Logical reasoning and mathematics are like two sides of the same coin. One cannot exist without the other. Together, they form the backbone of scientific inquiry and problem-solving. Logic provides the structure and framework for mathematical thinking, while mathematics gives us the tools to apply logical reasoning and thinking in the real world. From unraveling the mysteries of the universe to designing the latest technology, logical reasoning and arithmetic are the driving forces behind humanity’s greatest achievements.

In arithmetic, logical reasoning is used to understand concepts, make connections between different ideas, and solve problems. It is the foundation of numerical understanding and problem-solving and is a critical skill for success in the subject. In this article, we will explore the importance of logical reasoning in mathematics, the role it plays in numerical thinking, and how it is used in solving mathematical problems. We will also highlight some studies that demonstrate the importance of logical reasoning in arithmetic, and how it can be effectively taught to students.

**Cruciality of logical reasoning in mathematics**

Logical reasoning is an essential aspect of mathematics that allows students to understand the underlying principles of mathematical concepts and apply them in solving problems. It enables students to think critically and logically, analyze and understand problems, identify patterns and connections between different mathematical concepts, and construct logical arguments and proofs.

The ability to use logical reasoning in mathematics is crucial for problem-solving, as it allows students to break down complex problems into smaller, manageable parts and plan a solution. Additionally, logical reasoning helps students to make connections between mathematical concepts and real-world problems, which is essential for understanding the practical applications of mathematical knowledge.

Furthermore, logical reasoning plays a vital role in developing students’ ability to construct proofs and arguments in mathematics. The ability to construct proofs and arguments is a key skill for students as it helps them to understand the logical foundations of mathematical concepts and apply this understanding in solving problems.

**Which concepts demand more logical reasoning?**

In primary and elementary school, mathematical concepts that involve problem-solving and critical thinking, often demand more logical reasoning. Furthermore, many games and activities too can be used to boost a student’s logical reasoning skill, and then can ultimately help them in academics, for example, in subjects like Mathematics. The below-mentioned are just a few examples of such mathematical concepts. Overall, mathematical reasoning is a crucial skill that is developed through various mathematical concepts and is important for students to master early on.

**1. Addition and subtraction word problems**

Addition and subtraction problems might seem easy. However, these problems require students to read and understand the problem, identify the numbers involved, and apply the appropriate mathematical operation to find the solution. This requires logical reasoning to understand the problem and to figure out what operation to use.

**2. Multiplication and division **

The concepts of multiplication and division involve understanding and applying the basic principles of repeated addition and grouping. This requires logical reasoning to understand how the operation works and to figure out how to solve problems that involve larger numbers.

**3. Fractions **

Understanding fractions requires students to think about numbers in a different way and to understand concepts such as equivalent fractions, comparing fractions, and adding and subtracting fractions. This requires logical reasoning to understand the concepts and to be able to solve problems involving fractions.

**4. Decimals**

** ** Decimals involve understanding place value and how decimals relate to fractions. This requires logical reasoning to understand the concepts and to be able to solve problems involving decimals.

**5. Geometry**

Geometry requires students to understand and apply concepts such as angles, lines, and shapes. This requires logical reasoning to understand the concepts and to be able to solve problems involving geometric shapes and measurements.

**Verdict**

Logical reasoning is an essential aspect of mathematics because it is the process of making sense of mathematical concepts, understanding their relationships, and solving mathematical problems. Studies have shown that the ability to reason logically is a key predictor of success in mathematics.

Several studies^{[1]} have found that a strong ability to reason logically leads to better performance in maths. While others^{[2]} have found that students who were taught math using a problem-solving approach, which emphasizes logical reasoning, performed better on math tests than those who were taught using a traditional approach. A longitudinal study^{[3]} by Terezinha Nunes, found children trained in logical reasoning made greater progress in mathematics.

Educators and institutes now emphasize the importance of logical reasoning and problem-solving in math education. The standards stress the importance of developing students’ ability to make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments, and critique the reasoning of others.

**Conclusion**

In conclusion, logical reasoning is the foundation of mathematical thinking and problem-solving. It allows individuals to make sense of mathematical concepts, understands their relationships, and solve mathematical problems. Several studies have shown that logical reasoning is associated with success in mathematics and mathematical careers. The Common Core State Standards for mathematics, which are used in many states in the US, emphasize the importance of logical reasoning and problem-solving in math education. It is crucial for students to develop their logical reasoning skills early on in order to succeed in mathematics and in other areas that require critical thinking and problem-solving.

**References**

- E. Ramganesh and T. Sanjeevi Reddy, Logical Reasoning of School Students as Predictor of their Academic Performance in Mathematics, International Journal of Management, 12(1), 2021, pp 707-712. http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=12&IType=1
- Cresswell, C., & Speelman, C. P. (2020). Does mathematics training lead to better logical thinking and reasoning? A cross-sectional assessment from students to professors.
*PLOS ONE*,*15*(7), e0236153. https://doi.org/10.1371/journal.pone.0236153 - Nunes, Terezinha & Bryant, Peter & Evans, Deborah & Bell, Daniel & Gardner, Selina & Gardner, Adelina & Carraher, Julia. (2010). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology. 25. 147 – 166. 10.1348/026151006X153127.