Each evidence variable is quantized using the relevant data extracted from the performance data sources, a set of rules, sequence detection (see Figure 6.5), and count and summary statistics (see Figure 6.5). The purpose of sequence detection is to recognize sequences of actions that, for example, violate or meet particular expectations, such as safety procedure.
Description: Count and summary statistics are numeric values calculated based on UI events to characterize user behaviour
SEQUENCE DETECTION
Actions Target Sequences
Description: Sequence detection is the process of identifying occurrences of specified target sequences.
Events Count and Summary
Statistics COUNT AND SUMMARY STATISTICS
• Time on task • % idle time • Component removal count • simulation attempts count
Figure 6.5: Sequence detection and count and summary statistics
(Adapted from: [108]).
The quantization process uses a reference data set, as the “gold standard”, where necessary. The processes of data extraction and quantization of evidence variables, node 1, “UseOfCorrectComponents” (UCC), node 2, “CorrectPlacementOfComponents” (CPC), and node 33, “ExperienceUsingVEL” (EUV), (see Chapter 5, Figure 5.3) are hereby described. The quantization of the remaining evidence variables is described in Appendix C. The quantization of nodes 1 (UCC) and 2 (CPC) involves the comparison of a student’s built circuit with the reference circuit, for equivalence, by the CircuitComparator, which consists of two component parts: ComponentComparator and TopologyComparator. Two electrical circuit networks are equivalent if they both contain the same set of components in type and value, and the manner in which the components are connected result in the same branch currents and voltages [222]. The circuits are represented in the system as netlists.
6.2.1 Quantization of Node 1: “UseOfCorrectComponents”
The Quantization of UCC entails checking if a student’s built circuit is component- and value- wise equivalent to the reference circuit, by the ComponentComparator. The variable, UCC, is then quantized as:
100
1
n xi
UCC
q
m
n
i
=
×
∑
=
(6.1)Where, in this case, n = number of different types of reference circuits, m = number of circuits built and simulated by a student in the process of undertaking an activity, xi = number of
circuits built and simulated by student that are component- and value-wise equivalent to reference circuit type i, and q = number of xi’s not equal to zero (q is an indication that a
circuit of a particular type is built with the correct components and values, at least once).
6.2.2 Quantization of Node 2: “CorrectPlacementOfComponents”
The quantization of CPC necessitates that a student’s built circuit be compared to the reference circuit for topological equivalence, by the TopologyComparator. Two circuits are considered to be topologically equivalent if they have the same voltage/current characteristics across all terminals of the networks [222]. That is, the topological comparison of two circuits requires the explicit comparison of the branch voltage/current characteristics of the circuits. For this purpose, a directed graph, G, without self-loops, is used to completely describe the circuit (network) and the KVL and KCL equations of the network are then derived from the graph, using the relevant component of the graph [223]. A graph, G, is a pair (U,E) where U is the set of all the vertices on the graph and E is the set of pairs (u,v) called edges such that u,v∈U, u≠v [224]. The nodes and branches of the network make up the vertices and the edges of the graph, respectively. The orientations of the edges reflect the reference direction of the currents/voltages across the branches of the network. The relevant components of the graph, G, required for the derivation of the matrices/equations necessary for the characterization of the network represented by G include path, subgraph, loop, cutset, tree, and cotree (see [223][225] for details). The matrices include the Incident Matrix (IM), Aa, and Reduced
Incident Matrix (RIM), A; Loop Matrix (LM), Ba, and Fundamental Loop Matrix (FLM), B;
Cutset Matrix (CM), Da, and Fundamental Cutset Matrix (FCM), D. The IM, Aa,is generated
directly from G. For example, the network of Figure 6.6, is described by the graph, G, of Figure 6.7.
Figure 6.6: Circuit schematic of one of the laboratory activities used for the evaluation of the VEL: Twin-T Notch filter.
a b c d e f g h (1) (2) (3) (4) (0) a b c d e f g h (1) (2) (3) (4) (0)
Figure 6.7: The graph, G, describing the network of Figure 6.6.
In G, the edges represent the branches of the network, so that a, b, c, d, e, f, g, and h represent vcc, c1, c2, c3, r1, r2, r3, and r4, respectively. G has n vertices and b edges corresponding to
the n nodes and b branches of the network. The graph, G, is used to generate the KCL and KVL equations describing the network, such that, in this context, the check for topological equivalence between a student’s built and the reference circuit reduces to matrix comparison. The details of the generation of the KCL and KVL equations, from G, are given in Appendix C1. The result of the comparison is used to generate the quantized value for the node, CPC, using equation 6.1.
100
1
n xi
CPC
q
m
n
i
=
×
∑
=
(6.1)Where, in this case, n = number of different types of reference circuits, m = number of circuits built and simulated by a student, xi = number of circuits built and simulated by a student that
are topologically equivalent to reference circuit type i, and q = number of xi’s not equal to
zero (q is an indication that a circuit of a particular type is built topologically correctly at least once).
6.2.3 Quantization of Node 33: “ExperienceUsingVEL”
In order to quantize the variable, “ExperienceUsingVEL (EUV)”, the total time on task to date is used. The measure of experience is a real number, β, such that0 ≥ ≤β 100. β = 0 if a student has not previously undertaken any laboratory activity in the VEL environment. Each time a student undertakes a laboratory activity in the VEL environment, the activity counter is increased, and a value for the total time on activity to date, x, is derived, as x= +td tc, where
d
t is the total time on task to date, before undertaking activityn−1, and tc is the total time on task for activityn−1. That is, since activityn is the activity being assessed, the experience that will impact on the performance of activityn is the experience up to activityn−1. Using x, the measure of experience, β, is evaluated as a percentage of the set maximum total time on
activity, 4
18 10
m
t = × . tmis set based on the assumption/expectation that a student would have mastered the use of the VEL by the time of undertaking up to 50 laboratory activities in the environment, where the average time per activity is 3600secs (1 hr). Hence, using x, the measure of experience, β, is evaluated as follows:
(
)
0, if x
0,else,
xtm
100
β=
=
β=
×
(6.2)In this way, a student’s measure of experience, β, increases with each activity. The number of activities and average time per activity could in practical settings be varied to suit specific educational needs.