Mathematics is one of life's significant concepts that people deal with in everyday life. In fact, most people didn't recognize him. Teaching mathematics is not easy, in fact most students hate mathematics apart from other subjects. Most students say it is very difficult and contains a lot of calculations and the use of formulas. In reality, it all depends on how to teach it and what teaching approach to use to attract students' interest and how the approach can broaden and broaden students' learning capabilities. Therefore the intention of this essay is to discuss the role that the discovery and direct teaching approach plays in teaching mathematics in the classroom. The discovery teaching approach is a very effective teaching approach that has been mainly used in mathematics teaching. It simply means that children are given problems and have to conduct their own research and experiments using formulas and equations to find the results based on a given topic. In this situation, students must use their prior knowledge to solve problems. The discovery approach is a very interesting concept; has captured the interest of individuals in finding solutions to satisfy them. According to Borthick & Jones (2000) explained that, in discovery learning, participants learn to recognize a problem, characterize what a solution would look like, search for relevant information, develop a solution strategy, and execute the chosen strategy. Discovery teaching approach is very useful in teaching mathematics. It is one of the teaching methods that most teachers use as one of their teaching strategies. They found that this contributes a lot to the development of their cognitive skills, engaging... in the middle of the paper... expressing their personal interest in how to convey the topic. It is efficient and useful when there are not enough resources for students to work individually. In conclusion, mathematics is a very important subject that can be taught using both of the previously mentioned teaching approaches. Indeed, both teaching approaches discussed are useful for teaching mathematics. The very important thing that teachers need to consider is how to prepare them before they behave in each of the teaching approaches. Both teaching approaches have their own strengths and weaknesses that teachers can consider to bring about a change in children's learning abilities. Children's learning is in their hands, so it is best for teachers to acquire the skills of teaching each concept so that they are able to deal with any challenges that may arise in their teaching..