Divide each difficulty into as many parts ...

"Divide each difficulty into as many parts as is feasible and necessary to resolve it."

--- Rene Descartes

Chunk Learning and Acquisitions of Knowledge

People usually learn to exploit predictable structure. When we translate it into learning, there are two ways of learning:

* Acquisition of information/knowledge through memorizing, i.e.,have the predictable structure repeated many times and let it goes into our RAM (Random Access Memory) automatically! Good example of such learning is the acquisition of mother tongue (if the mother tongue is being used at home from very young age)!


* Using separate chunks and progressively composed with extended practice, i.e., learning how to add single digit numbers, then use the acquired skills of addition and apply them in solving summation problem of double digits or triple digits.

Good application of chunk learning can lead to acquisition of mathematics knowledge if one learns how to migrate the learning, i.e., use the chunk of knowledge in summation, subtraction, multiplication and division and apply them together in suitable situations.

For example, work out this sum

89 divided by 3...

(Please do not use any calculator)

Answers:


3 89 (3 goes into 8 2 times)
__6 (3 times 2 is 6)
__29 (Subtract 8-6=2, and drop down the next number 9)
__27 (3 goes into 29 9 times and 3 times 9 is 27)
___2 (Subtract 29-27 = 2, 2 is the remainder)
89 divided by 3 is

29 & 2/3

--------------------------------------------------------------------------------
or

29.666667
--------------------------------------------------------------------------------

The easier way to solve this mathematical problem for a simple-minded person like me maybe:

89 / 3 is the same as (90 -1) / 3
= (90 / 3) - (1 / 3)
= 30 - 1/3
= 29 2/3 (or 29.66666...)
--------------------------------------------------------------------------------

The first chunk of knowledge we use is

90 = 89+1
or
89 = 90-1

The second chunk of knowledge we use is

30 = 90/3
or
90 = 30*3

The third chunk of knowledge we use is

1/3= 0.33333....

2/3=0.66666...

or 1 = 1/3 + 2/3

Hence, we can use of our simple chunks of knowledge in addition, subtraction to change 89 to 90, then use division or multiplication to make up 30 from 3* 30 or 90 / 3. The additional 1 is being divided by 3, hence we can get the answer 29 2/3 or 29.66666... .


Q & A of mathematic problem extracted from:
http://uk.answers.yahoo.com/question/index?qid=20070122133325AA22PtK&show=7


Dexterine Ho

Use some exercises to learn memory techniques: chunking

Short-Term Memory (STM) has a limited capacity, about 7 items, and a limited duration, about 30 seconds.

Reflecting from your own learning experience, you will notice that the limited capacity in STM is the problem in most of your study.

Remember that if one can only hold about 7 items at a time in STM, then there are limits on how much information one can transfer to Long-Term Memory. All our Long-term memory are build and selected from our STM. Hence, if you cannot remember what is learned in the classroom everyday, it is hard for you to recall them in examination.

Demonstration

To demonstrate the limits of STM, look at the letters printed below for about 10 to 30 seconds and try to write them down without looking at the screen.

---

XIBMSATMTVPHDX

---

Are you capable of writing down all the letters or recalling them in segments without mistakes? It is difficult as 14 letters exceeded the capacity of your STM.

---

Since 14 letters is difficult for most people to store in their STM, chunking can be applied here to increase the capacity of STM.

Instead of trying to remember 14 letters you must first chunk the letters into a few segments.

For example:.

---

X IBM SAT MTV PHD X

---

If you chunk the 14 letters into 6 chunks as shown above, it is easy to keep all the letters in STM.

Having the 6 chunks in your first level of chunking, you can move further and map some patterns.

You will notice that X is the first and last letter. IBM-SAT-MTV-PHD are the 12 letters between the two Xs.

The pattern "X------------X" and "IBM-SAT" + "MTV-PHD"complete the 14 letters.

If you can translate the middle chunks to sentences, like "I used IBM on SAT" and "he watched MTV to get his PHD". It is alright to have meaningful or meaningless sentences so long as it help you in your recall.

The key is to actively chunk letters, words, sentences, or numbers such that there are 7 or less chunks.

If you use an active imagination, you can chunk anything.

But chunking takes work, and to get good at chunking it takes practice. To practice chunking on your own, click the link here:

http://daphne.palomar.edu/stat/mark/stm%20chunking.htm#PRACTICE



Source of information:

Memory techniques "Chunking" by Dr. Mark W. Vernoy, Professor of Psychology, Dean of Social & Behavioral Sciences. Palomar CollegeSan Marcos

at:

http://daphne.palomar.edu/stat/mark/stm%20chunking.htm

Chunking

In most learning, sequences can consist of sub-sequences and these can in turn consist of sub-sub sequences.

Chunks in motor learning are identified by pauses between successive actions...

Chunking in cognitive psychology and mnemonic, refers to a strategy for more efficient use of short-term memory by recording and retrieving information in small segments.

