## Appendix C The ST Method
### Agreeing to Equation (45), We Arrange the Matrix \(D\) Hosting a Number \(n=5\) of Directions  
\[D= \begin{pmatrix}d_{1}\\ d_{2}\\ d_{3}\\ d_{4}\\ d_{5}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Comprehension and Concept Identification}\\ \text{Problem}-\text{Solving Application}\\ \text{Research and Evidence Integration}\\ \text{Practical Implementation or Experimentation}\\ \text{Reflection and Synthesis}\end{pmatrix}  \tag{138}\]  
Now, as described in Equation (46), to shape the configuration of the ST structure, we need to combine the matrices \(L^{i}\), \(P^{i}\), and \(A^{i}\). We do so by referring to each direction \(d_{i}\). Direction \(d_{1}\): Comprehension and Concept Identification (Task: read and summarize key concepts from material provided)  
For the assemblage of matrices \(L^{1}\), \(P^{1}\), and \(A^{1}\) (cf. Equation (46)), we let \(\pi(L,1)=3\), \(\pi(P,1)=5\), and \(\pi(A,1)=2\); thus, we obtain  
\(L^{1}:\) (Cognitive Attributes)--Knowledge required for the task  
\[L^{1}= \begin{pmatrix}L^{1}_{1}\\ L^{1}_{2}\\ L^{1}_{3}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Definition ofkey terms}\\ \text{Understanding of fundamental principles}\\ \text{Recognition of essential facts}\end{pmatrix}  \tag{139}\]  
\(P^{1}:\) (Practical Application Attributes)--How knowledge is applied  
\[P^{1}= \begin{pmatrix}P^{1}_{1}\\ P^{1}_{2}\\ P^{1}_{3}\\ P^{1}_{4}\\ P^{1}_{5}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Identifying key points in a text}\\ \text{Summarizing concepts concisely}\\ \text{Relating ideas to prior knowledge}\\ \text{Categorizing information logically}\\ \text{Distinguishing essential vs. non $-$ essential detail}\end{pmatrix}  \tag{140}\]  
\(A^{1}\): (Performance and Behavioral Attributes)--Cognitive engagement  
\[A^{1}= \begin{pmatrix}A^{1}_{1}\\ A^{1}_{2}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Critical Thinking}\\ \text{Logical Reasoning}\end{pmatrix} . \tag{141}\]  
Direction \(d_{2}\): Problem-Solving Application (task: apply identified concepts to solve a given problem)  
To obtain the matrices \(L^{2}\), \(P^{2}\) and \(A^{2}\), we let \(\pi(L,2)=2\), \(\pi(P,2)=2\), and \(\pi(A,2)=5\), (cf. Equation (46)); thus, we have  
\(L^{2}:\) (Cognitive Attributes)  
\[L^{2}= \begin{pmatrix}L^{2}_{1}\\ L^{2}_{2}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Knowledge of problem $-$ solving techniques}\\ \text{Understanding of relevant formulas}\end{pmatrix}  \tag{142}\]  
\(P^{2}:\) (Practical Application Attributes)  
\[P^{2}= \begin{pmatrix}P^{2}_{1}\\ P^{2}_{2}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Applying concepts to structured problems}\\ \text{Identifying appropriate methods for solutions}\end{pmatrix}  \tag{143}\]\(A^{2}:\) (Performance and Behavioral Attributes)  
\[A^{2}= \begin{pmatrix}A_{1}^{2}\\ A_{2}^{2}\\ A_{3}^{2}\\ A_{4}^{2}\\ A_{5}^{2}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Logical structuring of thought processes}\\ \text{Abstract reasoning}\\ \text{Detail -- oriented problem solving}\\ \text{Justification of chosen methodology}\\ \text{Persistence in finding solutions}\end{pmatrix}  \tag{100}\]  
Direction \(d_{3}:\) Research and Evidence Integration (task: find and integrate external sources into analysis)  
For building up the matrices \(L^{3}\)\(P^{3}\) and \(A^{3}\), we let \(\pi(L,3)=2\), \(\pi(P,3)=1\), \(\pi(A,3)=4\), respectively (cf. Equation (46)) then, we have  
\(L^{3}:\) (Cognitive Attributes)  
\[L^{3}= \begin{pmatrix}L_{1}^{3}\\ L_{2}^{3}\end{pmatrix} \rightarrow \begin{pmatrix}\text{Understanding of credible sources}\\ \text{Awareness of different perspectives}\end{pmatrix}  \tag{101}\]  
\(P^{3}:\) (Practical Application Attributes)  
\[P^{3}= \begin{pmatrix}P_{1}^{3}\end{pmatrix} \rightarrow \begin{pmatrix}\text{ Identifying relevant academic sources}\end{pmatrix}  \tag{102}\]  
\(A^{3}:\) (Performance and Behavioral Attributes)  
\[A^{3}= \begin{pmatrix}A_{1}^{3}\\ A_{2}^{3}\\ A_{3}^{3}\\ A_{4}^{3}\end{pmatrix} \rightarrow