**6. Roadmap of research**

Researches that have been carried out by the authors that contribute to this study were presented in the form of road maps (fish backbone), such as research on RME (Realistic Mathematics Education), contextual learning of mathematics [3, 4, 18], mathematical mod‐ eling [2], planting consciousness of innovation on mathematics teacher [7], research on ethnomathematics [19, 56], learning with the nuanced phenomenon of didactic in junior secondary student [20], as well as the learning of mathematics using didactical phenom‐ enology in primary school students [54]. The results of the study of RME turned out to encourage students' enthusiasm for learning mathematics [3, 4, 18], mathematical mod‐ eling has opened the horizons of students to be able to see the phenomena that can be modeled [2], it turns ethnomathematics research opens up new horizons of research in the domain of mathematical culture [19, 21]. **Figure 9** is a fish bone of research roadmap within several years which covered realistic mathematic education and contextual teaching of mathematics, mathematical modeling, ethnomathematics, didactical phenomenology in mathematical areas.

Further, Ref. [22] added that for a group of teachers they observed, "the teachers reflection anf involvement in professional development opportunities seemed to provide of catalyst and

**Figure 9.** Fish backbone of research roadmap.

change" (p. 130). Professional development of teachers often focuses on helping the teachers to improve learning in the classroom by developing the knowledge and pedagogical skills of the teachers. Professional society engaged in teaching suggests effective ways to provide support to teachers in implementing models of the new learning in their practice [23–27]. But Ref. [27] notes, "… is not so clear how people do or how they create or continue programs and policies" (p. 165).

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

Researches that have been carried out by the authors that contribute to this study were presented in the form of road maps (fish backbone), such as research on RME (Realistic Mathematics Education), contextual learning of mathematics [3, 4, 18], mathematical mod‐ eling [2], planting consciousness of innovation on mathematics teacher [7], research on ethnomathematics [19, 56], learning with the nuanced phenomenon of didactic in junior secondary student [20], as well as the learning of mathematics using didactical phenom‐ enology in primary school students [54]. The results of the study of RME turned out to encourage students' enthusiasm for learning mathematics [3, 4, 18], mathematical mod‐ eling has opened the horizons of students to be able to see the phenomena that can be modeled [2], it turns ethnomathematics research opens up new horizons of research in the domain of mathematical culture [19, 21]. **Figure 9** is a fish bone of research roadmap within several years which covered realistic mathematic education and contextual teaching of mathematics, mathematical modeling, ethnomathematics, didactical phenomenology in

Further, Ref. [22] added that for a group of teachers they observed, "the teachers reflection anf involvement in professional development opportunities seemed to provide of catalyst and

students are allowed to consume the watermelon.

**6. Roadmap of research**

16 Science Education - Research and New Technologies

mathematical areas.

**Figure 9.** Fish backbone of research roadmap.

In conjunction with the program of learning and professional development of teachers, Ref. [28] notes that "one of the two premises report of Glenda (US dept of Education‐2000), that better quality learning is at the heart of change, and professional development program can‐ not be separated from the essence of improving the quality of learning" (p. 331). Our team of researchers, looked at the strength and nature of the professional teacher community, some‐ where has significance because (1) the professional community can bridge and translate the efforts of renewal, (2) the professional community can provide support in introducing the kinds of renewal of learning mathematics (e.g., inquiry) required for the practical develop‐ ment of the principles and values are discussed. Empirical evidence and theory suggest that the strength, nature, and focus the professional community in the field of teacher training can bridge the efforts of the school when students learn. Furthermore, the school community can filter the principles, which vary knowledgeably as well as affect the interpretation of the goals of reform (renewal) in mathematics [29–31].

There is a serious criticism of the views of the previous example of the insights that math‐ ematics is a knowledge that is fixed and static [32], as a system, rule, and formal procedure [33], as the rules and right procedures [34], as a set of concepts and skills that must be mas‐ tered by students [35]. Suggestions successor is the shift to alternative views, suppose the mathematics as a dynamic subject, as a human activity [10, 32], as the activity of the human senses and problem solving activities [35], or mathematics as humanized and antiabsolutist [36–39]. To facilitate students actively learn mathematics through investigation and explo‐ ration, there should be provided a phenomenon that was built by the designer of learning mathematics.

Research on realistic mathematics and their implications on the performance and abilities of students in mathematics further encourages depth curiosity of the research team, how much effect if we add or take properties of learning [56, 40]. From studies conducted on RME, con‐ textual learning, ethnomathematics, modeling, and the phenomenon of didactic raise new questions, "What if the mathematics and science synergize so that students can conduct investigations either individually or together in group in the classroom." Let the students simulated such as how long the water flow from each faucet with various diameter sizes that range from a tub of water.

Suppose a liter of water was expelled through a Faucet A with hole diameter of 2 mm, then we measured how long the pouring time, compared to a Faucet B with hole diameter of 4 mm, we also measured how long the pouring time. Students are required to collect and record the information obtained in the form of a table for which they are asked to describe the graph and determine the mathematical models, equations associating the faucet diameter with the flowing time.

Further to the solution of sugar water with various concentrations of submerged objects that sank in all of the solution, students are asked to interpret the meaning of drowning and are associated with a ratio of the density of objects with the density of each solution. Students are also asked to investigate for how long the objects undergoing the process of sinking from the surface of the solution to the base of the tube solution. The stopwatch is used for recording of each liquid in the tube. Students are also able to model mathematically the magnitude of the solution concentration by the length of the time (in seconds) the object taken to fell from the surface of the solution to the bottom of the bottle.

I wonder what effect it has on the health of the body, if someone drinks a thick liquid of sugar continuously compared with drinking fluids diluting the sugar. Continued impact of what happened to our body turns into increased blood viscosity? How did it effect the blood circulation and the transport of oxygen from the lungs to the brain by the blood? These con‐ sequences are expected to sensitize students to maintain their own health.
