啟蒙數學

COURSE TITLE: Memory Mastery

 

課程名稱：Memory Mastery -永久記憶力的開發
 
永久記憶力的要旨：
1)      運用已經記住的知識來記住還沒記住的知識
2)      須證明用來記未知的連結永遠不會忘掉
3)      已經記住的知識的定義是自然的記住而不是刻意的記住
4)      認知死背或重複而記住的知識一定會忘掉 (* 您有忘掉過曾經可以閉著眼睛做幾年的工作或用過的電腦語言的經驗嗎?)
5)      認知能夠或已經記住的知識不會寫在記憶卡上來背
 
 
見證:
 
?茉莉,十一歲, 生於美國. 在學習了本永久記憶方法後, 她不但於2012年年底代表班上(共33名學生)參加Spelling Bee 的拼字比賽, 並進入複賽, 她的最後一次比賽, 因學校配合募款,比賽地點在校外舉行, 最後因緊張只獲得同年級的第四名(同年級大約有五百名學生). 之後, 她更能夠在短短的兩個月內(12/11/12~2/10/13), 利用課餘之後的時間學習中文, 從一個中文文盲進步到認識至少一千個以上的正體字, 並能閱讀二十四孝的故事. 故事部份內容如下: “在歷史上留名的偉人, 有幾位具有異於常人之相, 舜就是其中之一. 據說舜的眼睛裡各有兩顆眼珠子, 所以大家又叫他「重華」, 除此之外, 跟一般人沒有什麼不同.” 因要測驗她的學習效果. 我請她隨意寫一些她知道字音和字義的字. 以下是她花了約一小時45分鐘從頭腦寫下來的字:
 
友樹發工左本人入忍火水冰凡殳凶冂方匚匸蟲中小事王玉古天田白百子豆也了看言說她好广女奶雙來回口月朋面由袖沖兒這去把出只學老生的土鳥馬媽推尸雨傘電要自己小東西飛心耳禾為不並劉家然辶個黑點身麼我帶愛位名外無錢魚可以樂牛年間象像仙山父巴爸爫木但日刀力閔騫雖天同幾多爹孝立舜親他繼米高貝非壞如後母法呢承弟平因囡此花化正洪和才丁丙已派都娥嫁兩國過片爿想們頂順話開把金梯堯忄心之卜辦匕筆次香吃茶奇柿坡隻成流太蝴蝶彎頭炒少瓜紅甜果摘杷皮胖婆抓熱草兔哈李滿皿甘書龍公雞啼圓蜘蛛酉兮洗石碧當教黃斗吹做鵝爺妃美肉番春森林房英用釣江
 
以下操作步驟是?茉莉如何利用我的記憶方法記住中國字
1。選擇她想記住的部首
2。將部首與她牢記心中的事件或知識做聯繫並記住部首的字形
3。從她的記憶裡，選擇一個主題與部首做連結，來記其部首的字音和字義
4。利用她學的所有部首，來記其他的中國字。例如，春是三人日和婆是皮水女。
例如：
戶：?茉莉的連結主題是電視連續劇“家有仙妻”，用它來記住戶的字音和字義
 
形：戶看起來像一個拍電影道具，它經常在電影NG（不好）之前出現（它也被稱為電影的一個拍不好有趣的部分）。因此，她連結電視連續劇“家有仙妻”。
 
音：（Who），她用它來聲音，因為她聯想“誰(who)是電影的主角
 
意：“家有仙妻”有一集在電影內拍電影，其背景是在一所房子，因此，她連結戶有房子的意思。
 
皿：主題是，她和她小時候我的朋友（敏敏）玩扮傢傢酒。
 
形：看起來像一個持盤子或碗玩具器具，因此，她要記住字的形狀。
 
音：她的玩伴的名字叫敏敏（ㄇㄧㄣㄇㄧㄣ），因此，她記得的字的音
意：玩具是一個持盤子或碗器具。因此，她連結皿有盤子或碗器皿的的意思。 
 
除此之外, 並附上她如何用本方法來記英文單字的例子. 以下是她從頭腦寫下來的單字: (她用cue (提示)來記單字如何拼及其字義)
 
