Mathematics is not just about calculating or memorizing formulas, but it's also developing a way of thinking logically, systematic and analytical thinking. Mathematical reasoning is a skill that has to be built in the early learning process so they can solve problems and understand concepts. In this increasingly complex world, mathematical reasoning is required because it helps individuals make the right decisions and face the challenges of everyday life.

Math education is meant to develop math reasoning by using the approach to learning that emphasizes problem solving, logical thinking and analysis skills. However, to achieve this goal, it is important for teachers and educators to understand the concept of mathematical reasoning and the best method of teaching it to students.

1. Mathematical reasoning concept

Mathematical reasoning is a logical thinking ability to make arguments, make conclusions, and connect concepts that exist in mathematics. This ability helps students understand the relationship between theory and applications and see how concepts they learn can be applied in real situations. There are two types of reasoning that are often integrated in mathematics:

1. Inductive Reason: Involving pattern drafting or general rules based on observations of specific cases. This reasoning developed a student's creative thinking ability to find patterns of existing data.
2. Deductive Reason: Involving drafting arguments based on principle or general rule. This reasoning helps students draw logical conclusions from existing assumptions or rules.

These two kinds of reasoning are important in mathematical learning, because it helps students analyze, make hypotheses, and solve problems in a structured and logical way.

2. It's a systematic Production Development

Developing mathematical reasoning in students has many benefits in improving their learning qualities, among other things:

• Increase problem solving capabilitiesA student capable of mathematical reasoning would be more skilled at analyzing problems, making hypotheses, and organizing effective resolution strategies.
• Enhancing Critical ThoughtsThis ability makes students more critical in processing information, verifying answers, and validating the solutions they find.
• Connecting Theory to Real Application: With mathematical reasoning, students can apply mathematical concepts in various situations of life, such as determining financial or understanding statistics.
• Increasing Self-TrustWhen students are able to solve complex problems with proper reasoning, it increases their confidence in the face of academic or non-academic challenges.

3. Methods Develop Mathematical Awareness in Learning

There are several methods and strategies that can be applied in the learning process to develop student mathematical reasoning, among other things:

• Problem Solve Approach: This method involves students in real problem solving activities or contextual problems that allow them to think analytically and systematically. Problem solving helps students implement mathematical concepts with logical reasoning to find the right solution.
• Group discussionA group discussion allows students to exchange ideas and listen to different angles. It enriches their understanding of concept and helps them improve mindset and develop critical thinking abilities.
• Approach Guidance Discovery (Guided Discovery)In this method, teachers provide instructions and help students to find their own concept or mathematical formula. These approaches hone student inductive reasoning skills and encourage them to be more active in learning.
• Project Base Learning: With projects, students can apply math in real situations, like measuring an area or calculating costs in a mini project. It allows students to apply concepts that have been studied and creative thinking and analytical thinking.
• Integrated Learning (Integrative Learning)This approach combines math with other disciplines, such as science or technology. Through this integration, students learn how mathematics plays into various fields and develop cross-disciplinary thinking skills.

Four. The challenge in Student Political Development

Although the development of mathematical reasoning is very important, there are several challenges faced by educators in application, among other things:

• Student unprepared in facing Open Problem: Many students are used to routine problems and tend to be difficult to adapt when given more complex problems or not have one sure answer.
• Lack of Time: Maths reasoning development takes a long time. In a dense curriculum, teachers often have difficulty giving it enough time to train these skills to students.
• Student skills differenceEvery student has different abilities in understanding mathematical concepts. This challenge can be difficult for teachers to give an approach to every student's needs.

5. Solutions and Strategies Overcoming Challenge

To overcome the challenges above, there are some strategies that the teacher can apply, among them:

• Graduated Presents: Start from simple problems to more complex ones, so students can learn gradually and improve their confidence in solving problems.
• Technology Enforcement: The use of technology, such as math applications and problem-solving software, can help students understand the concept better through visualization and simulation.
• Distribution Approach in Learning: Teachers can make variations of teaching methods according to student skills, such as giving extra challenges to faster students who control matter, or extra help to those in need.
• Pushing Self and Evaluation Reflection: After solving problems or projects, students are asked to do reflections and evaluations on the processes they've been through, so they can learn from mistakes and improve their thinking methods.

Six. Mathematical Awareness Implementation Recommendations

To increase the effectiveness of student mathematical reasoning development, it's important for schools and educators to consider some of the following recommendations:

• Teacher's training: giving training to teachers in teaching mathematical reasoning, especially in problem solving techniques and critical thought use.
• Various Source of Studies Providence: Provides reading materials, visual tools and other learning media that supports mathematical reasoning development.
• Pushing Interactive Learning: Enlarge activities involving student interactions, such as shared groups and projects discussions, to develop social skills and their critical thinking.

Conclusion

The development of mathematical reasoning is very important for students to be able to understand mathematics more deeply and apply it in everyday life. Through various approaches of learning, students not only study math as science, but also as a way of thinking. With the method of solving problems, the group discussion, and integration with other fields, students can increase the critical and logical thinking skills that are indispensable in the face of modern world challenges.

With the proper approach and the adequate support of educators and schools, students can develop their mathematical reasoning skills well, paving the way for their academic and non-academic success in the future.

Source: Polya, G. How to Save It: Princeton University Press.