Chapter 4 Knowledge Representation (KR)
4.2 Instructional Activity Model (IAM)
As mentioned above, in addition to describe the learning contents associated with learning objects, SCORM standard also defines a hierarchical structure, namely, an Activity Tree (AT), used to sequence the delivery of learning content to the learner. By defining the sequencing behavior rules within an AT, we can develop an intelligent approach to (semi-)automatic course and exercise sequencing. Therefore, how to create, represent, and maintain the Activity Tree and associated sequencing definition is our concern. For a large-scale learning activity, the Activity Tree will become too complex to be managed and reused. Besides, it is hard to reuse and integrate ATs without knowing the inter-relations among ATs. This implies that the scalability and flexibility of an adaptive learning system will be limited. Moreover, for modern personalized learning, many researches have used Pedagogical Theory [19] [40] [87] [122] to enhance the evaluation of the personal learning characteristic.
Hence, in this dissertation, we first define the interrelation attributes of an AT, e.g., capability, weight, etc. Then, we extend and modularize the structure of AT by means of Pedagogical Theory and the concept of the Object Oriented Methodology, respectively.
As shown on the right side of Figure 4.3, a large AT is divided into three small AT nodes with interrelation attributes. Therefore, by means of the interrelation attributes, the small AT nodes can be integrated and further connected with other AT nodes; e.g., AT1 connects AT4 and AT5. Thus, we propose a novel model, the Instructional Activity Model (IAM) [115], which is composed of related Activity Tree nodes. Based upon Pedagogical Theory, each AT node in IAM is modularized as a learning unit with inter-relations and specific attributes, which can be easily managed, reused, and integrated. We also propose an AT Selection algorithm with a pedagogical strategy used to traverse IAM in order to generate dynamic learning content for the learner. In this
section, we describe the Instructional Activity Model, including its properties, and the AT Selection algorithm.
Figure 4.3: The Concept of Modularizing an AT
4.2.1 Instructional Activity Model
In Sequencing and Navigation (SN), we can create an AT on the fly. As mentioned above, in a large AT, its organization and sequencing rules are hard to manage and reuse. However, a large number of ATs will also make the management of AT nodes and rules complicated. Therefore, to strengthen the scalability and flexibility of AT, we must define a suitable unit of an AT. According to Bloom’s Mastery Theory [10], a suitable unit of learning content is a chapter or a section for learning. Thus, in IAM, we define the unit of an AT as a chapter or a section.
Assume there are n ATs. We define an AT set as ATset = {AT1, AT2, …, ATn}.
According to the formulation of Gagne [42], “A capability is a knowledge unit stored in a person’s long term memory that allows him/her to succeed in the realization of physical, intellectual or professional activity.” Suppose there are m capabilities; we can obtain Cset = {c1, c2, …, cm}. Before learning an AT, students are supposed to possess some capabilities, called Prerequisites. Similarly, after learning an activity tree,
students can acquire further capabilities, called Contributions. Every prerequisite or contribution has its own weight representing the significance of learning capabilities before and after learning. Therefore, in IAM, the Cset can be regarded as the union of all prerequisites and contributions, and an AT, thus, has several capabilities.
A learning activity or a course is composed of several ATs with input/output capabilities. The student learns a suitable AT and gains further capabilities, which enable the student to learn another advanced AT. This learning process is repeated until the student has finished all the learning objectives predefined by teachers. Then, every student will have an individual value of Cset. Figure 4.4 shows a diagram of IAM.
In Table 4.1, we define the related attributes of interrelations, measure functions, AT selecting criteria, etc. in IAM as shown in Figure 4.4
Figure 4.4: The Diagram of IAM
Table 4.1: The Definitions of Related Symbols in IAM
Symbols Description
eij The edge from ci to ATj, called “prerequisite edge”, means that before learning ATj, the student is supposed to possess this ability ci.
e'ij The edge from ATi to cj, called “contribution edge”, means that after learning ATi, the student will gain the ability cj.
w(eij) The weight of eij denotes the significance of ci before learning ATj where the sum of w(eij) of an AT is 1, i.e.,
∑
iw(eij)=1,∀j.w(e'ij) The weight of e'ij denotes the significance of cj after learning ATi where the sum of w(e'ij) of an AT is 1, i.e.,
∑
jw(e'ij)=1,∀i.mReqij The minimum requirement of ci for learning ATj is used to determine whether the student is qualified to learn ATj or not.
grade(e'ij) The learning grade after learning ATi.
val(cm)
Table 4.1: (Cont’d) The Definitions of Related Symbols in IAM
The Related Measure Functions of AT
Acquired Capability (AC) It records student’s learning results. AC=∪(ci, val(ci)), Course Objectives (CO) It records student’s learning objectives. CO=∪(ci).
