Inquiry-based learning is one of the instructional approaches which teachers implement in science learning. Related to this issue, Van Rens et al. (2009) stated that for some decades, inquiry tasks have been a feature of school science in various countries. A research in high school biology students in Israel found that students felt more involved in the project and get deep understanding through inquiry learning (Sadeh & Zion, 2011). The similar trends are also revealed in both physic in the United States and chemistry in The Netherlands (for a review see McBride et al., 2004; Van Rens et al., 2009). In general, inquiry as an instructional approach has shown positive effects on students’ understanding of science concepts.

Talking about inquiry, it is defined as seeking information by questioning (Exline, 2004). Moreover, Exline explained that the process of inquiring begins with gathering information and data through applying the human senses which are seeing, hearing, touching, tasting, and smelling.

The positive effects of applying an inquiry approach in the teaching and learning process which have been shown in science education confirm the idea of applying the approach for other disciplines besides science. However, this essay will only focus on mathematics. In science learning, the implementation of inquiry is clearly helpful because students experience kinds of experiments resemble real researches. Yet, in mathematics, it is not easy to create an inquiry-based learning which resembles a real research as in biology, physic or chemistry. Nevertheless, Lederman and Niess (2000) said that inquiry as a teaching approach is the best way to facilitate students’ understanding of the mathematics as problem solving and mathematics as reasoning which are analogous to the process skills in science. Based on this contradiction, the purpose of this essay is to discuss whether inquiry approach can be applied in mathematics learning or not and what characteristics of an inquiry-based learning which should be applied in mathematics learning.

The first important thing to be considered is observing the characteristics of mathematics as a discipline. According to scientists and mathematicians, mathematics is a part of science or likely has a close relationship with sciences. Pierce in Campos (2010) classified mathematics as the most general science in close interrelation with logic, philosophy, the natural and social sciences, and as creative, the arts. In particular, he conceived of the general method of mathematical investigation as being applicable to inquiry in all other areas of knowledge. Hence, the similarity between mathematics and science can be a potential idea to design an inquiry-based learning in mathematics. The idea of designing inquiry-based learning which involving students as researchers can be analogues to design an inquiry-based learning which resemble an investigation of a mathematician. Moreover, according to Lederman and Niess (2000), mathematics as problem solving and mathematics as reasoning heavily emphasize students’ ability to solve problems, complete proofs, test conjectures, and assess the validity of arguments. A mathematician has to prove and to reason in doing mathematics and inquiry is an important part of the proving and reasoning processes. Hence, inquiry approach could be an appropriate approach which can support mathematics learning.

Furthermore, the second important thing which has to be considered is what kind of inquiry preferred use in mathematics learning. Based on literature, there are two kinds of inquiry which are open inquiry and guided inquiry (Sadeh & Zion, 2011). Moreover, the experiment of Sadeh and Zion (2011) said that there are different effects on the implementation of open inquiry and guided inquiry in high school biology. By using open inquiry, students felt more involved in their project, and felt a greater sense of cooperation with others, in comparison to guided inquiry. This fact should also be considered in mathematics learning. However, by considering the characteristics of mathematics learning, students learn by questioning, making decision and negotiating (for a review see Lederman and Niess, 2000). Let they work without giving sufficient guidance is possible leading to misconception. Hence, providing sufficient guidance will be very important to make the inquiry-based learning process become more effective and to reduce students’ difficulties to understand mathematics concepts.

The use of technology is also very helpful to support inquiry-based learning. A research which is conducted by Bakker and Gravemeijer (2004) in a topic of reason about distribution presented that technological learning environment developed students’ informal reasoning in this topic. By using applets which is available online students created graphs, and prediction tasks supported the learning of different aspects of distribution. In another research about inquiry-based learning in chemistry, Van Rens et al. (2009) in collaboration with five secondary school teachers in The Netherlands designed material consists of a Web site with a student workbook with explanatory text and worksheets, a teacher guide, a cyber tracker, and an internet symposium. They found that the product which was designed based on Procedural and Conceptual Knowledge in Science (PACKS) model is helpful for students to handle chemical concepts. Moreover, there are many applications provided online nowadays. Those applications can be used to support the occurrence of inquiry learning. Moreover, teachers can also design applications based on the aims of learning.

Based on the literature and the previous research which have been discussed in the previous paragraphs, the inquiry-based learning can also be implemented in mathematics learning. However, there are three characteristics which should be applied in the mathematics teaching and learning posed in this implementation. Firstly, the learning process can be an activity resembles an investigation of mathematicians. In other words, students reinvent mathematics concepts by themselves as mathematicians. Secondly, teachers should provide sufficient guidance to support students’ thinking. Thirdly, the design can use technology to support students’ investigations. Inquiry-based learning is in line with the theory of teaching and learning in mathematics which is focus on questioning, making decision and negotiating activities.

**REFERENCES**

Bakker, A., & Gravemeijer, K., P., E. (2004). Learning to Reason about Distribution. In Ben-Zvi, D., & Garfield, J.* The Challenge of Developing Statistical Literacy, Reasoning and Thinking, *(pp. 147–168)*.* Utrecht: Kluwer Academic Publisher.

Campos, D., G., (2010). Pierce’s Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry. *Studies in Philosophy and Education*, 29, 421-439. doi: 10.1007/s11217-010-9188-5

Exline, Joe. (2004). What is Inquiry-based Learning? Message archived at http://www.thirteen.org/edonline/concept2class/inquiry/index.html

Lederman, N. G., Niess, M. L., (2000). Problem Solving and Solving Problems: Inquiry about Inquiry. *School Science and Mathematics*, *100*, 113-116.

Sadeh, I., & Zion, M. (2011). Which Type of Inquiry Project Do High School Biology Students Prefer: Open or Guided? *Research in Science Education*, *42*, 831–848. doi: 10.1007/s11165-011-9222-9.

Van Rens, L., Van der Schee, J., & Pilot, A. (2009). Teaching Molecular Diffusion Using an Inquiry Approach (Diffusion Activities in a Secondary School Inquiry Learning Community. *Journal of Chemical Education, 86*, 1437-1441.

###

The second trial essay, and again, it is still need a lot of improvement. And a lot of improvement means a lot of effort. Ganbatte!!! ^_^