Words that popped right in my head (from Molly):
-meniscus-the curved part of the graduated cylinder
Cue: Men +his +cups
-shallop – 2 part masted boat
Cue: she + all +loop
-notation -notes or marks to indicate something
Cue: note + action
-impact -change
Cue: limp+ act
-bodice -upper part of a women’s dress or blouse
Cue: body + nice
-rhetorically -language
Cue: re+ the + tour + ically(ending of a word)
-pinnacle - a lofty peak
Cue: pin + can +leap
-harass - annoying
Cue: hair + ass
-baylee -whales bone
Cue: bay + peel
-bailiwick-  office of bailiffs
Cue: bail + I + wick
-balderdash -nonsense
Cue: ba + older + dash
-ballad - folk song
Cue: ball +ad
-cardio -heart
Cue: card+ I +do
-derma -skin
Cue: add + germ
-cargo - the goods or merchandise conveyed in a ship, airplane, or vehicle
Cue: car + go
-manipulate - control
Cue: Man! + I + pull +late
-fiasco – a complete failure
Cue: F + bias + co.
-pan- every, always
Cue: nap (Good Luck Charlie)
-amity- friendship
Cue: I +am +pity
-ambi- on both sides, neutral
Cue: Bambi
 
見證2: By Kexin

No one would’ve thought that having four classes of memory training could be so
challenging, yet helpful. Before taking this class, the method most of us considered to use was
the basic memorization method with no specific strategies. As the list becomes longer and as
days past, the more vocabulary we take in, the more we’ll forget them, and all of the hard work
would end up as nothing. Overall, though, I found this memorization strategy quite useful for the
SAT, but would also help us a lot in the future.
I am really thankful of learning this new technique of memorization. Now that I
understood how to use it correctly, I’ve noticed how ignorant my way of memorization was,
which was basically spending the whole day memorizing these words and reviewing them.
Gladly, after learning a new and more useful way of memorizing information, I realized that
there is really no need to review because if you broke down the words correctly, then you will
definitely recall them. For me, I found this method really convenience; I can use it anytime.
When having to study vocabularies in school, instead of using my old method, breaking down
the words into smaller phrases would be more convenience. For example, I didn’t know the word
“matriarchy” at first, but based on the definition, “a society ruled or controlled by women” I
broke the word into “ma + tri(o) + archy”, this way, it was easier to remember the spelling and
the definition. “Ma” meaning mother, but in this case, you can say women; “trio” is like the
society, where there are three branches (legislative, executive, and judicial); “archy”, in Greek,
meaning “to rule”.
I didn’t find this method unsuccessful in any way, except the fact that maybe for every
word, it may take a while to figure out the clues. Other than that, everything went pretty well, but
even if it took a long to think of clues, and in some cases, there might not even be one, it’s still
worth it to take your time into doing these exercises. It not only benefits you on the SAT, but
also in the future. If you want to be pharmacists, a lawyer, or a doctor, it would be really
beneficial in trying to remember the long terms. In summation, I thought this memorization
method was really beneficial and I don’t regret taking the memory training classes. 
 
見證3: By Kimberly

 
 I feel like I learned quite a bit from memory training. Some of the words that we studied weren’t really words we would use in real life or in conversations with your friends. I think that’s what makes the SHSATs so hard. There is a mortifying and overwhelming amount of vocabulary. Yet I feel, that in the end, this will all pay off because not only will I be able to memorize 5,000 vocabulary words, I can use this method to memorize other things.

            By using the memory method, I can also memorize Chinese vocabulary. Because Chinese characters are very much like pictures; so much can be depicted in one word. I can break the words apart into smaller words and memorize what the smaller words mean in relation to the bigger word with more brush strokes. For example: 題＝是＋頁. I think of 頁 as pages. So there will be math questions in the pages of a textbook. I can also use this to memorize long lists of things I have to buy at the supermarket. I will associate the things I need to buy with other things. This is really hard to explain. I wonder how you teach lessons; I can’ even put these in words.

            I thought that the memory training was a lot of hard work. But I don’t really mind the work. As I said in the beginning of the essay, I feel like this will all pay off. The hard part of this is actually using the correct words to break apart. You can’t just use any word. They should be somewhat related to the word and it has to be a word that you would remember.
 
I learned that if I don’t use the correct words, I’m just wasting my time. I won’t remember most of the words I just did in a couple of hours.
 
課程描述：
你想提高你的記憶力嗎？用有效訓練記憶能力的方法來記住成千上萬的事物如電話號碼，名稱和數字而不會忘記應該是有用的。無論您是準備考試，或者已經是法學院或醫學院的學生，或高齡人士擔心記憶力衰退，這課程是適合你的。
本課程老師已經開發出一種記憶的方法，通過聯想，他成功功的記住- 1) 2009年用了大約4小時記住的圓周率的前100位數及美國50洲的面積，2) 整個週期表，3)六、七百個英文醫學名詞的字首，字根，和字尾，等。他的方法可以讓你不僅記住任何想記的事物，且能回想並運用它們經過數週，數月甚至數年之後。

