**4.3 A calculation example**

148 E-Learning – Organizational Infrastructure and Tools for Specific Areas

MALESAbrain DISPLAY (or POST) *learners' discussion issues based on "growth-factor* 

*kq* THEN /\* the AK-cell is a qualified AK-cell (Definition 1-5,7)\*/ INCREMENT a "qualified-mark" AK-cell *ki* to knowledge base *K* = {*ki* 

IF *wi* > parent(*wi* ) THEN /\* higher weight AK-cell should be in the front level \*/

*kr* THEN /\* the AK-cell is a worthless knowledge-piece (Definition 1-5)\*/

*sm* THEN /\* the AK-cell becomes an matured AK-cell in the knowledge base

INCREMENT a "mature-mark" AK-cell *ki* to *M* = {*ki* | *ki*  MALESAbrain *si,*<sup>j</sup>


> || K

% learning-rate)

M

thresholds and start another session of discussion whenever the learning-rate

M

*sd* THEN /\* the solution is worthless solution (Definition 1-5)\*/

room or next pieces of knowledge for discussion (Definition 1-2) \*/

MALESAbrain COMPUTE the *knowledge-weight*

Definition 1-6 \*/ /\* *Attention* \*/

MALESAbrain}

END IF

DELETE *ki*

(Definition 1-5,7)\*/

where *wi,j*

DELETE *si,j*

IF ( || || K

ELSE

END IF

END IF

END MALESAbrain

M

IF (dd:mm:yy = due-date) THEN

*sm*}

SWAP(*ki* ,parent(*ki* ) )

DISPLAY a "mature-mark" on solution *si,j*

) THEN /\* if learning-rate ||

PRINT (MALESAbrain meeting with ||

endDiscussion = TRUE /\* stop the meeting \*/

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

"" then end discussion (Definition 1-7) \*/

lower than when time is due \*/

endDiscussion = FALSE CALL MALESAbrain(

UNTIL (endDiscussion = TRUE) /\* *learning-rate* \*/

IF *wi* 

END IF IF *wi* < 

END IF IF *wi,j* 

END IF IF *wi,j* < 

END IF

Learners INPUT their *Pref*:( *learnerk* , *si,j* ) *→ agreementk,i,j* (-1 ~ +1) /\* learners' show their judgment score to others' problem-solutions while browse the forum (Definition 1-2) \*/

IF (*Pref* between –1 ~ +1 but not nil) THEN allow ENTER chat-room or MOVE to next pieces of knowledge /\* Learners must give their preference scores prior to moving on to chat

> *m*

*<sup>j</sup> <sup>i</sup> jiji sww* <sup>1</sup> ,, || /\* Definition 1-3 \*/

is greater or equal to convergent-factor

,,due-date ) /\* re-calibrate the learning

*"* /\* In this subsection, we use a knowledge retained snapshot and a calculation example to look into the internal storage structure of the knowledge base of MALESAbrain.

*X:* Discussion topic "How to Fix an Illegal Operation" - An operation requested to be performed by either the Operating System or CPU, which is not understood and therefore is illegal. *K1* Running a software or game when memory shortage can cause illegal operations. (*w1* = 3.1) *K2* Running a source with a dirty CD or diskettes can cause data to be read improperly causing illegal operations. (*w2* = 2.9) *K2.1* Corrupt, bad or missing files can cause illegal operations. (*2.1* = (*p2.1*, *j s2.1,j*), *w2.1* = 2.1) *s2.1,1* Finding program bugs in the program and fix them. (*s2.1,1* , *w2.1,1*=0.7) *s2.1,2*  It is recommended that you attempt to uninstall and or reinstall the program causing the illegal operation to verify that any corrupt, bad or missing files are replaced or repaired during the reinstallation. (*s2.1,2* , *w2.1,2*=1.4)

Fig. 12 shows a snapshot of knowledge pieces retained in the knowledge base. The knowledge posted by the learners has been organized in a tree-like manner according to the respective weights of individual nodes. In this example shown, the AK-cell *Ki = K2.1* includes a *knowledge-content i= 2.1* and a *knowledge-weight wi=w2.1*. For illustration the calculation on the knowledge-weight *wi=w2.1* bonds with solution *si,j=s2.1,1* and solution *si,j=s2.1,2*. Let us assume three visited learners have given their preferences on solution *s2.1,1* as 0.9, 0.5 and - 0.7; and two visitors have given their preferences on solution *s2.1,2* as 0.6 and 0.8.