Potential Capability List (PCL)
Each AT has a PCL recording all the contribution capabilities which can be reached from this AT via edges in IAM. It can be formulated as PCLATk=∪(ci), where ci can be reached from ATk by connecting edges, e.g., in Figure 7.2 the PCLAT1 equals {c2, c3, c4, c5, c6}.
Student’s Grade Prediction (SGP)
SGP denotes the performance prediction of the specific student related to the AT, i.e., SGPk=Σi (val(ci)×w(eik)).
Normalized Objective Weight (NOW)
NOW denotes the relativity between an AT and the student’s CO. Higher objective weight implies better learning efficiency. Empirically, selecting function tends to select the AT with higher SGP and higher NOW for students.
( )
CF, a linear combination of selecting criteria, is used to select a suitable AT for learner. For example, for ATi, CFi=αNOWi + βSGPi , where α+β=1, 0≤ α, β ≤1.
In brief, the Instructional activity model (IAM), a graphical representation of a learning activity or course, contains a set of ATs; Capabilities, including prerequisites
and contributions; a set of Relations Edges, including eij with mReqij and e'ij; and a set of Measure Functions. Assume IAM has n ATs and m capabilities. Then, it can be formulated as a quadruple, IAM = (ATset, Cset, Eset, E'set),
where
ATset = {AT1, AT2,…, ATn}.
z Cset = {c1, c2,…, cm}.
z Eset = ∪(Ej), where Ej = ∪i (eij, mReqij), eij∈ATj.
z Eset is the set of all prerequisite edges with minimum requirement value in an IAM.
z E'set =∪(E'j), where E'j = ∪j (e'jk), e'jk∈ATj.
z E'set is the set of all contribution edges in an IAM.
4.2.2 Basic Functionalities
Based upon the structure of IAM described above, we can develop several approaches to provide students with a learning environment for a dynamic and adaptive course. The learning process can be simply considered as the sequencing of activity trees in IAM in order to enable students to satisfy the learning objectives. The flowchart and algorithm of AT Selection is shown in Figure 4.5 and Algorithm 4.1, respectively.
Figure 4.5: The Flowchart of AT Selecting Process
Here, we will explain the AT Selection algorithm of IAM. First, we initialize the learning status by loading AC and CO, evaluate the PCLAT of every AT (Setp1), and then enter the loop of the learning activity (Step2). During the AT selection process, we mark each AT with Candidate or Blocking after comparing the mReq(eij) with val(ci) (Step2.1). Candidate indicates that this AT will be selected later, and Blocking indicates the opposite. Before delivering AT to the learner, we have to execute the selection process to choose a suitable AT. In general, we only use the CF value to choose one suitable AT (Step 2.2.2). However, to meet specific needs, e.g., to apply Pedagogical Theory, we can define other selection criteria and a strategy in the extended selection scheme, which will be described later in Section 4.2.3 (Step 2.2.1). After completing the AT selection process, we choose a suitable AT marked candidate and deliver it to the learner (Step 2.2). However, if no AT marked candidate exists, the AT selection process proceeds to the Remedy Course Process (Step 2.2.3-Step 2.2.7). In the Remedy Course Process, we select an AT with the largest value of cm ∈CO (Step 2.2.3-Step 2.2.4) and then find a ci with the smallest, largest, or medium value of (mReq(eij)－val(ci)), according to the type of SelectingPolicy (Step 2.2.5). In this algorithm, we use three policies to select different capabilities for adaptive learning. The policy “Easiest First” tends to select a ci in which the learner has earned a high grade, but the policy “Hardest First” does the opposite. After selecting a ci, we can decide which AT connected with ci to deliver to the learner by computing MAX((mReq(eij)－
grade(e'ki))×w(e'ki)), which implies that the progress of the learner is the largest (Step 2.2.6). Figure 4.6 shows in detail the Remedy Course Process. Finally, when the learner has finished and satisfied all the course objectives (CO), the AT selection process stops.
