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**Introduction**

Inquiry based teaching involves positively engaging the learner and leading him or her to understand concepts. In this case, inquiry implies the ability of the teacher to ask questions on new issues and concepts while gaining new information. Inquiry based learning involves learning ideas and concepts through asking questions. It also involves converting data and concepts into knowledge. This paper explores inquiry based learning of mathematics and its results and successes in comparison with other forms of learning.

**Discussion**

Inquiry-based learning relies on student activity and questioning rather than concentrate on teachers in the learning process. When teachers use inquiry based approaches on learning, they introduce a set of steps similar to those used by scientists when creating and testing hypothesis. A teacher comes up with some questions and encourages students to come up with their own questions relevant to the topic of discussion. The teacher then provides the students with resources from which they can obtain answers to those questions. The learning procedures ensure that students become active participants throughout the entire process (Baroody & Dowler, 2003).

Teaching and learning mathematics involve understanding ideas and concepts then applying certain procedures to solve mathematical problems. Inquiry based approach to learning mathematics requires that students come up with patterns and relationships which can help them try different approaches to solving problems.

Inquiry based teaching of mathematics proves to be the best teaching model for mathematics. The approach proves to be effective both before and after the teaching and learning exercise.

The goal of inquiry-based teaching of mathematics involves teaching students to think critically. When learning mathematics, teachers challenge a student to go beyond memorization and learn to solve problems independently. The approach does this by letting students answer questions and come up with their own questions. It shows the student the importance of the whole process involved in solving problems.

The inquiry-based approach to teaching mathematics uses techniques different from traditional techniques. Rather than demonstrations and lecture, it encourages hand on experience. For example, instead of the teacher demonstrating how to work a sum, on the blackboard, he places that role on students themselves. The students try to work out the solution to that problem using textbooks provided and the procedure outlined. After the procedure, the teacher now works with the students, to ascertain the right answer from the rest of the answers (Boaler, 2000).

Inquiry-based approach used in teaching mathematics challenges students to think of the procedure and ways of applying a formula. The approach ensures that students should not learn how to manipulate a formula and get answers. It helps them to come up with ways of manipulating the formula in order to come up with required answers.

The inquiry-based approach to teaching of mathematics requires that students form groups and come up with their own mathematical problems. The approach also requires students to look for solutions to certain mathematical problems using different approaches. Inquiry-based teaching of mathematics provides students with resources and procedures that they can use to solve problems in mathematics.

Inquiry-based approach to teaching of mathematics relies on teamwork as one of its main problem solving strategies. The approach involves many questions when looking for solutions to mathematical problems. Therefore, teamwork comes in handy. Through group work and other forms of teamwork, students can ask questions and help one another to answer questions to particular mathematical problems (Ebby, 2002).

Inquiry-based approach to the teaching of mathematics helps students to figure out solutions on their own. The students do not participate in classroom activities passive students. Each student must contribute in some way to the learnng process, either by asking questions or by answering questions.

The use of inquiry based approach to teaching of mathematics enables students connect between information that exists and new knowledge. The students use the little knowledge they have on certain concepts, to apply to other similar concepts and problems. This approach caters for the needs in terms of their engagement and challenges.

In a mathematics classroom that uses the inquiry approach to teaching, students engage themselves in the creation of knowledge. Inquiry based approach to teaching of mathematics involves certain characteristics such as discussion, queries, and explanation of mathematical thinking. Inquiry approaches to mathematical teaching use open-ended questions, investigations and thought experiences among other things. These characteristics and framework help to make sure that all students become active and reflect on their capability. This helps the teacher to know students that he should pay more attention to them. The inquiry-based approach to teaching of mathematics helps the teacher to know areas that he should teach more. This happens because students engage in group works and other teamwork arrangements. Therefore, their participation in these groups they reveal their weak points in mathematics (Mooney, 2000).

The inquiry-based approach to the teaching of mathematics engages learners to scientific oriented questions. The teacher acts as guides and not owners of the learning process. The approach makes learners look for evidence that supports their solutions to problems. The inquiry-based approach to teaching of mathematics ensures accuracy and clarity of data. It does not operate in assumptions. The approach uses question and answer characteristics to make sure that the solutions that result become valid and accurate. The evidence provided by students in the course of finding solutions to problems, the evidence act as explanations rather than the procedure that provides evidence. Students can evaluate the evidence by asking questions and carrying out consultations in teamwork. Inquiry based teaching of mathematics operates under certain guidelines. It requires that teachers offer no deceptive examples to students. This means that examples that teachers give to students should be concrete and applicable (Boaler, 2000).