課程目標：（本課程完成後，每個學生都應該能夠:)
學生將能夠記住名單，電話號碼，日期，名稱，英文單字等，回想它們經過週，月，甚至數年後。

教材：
講義

課程長度：
28小時

上課時間：
從7:00 PM至9:00 PM，週一和週四晚，2小時

課程大綱：
1。人們如何記憶？
2。示範 – 背週期表
3。詞彙記憶的方法
4。詞彙記憶演練
5。數字記憶的方法
6。數字記憶演練
7。符號記憶的方法
8。符號記憶演練
9。名單的記憶的方法
10。列表的記憶的方法

梅森數 M_p=2^p-1是素數的條件是(1) p 是素數 (2) M_p不能被任何2kp + 1這種型的數整除,其中k是整數且2kp + 1 < 2^p-1. 它的孿生兄弟K_x=2^x+1,其中x=2ⁿ. 它是素數的條件是K_x不能被任何2ix + 1這種型的數整除,其中i是整數且2ix + 1 < 2^x+1. 例如K₁=2²+1=5, K₂=2⁴+1=17, K₃=2⁸+1=257, K₄=2¹⁶+1=65537都是素數. 但K₅與K₆不是素數. K₅=2³²+1= 4294967297 = 641 * 6700417. 641 = (2)(32)(10)+1; x = 32 與 i = 10. 6700417 = (2)(32)(104694)+1; x = 32與 i = 104694. K₆=2⁶⁴+1= 18446744073709551617 = 274177 * 67280421310721. 274177 = (2)(64)(2142)+1; x = 64 與 i = 2142. 67280421310721 = (2)(64)(525628291490)+1; x = 64與 i = 525628291490. 它比梅森數的優點是不需要確定P是素數.

你知道下面的梅森數, M_1567271, M_1567259, M_1567103, M_1567031, and M_1566923,有下列的3134543, 3134519, 3134207, 3134063和3133847對應因子嗎？上例中的數字都是素數. 使得找的該數們的因子有其困難的程度. 尤其是當素數的值大到一定程度以上如前面所提的例子. 找他們的因子就很難了,甚至於用電腦來找. 相較下，2^ab – 1, 其ab不是素數, 證明它不是素數且有 (2^a– 1) 和(2^b– 1) 的因子就比較容易了. Do you know the following Mersenne Numbers, M_1567271, M_1567259, M_1567103, M_1567031, and M_1566923, have factors as 3134543, 3134519, 3134207, 3134063 and 3133847, respectively?  The above numbers are all primes that contribute the difficulty nature for people to find their cofactors.  When the values of the prime numbers become large to some extend as the aforementioned examples, it is hard to obtain their cofactors, even with the aid of a computer. On the other hand, it is relatively easier to prove and find the cofactor of M_composite that has the form of 2^ab – 1. Note that ab is not a prime.  The following is one of the proofs of 2^ab – 1 that shows 2^ab – 1 has (2^a– 1) and (2^b– 1) as its factors.

梅森數是指形如2ⁿ−1的數, 其記號為M_n;如果一個梅森數是質(素)數它被稱為梅森質(素)數.  如n 不是質(素)數則其梅森數絕對不是梅森質(素)數. 例子請參閱下列藍色部份的證明. 如n是質(素)數則梅森數有可能是梅森質(素)數.  以下是n是質(素)數其梅森數卻不是梅森質(素)數的例子. 例如2¹¹−1 被23整除; 2²³−1 被47整除;2³³¹⁰³¹−1 被662063 整除. 如需更多例子請參閱下列表格.A Mersenne number is the number of the form 2ⁿ-1, the symbol for it is M_n; if a Mersenne number is prime it is called Mersenne prime. If n of M_n is not a prime, the Mersenne number definitely not a Mersenne prime. For example: If x = 123456789123456789123456789  then 2^x-1 is not a prime.  Proof: x is not a prime, and it is dividable by 3.  Therefore,  2^x-1 = (2^y)³ – 1, (that 2^y = 2^{41152263041152263041152263} )  -> (2^y)³ – 1 = (2^y – 1) [(2^y) ² – 2(2^y) +1], therefore, 2^{123456789123456789123456789}-1 can be dividable by (2^{41152263041152263041152263}– 1). If n is a prime, the Mersenne number could be a prime. The following is n is prime for a Mersenne number but  it is not a Mersenne prime.  For example 2¹¹−1 is dividable by 23; 2²³−1 is dividable by 47; 2³³¹⁰³¹−1 is dividable by 662,063. For more examples please refer to the following table.