Algorithm 4.1: AT Selection Algorithm
Input: IAM, AC and CO of learner, and SelectingPolicy = {Easiest First, Medium First, Hardest First}.
Output: the new AC after learner has finished learning activity.
Step1: Evaluate the PCLAT of every AT in IAM.
Step2: while(CO⊄AC) //start the learning activity
// decide whether the type of AT is Candidate or Blocking state 2.1: for each ci with eij in AC
{ if (mReq(eij) > val(ci))
then mark the ATj with Blocking else if (ATj has not been learned yet)
then (compute CFj )and (mark the ATj with Candidate) } //select a suitable AT to be learned
2.2: if (∃AT with Candidate mark) // select the AT with Candidate mark then
2.2.1: if ∃ extended selecting scheme of AT then do it. // for specific needs 2.2.2: Select an AT with the highest CFand deliver it to the learner.
else if (∃AT with Blocking mark)
then //go to Remedy Course Process & select a suitable AT 2.2.3: for each ATj with Blocking mark
{Count the amount of cm∈CO which is connected by e'jm.}
2.2.4: Select the ATj with the largest amount of cm∈CO.
2.2.5: for all ci with eij
{ if SelectingPolicy = ”Easiest First”, ”Medium First” or ”Hardest First”
then Find the ci with the smallest, medium, largest value of (mReq(eij)-val(ci)), respectively.}
2.2.6: for all e'ki∈Ei in ci,
Select the ATk with MAX( (mReq(eij)–grade(e'ki))×w(e'ki)).
2.2.7: Clear the mark of ATj and deliver the ATk to the learner.
2.3: if learner passes the selected AT then mark this AT with Learned.
2.4: update AC after the learner learns selected AT.
Step3: return new AC.
Figure 4.6: The Diagram of Remedy Course Process
Example 4.1:
This IAM in Figure 4.7 can be represented as follows:
IAM = ({AT1, AT2 AT3, AT4, AT5,}, {c1, c2, c3, c4, c5, c6, c7, c8, c9}, {(e11,0.8), (e22,0.7) , (e23,0.8), (e33,0.8) , (e44,0.8) , (e55,0.8) , (e65,0.6)}, {e'14, e'15, e'25, e'36, e'47, e'48, e'58, e'59}).
Figure 4.7: The Example of IAM
Case 1: We assume that AC={(c1, 0.82), (c2, 0.75) } and CO={c4, c7, c8}. Note that the value in parenthesis is the val(ci).
The PCLAT has been evaluated as shown in Figure 4.7. After the first iteration of the While loop of Algorithm 4.1, we can get results as shown in Table 4.2. Thus, AT1
will be delivered to the learner because it has the highest CF value.
Case 2: we assume that AC={ (c1, 0.82), (c2, 0.75), (c4, 0.75), (c5, 0.6), (c6,unknown) }, CO={c4, c7, c8}, and Blocking AT={AT3, AT4, AT5}. The AT selecting process has moved into Remedy Course Process.
Before Step 2.2.5, because AT5 has one cm∈CO, AT5 is selected. If the Selection-Policy is “Easiest First,” the c5 with the smallest value, 0.2, of (mReq(e55)－
val(c5)) is selected. Then, by computing (mReq(e55) － grade(e'15))×w(e'15)) and
4.2.3. Applying Pedagogical Theories in IAM
As mentioned above, the Instructional Activity Model (IAM), which is composed of related AT nodes with inter-relations and specific attributes, can be easily managed, reused, and integrated. Our proposed AT Selection Algorithm can then generate the dynamic learning content for the learner by traversing the IAM. In addition, due to
strengthened the scalability and flexibility of IAM, appropriate pedagogical theories can be selected and applied to provide personalized learning guidance according to extension schemes for specific needs. Therefore, in this section, we will show how well-known pedagogical theories can be applied in IAM by means of extension schemes.