Mathematical content taught to students should offer students a structured content. Inquiry based teaching of mathematics should start from the recognized to the unknown. This means that students use the knowledge they already have on how to solve new mathematical problems. For instance, mathematical formula that students already know that help them to solve sums they have never come across in the course of their learning.

Inquiry-based teaching of mathematics requires teachers to form lesson plans that respond to changing, interrelating and valid communication of knowledge. For example, traditional ways of teaching mathematics required the teacher to demonstrate each step of solving a sum on the board. The students could only ask a question when the need becomes pressurizing. However, inquiry based teaching of mathematics require that teachers plan lesson plans that put the students as the owners of the lesson. Almost everything that goes on in class must give learners the first priority then the teacher (Ebby, 2002).

Inquiry-based teaching of mathematics offers students diverse ways of solving problems. It does not restrict students to a single formula of coming up with solutions to mathematical problems. When students engage in-group discussions, they get a chance to their ways of reasoning as well as listen to how others solve similar problems. They do this by asking and answering queries and coming up with innovative ways of solving problems together.

Inquiry-based approach to teaching of mathematics does not ignore the importance of teachers in the learning process. It gives the teacher a chance to develop thinking skills in students. The teacher may ask students to come up with their questions regarding a certain topic. Likewise, the teacher may decide to come up with questions on a ttopic. These two approaches provide learners with a chance to learn. The teacher acts as a guide to student learning as opposed to the initiator of learning.

Inquiry-based approach to teaching of mathematics makes use of open learning. Open learning involves learning, where students learn without a prescribed target or result they should meet. The approach puts responsibility to students. The students get an opportunity to learn new concepts without anticipating. In a middle school, class students can take a role of an official preparing a statistical report. They choose a topic and come up with a representation on their findings. The middle school students provide the results on graphs and written descriptions (Baroody & Dowler, 2003).

Middle school learners prove to have a difference compared to younger learners. Teachers can prove concrete learning experiences to middle school learners when they understand their characteristics.

Inquiry-based approach to teaching of mathematics proves to be the best teaching model for middle school students. Most middle school students display curiosity and willingness to learn things that they consider useful. Most of them engage themselves to learn new ideas. This stage of their lives presents them with exploration characteristics because of their curiosity.

They enjoy problems solving on their own. They require little guidance on how to solve problems because they get motivation from their curiosity. Learning becomes a delightful experience for them.

Most middle school learners focus attention on themselves, and the perception their peers have towards them. They engage in things that would boost their self-esteem and worth. Therefore, in anything that they do, they tend to be more cautious towards the results of their actions.

Middle school students tend to resist adult authority and force and look for independence. They believe that adults should let them handle problems and other situations in their own way. They seek assistance from adults when they cannot handle things on themselves.

Most of them experience conflicting values between their personal requirements and the requirements society puts on them. They value peers influence in a major way. They need to feel the presence in peer groups that comprise of boys and girls. They prefer active as opposed to passive learning activities. They prefer learning activities with their peers. They require frequent movement and numerous activities. Middle school students prefer calm, adult support and guidance (Boaler, 2000).

Compared to other forms of leaning, inquiry based approach to teaching of mathematics has proved a success. Students get an opportunity to learn as an active participant in the whole process of learning. Students bring out questions and answers that provide help to the whole learning process. Through this learning approach, students learn in a systematic way and grasp concepts in a concrete manner.

The approach provides students with concrete learning making it hard for them to forget concepts that they learn. This is because the approach does not encourage memorization like traditional forms of learning. Students engage themselves in the whole process of learning. They come up with questions and answers to questions and problems. The offers little help that provides guidelines towards reaching desired results. This helps students to remember whatever they learn for a remarkably long time.

The approach also breeds students who can respond to real-life problems as individuals and in the best way possible. This happens because the approach provides students with various ways of coming up with answers and solutions questions and problems (Mooney, 2002)

**Conclusion**

Inquiry-based approach to the teaching of mathematics rates as the best way of learning. Students learn as active participants in the learning process. They learn to think creatively and critically, ask relevant questions and learn how to use several methods to come up with solutions. Therefore, this approach should be applied to each problem solving process.

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