAME_OF_MOUNT_POINT_FOLDER
NOTE: NAME_OF_DRIVE is derived from "fdisk -l"

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Ubuntu is a derivitive of [...]
Debian

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Redhat is a derivitive of [...]
Fedora

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Centos is a free derivitive of paid/enterprise [...]
Redhat

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Question
Ubuntu command to install/upgrade/remove packages/apps is [...]
apt-get

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#### Annotation 3147856481548

 American consumers have done fabulously well in recent decades

TheMoneyIllusion
nsumers will do well. During Mao’s 27 years in office, China lacked a democratic form of government, private property rights, freedom of the press and an internet. Therefore . . . ???? And BTW, <span>American consumers have done fabulously well in recent decades, at least in terms of autos, TVs, phones, cameras, internet, entertainment choices, restaurant quality and choice, cheap clothing, etc., etc., etc. PS. I have a related post at Econlog.

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Question
Command to get linux distribution information is?
cat /etc/*release

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#### Flashcard 3147869850892

Tags
#test #to-remove
Question
This is a LaTeX test.
$$\begin{pmatrix}1 & cos(\theta) \\ -cos(\theta) & 0 \end{pmatrix}$$

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

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Question
How would you find file named testrunner in linux?
sudo find -iname *testrunner* --> RUN from /, note -iname is to keep search case insensative

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#### Annotation 3164471168268

 #strategy According to the skilled strategist Sun Tzu, strategy is about winning before the battle begins, while tactics are about striking at weakness.