Salwa Rifdah Rizqullah
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Kesalahan Umum dalam Penarikan Kesimpulan: Kajian Literatur Penalaran Induktif, Deduktif, Modus Ponens dan Modus Tollens Prihaten Maskhuliah; Salwa Rifdah Rizqullah; Sarmila Sarmila
Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam Vol. 4 No. 2 (2026): Juni: Pentagon : Jurnal Matematika dan Ilmu Pengetahuan Alam
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/pentagon.v4i2.1013

Abstract

The ability to reason is inherent in humans as rational beings and forms the basis for constructing knowledge and solving everyday problems. Logical thinking enables individuals to express ideas, build valid arguments, and make informed decisions. However, errors in drawing conclusions often occur due to insufficient understanding of systematic reasoning rules. This article aims to explain methods of drawing conclusions based on mathematical logic, including inductive reasoning, deductive reasoning, Modus Ponens, and Modus Tollens, while also discussing common formal reasoning errors. Using a library research method, the discussion focuses on the characteristics, practical applications, and validity of each reasoning method through logical truth tables. The analysis shows that deductive reasoning provides certain conclusions when valid premises are used, whereas inductive reasoning generates general conclusions based on probability derived from empirical observations. The study also identifies common logical fallacies, including affirming the consequent and denying the antecedent, which undermine argument validity. Understanding formal mathematical logic is expected to strengthen critical thinking, support valid argument construction, and help readers avoid reasoning errors in academic writing and everyday decision-making.
Penerapan Garis Bilangan Riil dalam Memahami Konsep Dasar Nilai Mutlak Prihaten Maskhuliah; Salwa Rifdah Rizqullah; Sarmila Sarmila
Algoritma : Jurnal Matematika, Ilmu pengetahuan Alam, Kebumian dan Angkasa Vol. 4 No. 4 (2026): Algoritma : Jurnal Matematika, Ilmu pengetahuan Alam, Kebumian dan Angkasa
Publisher : Asosiasi Riset Ilmu Matematika dan Sains Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/algoritma.v4i4.1040

Abstract

Absolute value is a fundamental mathematical concept that supports advanced topics, including algebra, calculus, and numerical analysis. Although often regarded as simple, absolute value involves considerable conceptual complexity. Many students develop misconceptions because conventional instruction tends to emphasize procedures rather than meaning. As a result, students often understand absolute value only as a rule for positive numbers or as a way to remove a minus sign. This limited understanding causes difficulty, confusion, and errors when students encounter formal definitions, absolute value equations, inequalities, and complex mathematical models. Therefore, this qualitative literature study aims to describe the use of the real number line as a concrete visual representation that can bridge the abstract nature of absolute value. The study was conducted through an in-depth review of literature, articles, textbooks, and previous research findings. The results indicate that a visual approach using the real number line is effective in developing students’ intuition. Through this representation, absolute value can be interpreted as distance. In a single-point context, the symbol represents the number of steps from the position of x to the reference point zero. In a two-point context, subtraction can be represented as the distance between two points, such as the distance from point A to point B. This distance-based approach also helps students understand the commutative property of absolute value logically and reduces calculation errors caused by reliance on formal formulas. Overall, the real number line can reduce procedural misconceptions and promote a complete, meaningful, and durable conceptual understanding of absolute value.