**5. Didactical phenomenology**

The idea of a didactical phenomenology of [42, 1] provided the inspiration to explore the mathematical content through a search phenomenon that is suitable for regions in Indonesia. Suppose how to introduce the concept of linear equations using scales [43], introduce the concept of equation of a straight line or linear function using taxi fares and the cost of photo‐ copying [44], teaches the volume of flat sides of space objects using sand beach [45], teaches the volume of balls and tubes using watermelon [46, 15], and many numbers of phenomena that can be appointed as a "bridge" to understand the concepts of mathematics for students.

An example of how the phenomenon of ball volume is approximated by cleavage of a water‐ melon is discussed as (**Figure 8** is personal collection of photograph) follows:

Mathematics Instruction Based on Science Using Didactical Phenomenology Approach... http://dx.doi.org/10.5772/intechopen.68437 15

**Figure 8.** Watermelon ball to show the formula of sphere volume.

Through the implementation of these learning materials, it was difficult for students to forget it, because it has a very deep impression and also encourages teachers to apply them in their

In a study paper, Ref. [15] recommends to examine deeply whether the teachers' willingness to improve their professionalism in teaching tasks can improve their perform in teaching? Moreover, whether their better perform can improve students' achievement in mathematics? What kind of professionalism improvement could boost their strong willingness to innovate mathematics instruction? To answer the challenge of the recommendation, the author offers a study on the implementation of learning mathematics using science‐based of didactical phe‐ nomena [1, 54], and empirically tested the implementation of this learning in the classroom. Mathematics classes with the types of "transmission" as described by Senk and Thompson [16], include the introduction of each topic by declaring a rule which is followed by an exam‐ ple of how to apply the rules (rules, the arguments, the law), and then given a number of exer‐ cises, have encouraged developers who are looking for alternatives. Now, the effort to reform the mathematics is to portray the students participation actively, to transform the learning characterized by the "transmission" and to the learning characterized by the "participation." In studying mathematics and science, the role of the students is constructing knowledge with the teachers. The teacher reveals the problems, asking questions, listening to students' answers, pursuing with follow‐up questions (probing questions), and then wait for the responses of the students in the formation of knowledge or mathematical concepts expected. Teachers should be little patience to listen to the arguments, presentation, and reasoning expressed by the stu‐

Hearing the mathematical ideas of students is an important aspect in learning sound con‐ structivism, i.e., to shift from "telling and describing" to "listening and questioning" and "probing for understanding" [17]. With science‐based instruction of mathematics, students are directly retrieving data, processing the data, presenting the data in tables, and describing the data in the table into a chart and then it becomes possible to make a mathematical model

The idea of a didactical phenomenology of [42, 1] provided the inspiration to explore the mathematical content through a search phenomenon that is suitable for regions in Indonesia. Suppose how to introduce the concept of linear equations using scales [43], introduce the concept of equation of a straight line or linear function using taxi fares and the cost of photo‐ copying [44], teaches the volume of flat sides of space objects using sand beach [45], teaches the volume of balls and tubes using watermelon [46, 15], and many numbers of phenomena that can be appointed as a "bridge" to understand the concepts of mathematics for students. An example of how the phenomenon of ball volume is approximated by cleavage of a water‐

melon is discussed as (**Figure 8** is personal collection of photograph) follows:

own learning accomplishments.

14 Science Education - Research and New Technologies

of images.

**5. Didactical phenomenology**

dents, either in the form of oral or written communication.

By adding the volume of "pyramid models" that are created from a watermelon ball accurately obtained the volume of ball [46], although students are still in doubt because the base of the pyramid‐like model was a curved surface. However, this is in line with that proposed by [47].

Using the third figure of **Figure 8**, you can notice the role of "pyramid" in the sphere, that in a sphere we can make many "pyramids‐like" models. One can make it easily by using watermelon.

Furthermore, the professional mathematics society which among them are mathematics teachers can help learning how to apply the kind of inquiry studied in the context of exploring didactical phenomenon. Ref. [48] distinguishes between the teachers who are looking for suc‐ cess in their career and teachers who tested their practice in relation to their thoughts. When teachers are tested on the basis of meaning of broad principles, in practice, they are involved in the alteration [48]. Such tests provide support for teachers to learn continuously and make them able to improve their teaching practices continuously anyway.

The existence of such a professional society is very important in supporting experienced teachers to teach in new ways [49, 50]. Professional societies not only provide space and time, but also can provide an environment for teaching practice. Mathematics teachers are the part of the communities involved in the effort to introduce the proceedings of their teaching prac‐ tices, and can experience this type of learning for students as suggested above. These reforms initiated teachers to strengthen their classrooms with "learning society" in which students explore mathematics in depth [51].

Furthermore, [52] explains that the assumption of "communities of learners" is a form of learning that occurs when people participate actively and discuss with each other. In learn‐ ing communities, students who are mature or not will share the responsibility to determine, direct, and manage the joint efforts. In view of the innovation, teachers organize students way of thinking, but the role of the teacher is a facilitator not a provider of answers. Mathematics class is seen as a place where students can actively make meaning of themselves and empha‐ size the process of learning mathematics [50].

The articles on the research and learning in the lesson‐study are a matter of joint publications between teachers and lecturers. Students see "the form of linear equations" by comparing it with the "model of scales" a very pleasant experience. Forming a linear function using the "taxi rates and photocopy expenses" is an attribution according to the mathematics teacher that mathematics is so close to the real situation that is faced by the students. Moreover, study the volume of the tube using a "long watermelon" and make it easier for students construct so that they can find the formula for volume of tubes and balls. After mathematics learning students are allowed to consume the watermelon.