Extension Scheme of IAM:
We can consider three aspects of pedagogical theories: 1. the Capability Taxonomy, 2. the Learning Style, and 3. the Organization of Teaching Material. We can describe these three aspects as follows.
z Capability Taxonomy: By learning different Learning content, the learner will acquire different knowledge or capabilities. Thus, Gagne [40] considered that the learning outcomes of learners can be classified into five types: Verbal Information, Intellectual Skills, Cognitive Strategies, Motor Skills, and Attitude. Accordingly, we can categorize the learning capabilities in IAM into five types and define each ci
in Cset = {c1,c2, …,cm} as having five dimensions: <vci, ici, cci, mci, aci>, where vci
denotes verbal capability, ici denotes intellectual capability, cci denotes cognitive capability, mci denotes motor capability, and aci denotes attitude capability.
z Learning Style: The learner’s learning style is the way s/he prefers to learn.
Therefore, learners have individual learning preferences during learning activities designed for specific instructional approaches or teaching materials. Many articles [26] [72] [107] [111] [120] [122] have proved that learners can achieve excellent learning performance if we can give them instruction and teaching materials according to their individual learning styles. Sternberg [102] also collected many taxonomies of learning style based upon different criteria. Thus, we apply three features of learning styles, Visual, Auditory, and Kinesthetic, in IAM to generate
adaptive learning guidance. To provide a learner with suitable learning contents, we have to define not only the learning style of the learner, but also the learning content of AT. Therefore, we need to select a suitable AT whose learning style is similar to that of the learner. Moreover, we can use existing questionnaires [50][102] to extract the values of individual learning styles of learners.
z Organization of Teaching Material: It is essential to organize suitable teaching materials for students. According to Bassing [7], we can categorize the organization of teaching materials into three types: (1) Logical Organization, where the teaching materials are ordered in a systematical fashion as traditional teaching strategies, e.g., teaching the mathematics from basic to advanced concept in a fixed order; (2) Psychological Organization, where emphasis is placed on the student’s own interest, ability, and needs; and (3) Eclectic Organization, which takes both Logical Organization and Psychological Organization into consideration. Therefore, in IAM, the learning guidance and selected AT have to be based on the concepts of Logical Organization and Psychological Organization, respectively. Table 4.3 shows the related symbol definitions used when applying Pedagogical Theory in IAM.
Table 4.3: The Symbol Definitions of Pedagogical Theory in IAM
Symbols Description
LgOrgi
This denotes the Logical Organization of ATi. The value of LgOrgi is mapped to the difficulty of ATi.
LnStyi
This denotes the value of Learning Style, including Visual, Auditory, and Kinesthetic in ATi. The LnSty is represented as a vector, i.e., <VATi, AATi, KATi>, where the value is between 0 and 1.
SLS
This denotes the Student Learning Style (SLS) for representing the learning style of the student. SLS is represented as a vector like LnStyi, i.e., <Vs, As, Ks>, where the value is between 0 and 1.
Based upon the symbols shown in Table 4.3, we can define the Similarity Factor, SF,
and redefine the Chosen Factor, CF, for ATi as follows:
z SFi = SLS‧LnStyi, where the symbol “•” represents the dot product.
z CFi = αNOWi + βSGPi +γLgOrgi, where α+β+γ=1.
The SF is used to compute the similarity of the learning style between the learner and ATs. Thus, we can filter out ATs with low SF values and then select the AT with the highest CF value. Although we have defined the selection formula and strategy according to Pedagogical Theory, teachers also can redefine them by themselves.
AT Selection Process Using Pedagogical Theories:
Therefore, in the AT Selection Algorithm, we can compute CF and SF to acquire the psychological organization and logical organization characteristics of every AT (Step 2.1). The SF, which is computed as the dot product of the student’s learning style vector (SLS) and the AT’s learning style vector (LnSty), can denote the similarity of the learning style between the AT and Learner. Thus, using the value of SF, we can get a suitable AT form IAM (Step 2.2.1). Finally, the CF can be used to determine the most suitable AT for the learner (Step 2.2.2).
Example 4.2: Learning in IAM using pedagogical theories
We present a simple example of learning in IAM using pedagogical theories. First, we define IAM and the related attributes of each AT, and then we demonstrate the process of the AT Selection Algorithm for a specific student. An example of IAM is shown in Figure 4.8.
Figure 4.8: An Example of IAM with Pedagogical Theories.
