Foundations of Logical and Logical-Mathematical Thinking

Course Framework and Learning Objectives

The course is part of the Undergraduate School (Pregrado) within the Faculty of Humanities. This specific session, titled "Logical Thinking Session 1," focuses on the foundations of human cognition, specifically exploring the concepts of "Thinking and Thought," "Logical Thinking," and "Logical-Mathematical Thinking." For the year $2026$ , the curriculum aims for a high level of analytical competence. The intended learning outcome for students is the ability to interpret contextual situations within their environment through the application of inductive or deductive inferences, demonstrating a firm grasp of the foundations of thought. The primary evidence of learning for this session is participation in an online forum (FO) where students discuss the vital importance of cognitive development. The specific goal (Propósito) for Session 2 extends this by ensuring students can recognize, analyze, and justify the application of both logical and logical-mathematical thinking across various real-world contexts.

Philosophical and Psychological Foundations of Thinking

The act of thinking (Pensar) is defined as a mental activity through which humans organize and assign meaning to perceived information. According to Valera ( $2013$ ), this process allows individuals to know, imagine, abstract, analyze, and compare environmental phenomena. It is the mechanism by which reason and emotion are articulated to interpret reality, project into the future, and construct new meanings. Jean Piaget ( $1952$ ) describes thinking as an internalized form of action that enables humans to mentally organize experiences to adapt to, understand, and transform their surroundings. This involves coordinating logical operations and building structures that grant sense to reality. Lev Vygotsky ( $1978$ ) characterizes thinking as a superior psychological process developed through social interaction and the employment of language as a reasoning tool. It allows subjects to reflect and make decisions by integrating cultural and social experiences into the construction of meaning.

Definitions and Forms of Thought

Thought (Pensamiento) is a complex mental process used to organize, interpret, and transform environmental information. Lira ( $2007$ ) notes that it forms the base of logical reasoning and the construction of significant knowledge. Valera ( $2013$ ) emphasizes that thought mobilizes cognitive capacities to compare, abstract, or imagine reality by integrating previous knowledge and emotions. According to Irving Copi in "Introduction to Logic" ( $1991$ ), logical thought manifests in three fundamental forms:

Concept: The mental representation of an object or a set of objects sharing common characteristics; it is the basic unit of logical knowledge.
Judgment: An assertion or denial established between two concepts, expressed as propositions that can be true or false.
Reasoning: The process of linking multiple judgments to reach a conclusion, representing the most complex form of logical thought.

Categorization: Logical vs. Logical-Mathematical Thinking

Logical Thinking is defined as the human capacity to understand everything surrounding us, specifically allowing for the comprehension of relationships and differences between actions, objects, or events. In contrast, Logical-Mathematical Thinking is the capacity to construct relationships between the properties of objects, elaborate mathematical content, and solve problems based on reality. The fundamental difference lies in quantification; while logical thinking deals with causal links and qualitative arguments, logical-mathematical thinking involves quantifying reality, handling numerical operations, and performing modelings. It is used to interpret and argue based on statistical data, proportions, and magnitude comparisons.

Importance and Application of Logical Thinking

Logical thinking is essential across various life domains for several reasons:

Problem Solving and Innovation: It fosters the development of problem-solving skills, the generation of new ideas, and the enhancement of creativity.
Scientific Method: It provides the basis for formulated hypotheses and establishing predictions.
Cognitive Organization: It provides order and sense, facilitates a deep understanding of topics, and assists in the organization of actions.
Decision Making: It grants clarity during decision-making processes and helps establish connections between different concepts.
Personal Well-being: It aids in the achievement of personal goals and milestones, which in turn increases self-esteem.

Contextual Situations and Case Studies in Peru ( $2025$ )

Several contextual situations were analyzed to distinguish between types of thinking:

Digital Divide (Context 01): CADE Educación $2025$ reports that the digital gap affects over $50,000$ public schools and $60\,\%$ of families ( $6$ out of $10$ ). This requires logical-mathematical thinking to analyze numerical data, establish proportions, and deduce consequences from statistics.
School Bullying (Context 02): The Ministry of Education's 'SíSeVe' platform recorded over $29,000$ cases in Lima since $2013$ . Between $2023$ and the first quarter of $2024$ , $20,604$ national reports were made, with $798$ cases of bullying specifically in $2024$ . Total school violence reached $73,261$ cases by March $2024$ . The distribution is: Secondary ( $57\,\%$ ), Primary ( $35\,\%$ ), and Initial ( $7\,\%$ ).
Education Access (Context 03): In $2022$ , only $30.9\,\%$ of youth transitioned to higher education, down from $36.6\,\%$ in $2019$ . Peru's population was $33,396,698$ , with youth ( $15$ - $29$ years) totaling $7,858,367$ ( $23.58\,\%$ ). Data from Enaho shows: $80$ out of $100$ youth ( $17$ - $18$ years) finished secondary school; $5$ out of $100$ ( $13$ - $19$ years) dropped out of secondary; while $21$ out of $100$ ( $22$ - $24$ years) finished higher education.
UNICEF Crisis (Context 04): UNICEF ( $2025$ ) warns that over $670,000$ children are out of the school system, and those attending have learning gaps equivalent to nearly $10$ years. This involves logical thinking to analyze social causes and consequences.
MINEDU Strategy (Context 05): A plan to reinsert over $200,000$ youth and adults who left school during the pandemic using flexible CEBA (Alternative Basic Education) modules. This requires logical-mathematical thinking to evaluate enrollment data and indicators of success.
Nutrition Analysis (Context 07): A study on eggs and avocado shows that one egg contains approximately $6\,\text{g}$ of high-quality protein and essential nutrients like Vitamin A, Folate, Complex B, Phosphorus, and Selenium.

Questions & Discussion

The session included interactive reflection based on a video from "Inside Out" (Intensamente) regarding emotions. The following questions were addressed:

What emotions were shown by the characters and how did they influence their decisions?
How does logical thinking help us understand our feelings and make better decisions?
Can thinking before acting help manage emotions better? Why?

Additionally, several self-evaluation questions (Quizziz) were presented:

Question 1: Focused on an INEI/MINEDU report where only $32\,\%$ of 6th graders reached the expected math level. Identified as logical-mathematical thinking because it requires reasoning with proportions and magnitudes.
Question 2: Discussed students unable to establish logical relations in texts. Identified as logical thinking as it involves critical reading and argumentation.
Question 3: The "Math for Life" program in Ayacucho and Puno. Identified as logical-mathematical thinking as it uses quantities and measures.
Question 4: The UNICEF report on $670,000$ non-enrolled students. Identified as logical thinking because it focuses on analyzing socio-economic causes.
Question 5: IPAE report stating $4$ out of $10$ schools lack internet. Identified as logical-mathematical thinking due to the quantification of the gap.