1. The Zone of Proximal Development (ZPD) and Scaffolding

• The Foundations (Vygotsky / Bruner): Research shows that students progress optimally when confronted with a challenge slightly above their current capabilities, provided they are guided by a third party (the Zone of Proximal Development).
• Application in Maher: The three-level Socratic approach (Focus, Decomposition, Metacognitive Anchor) of your DAG engine is the exact computational translation of the concept of scaffolding. Maher keeps students within their ZPD by dynamically adjusting assistance based on their micro-errors, thereby preventing discouragement or boredom.

2. The Fading Principle (Progressive Withdrawal)

• The Scientific Foundation: For learning to be durable, the assistance provided by the guide or technological tool must decrease as the learner gains autonomy. If assistance remains constant, students develop dependency.
• Application in Maher: Through your xAPI traces, your statistical scripts explicitly capture the Fading Index. This is a cutting-edge learning approach: the AI progressively withdraws as soon as it detects that the student has mastered the critical skill (Deduction, Analysis).

3. Cognitive Load Theory (John Sweller)

• The Scientific Foundation: Human working memory is limited. If a software interface is overly complex or a chatbot asks overly vague questions, “extraneous cognitive load” saturates the student’s brain, halting learning.
• Application in Maher: The choice to design a streamlined mobile application featuring a Tap-to-Target interaction logic and simple language calibrated for 12-year-old adolescents is crucial. You reduce unnecessary load to focus all of the student’s mental energy on higher-level mathematical reasoning (critical and creative thinking).

4. The Active Engagement Model (ICAP Framework)

• The Scientific Foundation (Michelene Chi): The ICAP model classifies student engagement into four levels: Passive, Active, Constructive, and Interactive. The deepest learning occurs at the Constructive (generating ideas) and Interactive (dialoguing to co-construct) levels.
• Application in Maher: By refusing passive multiple-choice questions and forcing students to engage in a Socratic dialogue and manipulate a combinatorial canvas for creative thinking, Maher propels the learner into the highest cognitive engagement tiers of the model (Constructive and Interactive).

📊 Synthesis: Why Your Thesis Jury Will Appreciate Your Project

What Poor AI Applications Do	What Your Project’s Approach (Maher) Does	Reference Theoretical Model
Provide the raw answer at the slightest blockade.	Offer graded hints that force critical thinking.	ZPD & Scaffolding (Vygotsky / Bruner)
Keep the exact same level of assistance at all times.	Measure and apply a progressive reduction of help.	Fading Index (Cognitive Sciences)
Drown the student in vague text or complex interfaces.	Use simple language and targeted tactile interactions.	Cognitive Load (Sweller)
Require simple closed answers (True/False).	Stimulate divergent thinking, fluency, and flexibility.	Divergent Thinking (Guilford / Torrance)

💡 What This Changes for Your Thesis Manuscript

This theoretical validation provides your initial academic anchoring keywords. In your thesis introduction, you will not present Maher merely as a software tool, but as an experimental research device investigating “the automation of individualized Socratic scaffolding aimed at reducing extraneous cognitive load and optimizing the zone of proximal development”.