**4.1 Definitions of MALESAbrain**

**Definition 1-1**. A piece of *knowledge-content <sup>i</sup>* in MALESAbrain for problem-based discussion is defined as a pair of problem and solutions: *<sup>i</sup>*= (*pi , j si,j*) where *pi* is a *problem j si,j* is the collection of suggested solutions associated with *pi*

Proposing Two Algorithms to Acquire Learning

**Definition 1-7**. The *learning-rate function* ||


compare the algorithm with the example in previous section.

*disagreement threshold* (Definition 1-5) \*/

branch tree in the forum. (Definition 1-6) \*/

achieved the educator's training target (Definition 1-7) \*/

SET due-date / \* *due-date* is an expected date to end the discussion \*/

,,due-date )

M

the educator's training target set up and

the learning-rate ||

consensus, where

**4.2 Algorithm of MALESAbrain** 

*kq*,*kr* ,*sm*,*sd*,

(Definition 1-5) \*/

SET 

SET 

SET 

SET 

SET 

REPEAT

/\* *Critical thinking* \*/

MALESAbrain} /\* Definition 1-4 \*/

*wi,j sm*}

MALESAbrain(

**Definition 1-6**. The *growth-factor* 

branch tree, in the forum.

Knowledge in Problem-Based Learning Environment 147

limit for constraining the posted number of AK-cells at each level, which converts the architecture of knowledge base from linear structure into a hierarchical structure, of -

> || K

learners to understand the progress of the discussion, where the *convergent-factor "*" is


To trace the algorithm, we suggest readers browsing the definitions first. Then reading the instructions, comments in the algorithm and checking definitions when tracing. Afterwards

a higher discussion position - called *qualification threshold* (Definition 1-5)\*/

*kq* / \* the minimum requirement of an AK-cell to join the competition for promotion to

*kr*, / \* the worthless AK-cells will be deleted whenever lower than the *rejection threshold*

*sm* / \* a consensus of the learning group agrees the solution is able to solve the problem whenever a solution reached the *solution maturity threshold* (Definition 1-5)\*/

*sd* / \* the worthless solutions will be deleted whenever lower than the *solution* 

/ \* *growth-factor* limits the posted number of AK-cells at each level, which converts the architecture of knowledge base from linear structure into a hierarchical structure of -

SET / \* *convergent-factor* is used to decide whether the percentage of mature AK-cells has

*COMPARE personal viewpoint "x" with retained knowledge pieces "ki" in MALESAbrain K* = {*ki* 


M

, an integer number, in MALESAbrain is defined as the

is a percentage of the discussion-problems resulted in

is defined to help the educator and

**Definition 1-2**. The knowledge *preferences Pref* in MALESAbrain is defined as a continuous function of real value ranged from -1 to +1

*Pref*:( *learnerk* , *si,j* ) *→ agreementk,i,j* (-1 ~ +1)

where ( *learnerk* , *si,j* ) is a pair such that

*learnerk* = a learner,

*si,j* = a solution in MALESAbrain (see the defined solution *si,j* in Definition 1-1).

*agreementk,i,j* = the preference score of an learner's, *learnerk*, judgment of a solution *si,j* (value from –1 ~ +1).

#### **Definition 1-3** The *knowledge-weight wi* in MALESAbrain is defined as

 *m <sup>j</sup> <sup>i</sup> jiji sww* <sup>1</sup> ,, || where *wi,j* is the summation of all learner *learnerk* preferences towards *si,j*

*wi,j* = *k agreementk,i,j* (see Definition 1-2 *Pref*: < *learnerk* , *si,j* > *→ agreementk,i,j* )

*j*

*si,j*)) and

Note: we define a symbol "| |" here, which will be used to test the existence of a solution, for transfer the existence of a solution into the value "0" or "1", to allow the knowledgeweight *wi* calculation. )(1 )(0 || *xwhen xwhen <sup>x</sup>* where is a solution. (see Example 1: the calculation of knowledge weight )

**Definition 1-4**. An *artificial-knowledge-CELL* (AK-cell) *ki* in MALESAbrain is a combination definition of Definition 1-1 and Definition 1-3, which is defined as a pair of knowledge-content and knowledge-weight:

*ki* = < *<sup>i</sup>*, *wi* > where *i* is the knowledge-content (see Definition 1-1 *<sup>i</sup>*= (*pi ,* 

*wi* is the corresponding knowledge-weight(see Definition 1-3 *<sup>m</sup> j jijii sww* 1 ,, || )

**Definition 1-5**. The *learning threshold* is defined as a collection of two decision pairs = {<*kq*,*kr*>, <*sm*,*sd*>}, for comparing the retained AK-cells and their respective solutions, where


*sd* is a *solution disagreement threshold*, if *wi,j* < *sd* then delete the solution *si,j* Whenever any of the thresholds are triggered by an AK-cell or a solution, MALESAbrain will re-organize the knowledge structure.

*Pref*:( *learnerk* , *si,j* ) *→ agreementk,i,j* (-1 ~ +1)

*si,j* = a solution in MALESAbrain (see the defined solution *si,j* in Definition 1-1). *agreementk,i,j* = the preference score of an learner's, *learnerk*, judgment of a solution *si,j*

*<sup>j</sup> <sup>i</sup> jiji sww* <sup>1</sup> ,, || where *wi,j* is the summation of all learner *learnerk* preferences towards *si,j*

Note: we define a symbol "| |" here, which will be used to test the existence of a solution, for transfer the existence of a solution into the value "0" or "1", to allow the knowledge-

combination definition of Definition 1-1 and Definition 1-3, which is defined as a pair of

*xwhen <sup>x</sup>* where is a solution. (see Example 1: the

*sd*>}, for comparing the retained AK-cells and their respective

cell, which is the minimum requirement to join the competition for promotion to a

Whenever any of the thresholds are triggered by an AK-cell or a solution, MALESAbrain

*<sup>i</sup>*= (*pi , j*

is defined as a collection of two decision pairs

*kr* then delete the AK-cell *ki*

*sd* then delete the solution *si,j*

*sm* , the learning group agrees the

*si,j*)) and

*kq* then *ki* becomes a qualified AK-

 *<sup>m</sup> j jijii sww* 1

,, || )

*agreementk,i,j* (see Definition 1-2 *Pref*: < *learnerk* , *si,j* >

**Definition 1-2**. The knowledge *preferences Pref* in MALESAbrain is defined as a

**Definition 1-3** The *knowledge-weight wi* in MALESAbrain is defined as

*→ agreementk,i,j* )

**Definition 1-4**. An *artificial-knowledge-CELL* (AK-cell) *ki* in MALESAbrain is a

*wi* is the corresponding knowledge-weight(see Definition 1-3

*wi,j* = *k*

 )(1 )(0 || *xwhen*

*i* is the knowledge-content (see Definition 1-1

*kq* is an *AK-cell qualification threshold*, when *wi*

higher order of discussion position

*kr* is an *AK-cell rejection threshold*, when *wi* <

*sm* is a *solution maturity threshold*, when *wi,j*

*sd* is a *solution disagreement threshold*, if *wi,j* <

will re-organize the knowledge structure.

solution *si,j* is able to solve the problem *pi* .

 

continuous function of real value ranged from -1 to +1

where ( *learnerk* , *si,j* ) is a pair such that

*learnerk* = a learner,

(value from –1 ~ +1).

weight *wi* calculation.

*ki* = < 

solutions, where

 = {<*kq*,*kr*>, <*sm*,

calculation of knowledge weight )

knowledge-content and knowledge-weight:

*<sup>i</sup>*, *wi* > where

**Definition 1-5**. The *learning threshold*

 *m*

**Definition 1-6**. The *growth-factor* , an integer number, in MALESAbrain is defined as the limit for constraining the posted number of AK-cells at each level, which converts the architecture of knowledge base from linear structure into a hierarchical structure, of branch tree, in the forum.

**Definition 1-7**. The *learning-rate function* || || K M is defined to help the educator and learners to understand the progress of the discussion, where the *convergent-factor "*" is the educator's training target set up and the learning-rate || || K M is a percentage of the discussion-problems resulted in consensus, where