您可能會問有少數的字找不到記它們的邏輯應如何處理呢? 假如用分解成小字來記住字型及字義的方法不適用時,可以用字義來造一個句子,而句子所用的每一個字的最前面的字母的組合就是需記的字的字型. 這也是一種方法. 例如要記的字是bauxite(礬土),我造下面的句子來記它的字型及字義~ beware! Aluminum used (x) inside TV ends (當心！鋁被使用（不）在電視端的內部.) 其中的Aluminum(鋁)是用來記礬土字義的提示,其原因是礬土是製鋁的材料,而藍色字母用來記住bauxite的字型. 一般人記住東西是靠不斷的重複記憶的結果,而時間有限,所以能記住的量也有限. 加上任何東西在沒有了解它之前是很難記住的. 因此要記住數字39164與bidet(低浴盆)是沒有甚麼不同的.
若想要輕鬆容易記住它們, 其中一種方法是把它們與自己已經知道的知識做結合來記.  數字可用諧音的方法來處理,記住 “三舅已六十” 應該會比記39164好記多了,除了下列一些特殊情況以外, 例如39164是您很熟的門牌號碼,電話號碼的一部份,等等等.
至於bidet,我用E.T. dib (bid => dib) 來記它. E.T. dib (E.T.輕輕垂釣)給我的第一個提示是與水有關.
E.T.(外星人)如果要釣魚的話必須在一個隱避的地方. 那可能是甚麼地方呢? 湖,溪,游泳池,浴缸等等等. 一個小浴缸是最合適的.
這邏輯推理使我記住bidet這個字. 以上邏輯只供參考請勿強記. 簡單的說如要記住對您沒有意義的東西或字的竅門是將它對應到對您有意義的知識或系統上.

時間過的很快,今天已經是雪背字典的第十四天. 雪用邏輯來記英文單字也有顯著的進步. 在這段時間裡雪做了不少的調整,在此與您分享.
 
(1)         因為習慣了學校的“除了背還是背”的學習方法. 用邏輯來推理的時間實在少之又少. 就連推理的數學課也是用背的,不是用想的. 舉一個例子,我問雪為甚麼a⁰ = 1,如a不等於零的話. 雪說她不知道,她沒有記住有a不等於零的條件,老師也不知道如何證明,把它記住就是了. 我說要證明a⁰ = 1,如a不等於零不難. 我問a x a x a =? 她回答a³,a自乘3次就把3寫小一點在a的右上角. 我說那你就應該會證明了. 雪搖搖頭. 我問a² x a =? 她回答a³,指數2+1 = 3. 我又問 a⁰ x a³ = ? 她又回答a³. 我說a⁰ x a³ = a³, a⁰ 必須等於多少? 雪回答是1,她懂了. 我說要能證明a不等於零才有真正的懂整個證明. 並非我要在此討論數學,祇是要強調“想”的重要性. 起先雪想的很少,都是記住我的提示. 我說如果你的邏輯與我一樣的話,記住我的提示是可以的. 不過它的壞處是你沒有做想的訓練,你就沒有辦法自已想.例如arsenal(軍火庫) 雪想不到提示, 雖然我給了我的提示arms(軍火) + senal,雪還是不懂. (您能幫雪想一下我的提示是甚麼嗎?) 我說senal倒過來拼是lanes (巷),你懂了這個字的提示了嗎? 雪點頭. 有了這種想的訓練, 雪記單字的效率提升的.

上一次在討論結束之前提出的問題: queen orange對應到31415,與exact good對應到92653中,queen orange 與exact good之間的連接的邏輯是甚麼呢? 不知道您有沒有時間思考看看呢? 假如您須要知道已討問過的過程,請參閱數學也可以這樣子玩 (記圓周率的前一百位數)與數學也可以這樣子玩 (記圓周率的前一百位數(1)) 兩篇文章. 現在我們就來討問它們之間的邏輯. 其間之邏輯是漸接的. 我的方法是造詞來描述一個具有順序邏輯的已知系統. 例如十二生肖(鼠牛虎),十二個月份,家譜,歷代元首,等. 只要是您已經記住有順序的系統都可以. 我與雪應用造詞描述十二個月份加上蔬果的英文名稱~ apple,banana,cherry,date,eggplant,fig,grape,和honeydew來記憶. Queen orange是用描述與一月有關的事件,東西,經驗等. 我一想到一月份就想到小時後過年時吃的又大又甜的橘子. 很自然的我選擇了queen orange來記住31415. 以下是我們記其他十九組數的邏輯. 只供參考,不一定適合於您,除了您有相同的邏輯.

在第一天我先告訴雪我的邏輯記憶法的基本規則如下:
一.  單字是用想的, 不是用背的.