IAM in Figure 4.8 is represented as follows:
IAM=({AT1, AT2, AT3, AT4, AT5}, {vc1, cc2, mc3, vc4, ic5, vc6, mc7, ic8, cc9, ic10}, {(e11,0.3), (e12,0.6), (e22,0.5), (e33,0.4), (e44,0.5), (e55,0.6), (e65,0.5)}, {e'14, e'15, e'25, e'26, e'36, e'37, e'48, e'49, e'5,10})
Table 4.4: Learning style and logical organization of each AT.
AT1 AT2 AT3 AT4 AT5
LnSty <0.8, 0.1, 0.1> <0.1, 0.8, 0.1> <0.6, 0.1, 0.3> <0.2, 0.1, 0.7> <0.1, 0.2, 0.7>
LgOrg 0.3 0.3 0.5 0.3 0.7
The Learning Style and Logical Organization used in the AT Selection Algorithm are shown in Table 4.4. Because the value of LgOrg is mapped to the difficulty of AT, the difficulty of the metadata in SCORM can be used to define the value range, e.g., {Very Easy, Easy, Medium, Difficult, Very Difficult} corresponding to {0.1, 0.3, 0.5, 0.7, 0.9}. Suppose there is a learner who is learning in this IAM; her/his personal information is as follows:
z AC = {(vc1, 0.5), (cc2, 0.8), (mc3, 0.1), (vc4, 0.6), (ic5, 0.43)}, z SLS= <0.1, 0.2, 0.7>,
z CO = {ic5, vc6, mc7, ic8, cc9, ic10}.
Since s/he has learned AT1, the AT Selection Algorithm will choose the next AT for her/his learning. CFi and SFi are defined as follows:
z CFi=0.25×NOWi+0.25×SGPi+0.5×LgOrgi, z SFi= SLS‧LnStyi .
The related results obtained by the AT Selection algorithm are shown in Table 4.5.
Table 4.5: Selecting Criteria for Each Activity Tree.
AT2 AT3 AT4
PCL {ic5,vc6,ic10} { vc6,mc7,ic10} {ic8, cc9}
NOW 1 1 1
SGP 0.5×0.4+0.8×0.6=0.68 0.1×1=0.1 0.6×1=0.6
LgOrg 0.3 0.5 0.3
SFi 0.24 0.29 0.53
CFi 0.57 0.525 0.55
Then, we can use the following selection strategy: for smart students, select the AT with the highest CFi value; for other students, select the AT with the highest SFi value.
With this strategy, we select AT2 for smart students, and AT4 for other students. In addition, we can revise CFi and SFi for specific purposes. For example, some teachers believe that learning style of a student is related to student’s grade, and they can modify CFi and SFi as CFi = 0.5 × NOWi + 0.5 × LgOrgi, SFi = 0.5 × SGPi + 0.5 ×
(SLS‧LnStyi). If the selection strategy remains the same, we will provide AT3 for smart students and AT4 for other students.
Evaluating of the Expressive Power of IAM:
We have shown that it is possible to apply pedagogical theories in IAM for specific need. How many pedagogical theories can be applied in IAM? In this section, we will evaluate that how many different structures IAM can support to meet pedagogical needs.
Educational researchers have proposed various types of course structures to facilitate learning. Posner [90] proposed three types of structures including discrete structure, linear structure, and hierarchical structure. Bruner [12] proposed the concept of a spiral curriculum. Efland [34] also proposed the lattice curriculum. Each structure satisfies certain kinds of pedagogical needs. IAM can be applied to these course structures, as shown in Figures 4.9 and 4.10.
Figure 4.9: IAM Mapping to Discrete Structure, Linear Structure, and Hierarchical structure
Figure 4.10: IAM Mapping to Spiral Curriculum and Lattice Curriculum.
4.2.4 The Construction of IAM
As mentioned in previous sections, based upon the OO Methodology and SCORM standard, we have proposed an Instruction Activity Model (IAM) which is composed of related AT components with inter-relations and specific attributes designed to meet pedagogical needs. However, for teachers and authors, how to apply IAM in real learning environments is also an important issue. Therefore, in this section, we propose a systematic approach to fast and easily construct IAM using traditional course resources. First, the teacher has to create the Content-Contribution Relationship Table denoting the potential concept which will be acquired by learning the learning content.
For example, assume that a course, Introduction to Computers, includes three chapters
For example, assume that a course, Introduction to Computers, includes three chapters