By Definition 1-3 *wi,j* is the learners' judgment scores towards *si,j* ∵ *s2.1,1* has three visited learners' judgment scores (0.9, 0.5 and -0.7) ∴*w2.1,1* = 0.9 + 0.5 + (-0.7) = 0.7…① ∵ *s2.1,2* has two visited learners' judgment scores (0.6 and 0.8)

∴*w2.1,2* = 0.6 + 0.8= 1.4…② *2.1* includes the problem *p2.1* and two solution *s2.1,1* and *s2.1,2* (because the number of solutions is two, therefore *m* = 2), so the knowledge-weight is:

$$\begin{aligned} \left|w\_{2,1} = \sum\_{j=1}^{m} w\_{2,1,j} \cdot \left|s\_{2,1,j}\right| \right| &= \sum\_{j=1}^{2} w\_{2,1,j} \cdot \left|s\_{2,1,j}\right| \\ &= w\_{2,1,1} \cdot \left|s\_{2,1,1}\right| + w\_{2,1,2} \cdot \left|s\_{2,1,2}\right| \\ &= 0.7 \cdot \left|s\_{2,1,1}\right| + (1.4) \cdot \left|s\_{2,1,2}\right| \text{ ( $\uparrow$  \square $ and $ \langle \Sigma \rangle $)} \\ &= 0.7 \cdot \text{(1)} + (1.4) \cdot \text{(1)} = 2.1 \text{ ($ \uparrow $)} \text{ ($ \uparrow $)} = \begin{cases} 0 & \text{when ($ \neg $\exists x$ )} \\ 1 & \text{when ( $\exists x$ )} \end{cases} \text{see Definition 1-3)} \end{aligned}$$

Example 1. The calculation of knowledge weight(*w2.1*).

Proposing Two Algorithms to Acquire Learning

learners make their problem-solving plan.

Fig. 13. The interfaces of assessment model in MALESAassessment.

base; and output them to the consultation screen (2).

The inquiry screen (1) shows that the learner enters his/her problem in order to seek advice. The learner types his/her question on the inquiry-board, choose one to three keywords, and input his/her contact email address if s/he wants the feedback from the educator after assessment; then submits or resets his/her request. In the mean time, behind the screen, MALESAassessment will retrieve the keyword-matched AK-cell from its CBR knowledge

When the learner changes his/her screen to consultation screen (2), the system will provide some preliminary suggestions to the learner according to the request on the inquiry screen (1). The retrieved cases are sorted according to their similarity and knowledge-weight. The learner still has to revise them to construct his/her own troubleshooting plan as the testing request. S/he will be encouraged to choose his/her interested AK-cells from screen (2); and output them into attention screen (3) for reuse and study. Whenever s/he clicks an AK-cell,

to help educator in marking.

**5.1 Inquiry screen** 

**5.2 Consultation screen** 

Knowledge in Problem-Based Learning Environment 151

(troubleshooting plan) and thinking processes (log file) will also be recorded in the system

Fig. 13 shows the assessment interfaces in MALESAassessment. The CBR expert system consults the learners when making their troubleshooting-plans for answering the test. There are four screens or interfaces for consulting the learners to arrange their troubleshooting plans. First, the "*Inquiry"* screen can enter clients' query problem. Secondly, the "*consultation"* screen will offer the advice. Thirdly, the "*attention"* screen can help clients pay attention to their chosen cases/AK-cells. And the last/forth "*plan"* screen will help the

This value of 2.1 represents the weight (*w2.1*) of the knowledge-content (*2.1*) in the knowledge (AK-cell *K2.1* ), which provides a quantitative measure of the synergic viewpoint on *2.1* obtained from the discussion and it forms the basis for MALESAbrain's knowledge judgment capability. In the example the qualification threshold *kq* is set to "2" (see Fig. 3). Then any AK-cell weights higher than 2 point will be qualified to join the competition for promotion (see Definition 1-5). This means that the moment the knowledge-weights "3.1" of *K1* and "2.9" *K2* are greater than *K2.1* "2.1" (see Fig. 12); otherwise the system will swap the positions of the lower-weighted AK-cell with the higher-weighted AK-cell. Furthermore, the *AK-cell rejection threshold kr* is set up as "-3.2" and the knowledge-weight *w2.1*=2.1, therefore *K2.1* will not be deleted. The *solution maturity threshold sm* is set up as "4.2" and the solutionweight *wi,j* = *w2.1,2* = 1.4, therefore the learning system does not agree the solution *s2.1,2* is able to solve the problem *p2.1*. The *solution disagreement threshold sd* is set up as "-3" and the solution-weight *w2.1,1* = 0.7, therefore the solution *s2.1,1* will not be deleted by the system.

There is one definition worth to memtion here, the growth-factor, in definition 1-6, is introduced to convert the linear structure into a hierarchical structure of discussion-issues posted on the forum. The hierarchical structure helps our learners decide on different important positions, the learning-issues posted on the forum must not appear as a linear structure on the separate pages on the web site, but as hierarchical on demand. The growth factor normally is set up before discussion; however, it can also be changed after discussion if the educator wants to view the forum from a different angle. If the growth-factor has been set to 3 then the decision tree will be turned into three AK-cells on the top level and become a three-branch tree; if it has been switched to 5 then the decision tree will be turned into five best AK-cells on the top level for the learning decision and become a five-branch tree; if set up as one AK-cell then there is only one best decision to be made and become a linear-tree.