It is like eating an elephant, we can only eat one small piece at a time, yet, given time, we can finish the whole elephant!

For more academic explanation on Chuncking, read the following!

Source of information:

"Chunking (psychology)" from Wikipedia
at:

http://en.wikipedia.org/wiki/Chunking_%28psychology%29#Chunking_in_Motor_Learning

Break it down to small pieces

Disease comes from “dis-ease”.

Research comes from "re-search".

The word cardigan contains "car, dig, an" or "card,i, gan".

The easiest way to learn to spell compound words is to break them down into their component parts.


Dexterine

Magic Number Seven

The Magical Number Seven, Plus or Minus Two

"The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information" is a 1956 paper by the cognitive psychologist George A. Miller.

Millers concept goes beyond numbers. For example, most of us can remember about seven recently learned chunks of similarly classified data. Keep this in mind when you are presenting information to other people.

The chunking principle requires you to classify the items into groups to reduce the information overload.

Benefits

By chunking information the author improves the reader's comprehension and ability to access and retrieve the information.

Miller showed a number of remarkable coincidences between the channel capacity of a number of human cognitive and perceptual tasks.

In each case, the effective channel capacity is equivalent to between 5 and 9 equally-weighted error-less choices: on average, about 2.5 bits of information.

Miller hypothesized that these may all be due to some common but unknown underlying mechanism.

He noticed that the memory span of young adults was around seven elements, called chunks, regardless whether the elements were digits, letters, words, or other units.

Later research revealed that span does depend on the category of chunks used (e.g., span is around seven for digits, around six for letters, and around 5 for words), and even on features of the chunks within a category.

In general, memory span for verbal contents (digits, letters, words, etc.) strongly depends on the time it takes to speak the contents aloud, and on the lexical status of the contents (i.e., whether the contents are words known to the person or not).

Several other factors also affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks.

Nonetheless, N. Cowan has proposed that working memory has a capacity of about four chunks in young adults (and less in children and old adults).

A variety of studies could be summarized by saying that short term memory had a capacity of about "seven plus-or-minus two" chunks.

Miller wrote that "With binary items the span is about nine and, although it drops to about five with monosyllabic English words, the difference is far less than the hypothesis of constant information would require.

The span of immediate memory seems to be almost independent of the number of bits per chunk, at least over the range that has been examined to date."

Miller acknowledged that "we are not very definite about what constitutes a chunk of information."

Miller noted that according to this theory, it should be possible to effectively increase short-term memory for low-information-content items by mentally recoding them into a smaller number of high-information-content items.

"A man just beginning to learn radio-telegraphic code hears each dit and dah as a separate chunk. Soon he is able to organize these sounds into letters and then he can deal with the letters as chunks.

Then the letters organize themselves as words, which are still larger chunks, and he begins to hear whole phrases."

Thus, a telegrapher can effectively "remember" several dozen dits and dahs as a single phrase.

Naive subjects can only remember about nine binary items, but Miller reports a 1954 experiment in which people were trained to listen to a string of binary digits and (in one case) mentally group them into groups of five, recode each group into a name (e.g "twenty-one" for 10101), and remember the names.

With sufficient drill, people found it possible to remember as many as forty binary digits. Miller wrote:

"It is a little dramatic to watch a person get 40 binary digits in a row and then repeat them back without error. However, if you think of this merely as a mnemonic trick for extending the memory span, you will miss the more important point that is implicit in nearly all such mnemonic devices. The point is that recoding is an extremely powerful weapon for increasing the amount of information that we can deal with".

Sources of Information:

http://en.wikipedia.org/wiki/George_A._Miller

http://www.chambers.com.au/glossary/chunk.htm

http://en.wikipedia.org/wiki/The_Magical_Number_Seven%2C_Plus_or_Minus_Two

http://en.wikipedia.org/wiki/Chunking_%28psychology%29#Chunking_in_Motor_Learning

Please visit the above Wikipedia pages to gain more comprehensive understanding.

Memory training systems

Memory training systems

The phenomenon of chunking as a memory mechanism can be observed in the way we group numbers and information in our day-to-day life.

For example, when recalling a number such as 14101946, if we group the numbers as 14, 10 and 1946, we are creating a mnemonic for this number as a date, month and year.

An illustration of the limited capacity of working memory ... can be seen from the following example:

While recalling a mobile phone number such as 9849523450, we might break this into 98 495 234 50.

Thus, instead of remembering 10 separate digits that is beyond the "seven plus-or-minus two", we are remembering 4 groups of numbers.

Various kinds of memory training systems and mnemonics include training and drill in specially-designed recoding or chunking schemes.

A chunk can then be defined as "a collection of elements having strong associations with one another, but weak associations with elements within other chunks"

Information extracted from:
http://en.wikipedia.org/wiki/Chunking_%28psychology%29#Chunking_in_Motor_Learning

Please visit the wikipedia page above to read the full text.