**1. Introduction**

Didactic phenomena in our understanding are exploiting the phenomenon as medium or bridge for learning concepts. In learning mathematics, didactical phenomenology interpreted as a means to learn math concepts as [1] stated that the didactical phenomenology is a way to show the teacher place where the learner may step into the learning process of mankind (p. ix).

Starting from the situation that the human body contains thousands or even millions of myste‐ rious phenomena, some of which we can observe through the sheets of the doctor who advised us to go to the lab for having general checkup for our health, having our solutions or body fluids to be tested. It turned out that the concentration of the solutions in the body affects the healthy condition of our body. When the glucose in our body exceeding the normal size, then our health would be affected. When a less glucose (very low concentration) is present in our body then obviously the balance of our body also affected. This situation encourages the research team to take advantage of this phenomenon in mathematics.

Data in the **Figure 1**, represent the result of health lab test of the first author of this chapter (health of Turmudi's lab test) which was conducted in February 25th, 2014 in the Pramita Lab of Bandung. Suppose the number 130 mg/dl for triglycerides showed that as many as 130 mg of triglycerides in 1 dl solution, a healthy person is when she/he has less than 150 mg/dl (<150 mg/dl).

Learning mathematics using mathematician framework usually takes place when introduc‐ ing the concept of sets and functions and then the "set approach" is used. Therefore, the func‐ tion is understood without using illustration. Function concept is understood as verbatim. Most mathematics teachers in Indonesia usually introduce relationship or function concepts using arrow diagram. Relating two sets of quantities, such as group of students in one hand, and their shoes number size in the other hand. He/she used arrows to link among two sets of quantities.

**Figure 2** represents the relationships among two quantities such as name of persons in set A and numbers of their shoes in set B. The research team, however, prefers to take advantage of this phenomenon by associating two specific situations. Rather than using data without


**Figure 1.** Data from a health laboratory.

Mathematics Instruction Based on Science Using Didactical Phenomenology Approach... http://dx.doi.org/10.5772/intechopen.68437 9

**Figure 2.** Example of relation between name and shoes number.

**1. Introduction**

8 Science Education - Research and New Technologies

mg/dl).

quantities.

**Figure 1.** Data from a health laboratory.

Didactic phenomena in our understanding are exploiting the phenomenon as medium or bridge for learning concepts. In learning mathematics, didactical phenomenology interpreted as a means to learn math concepts as [1] stated that the didactical phenomenology is a way to show the teacher place where the learner may step into the learning process of mankind (p. ix). Starting from the situation that the human body contains thousands or even millions of myste‐ rious phenomena, some of which we can observe through the sheets of the doctor who advised us to go to the lab for having general checkup for our health, having our solutions or body fluids to be tested. It turned out that the concentration of the solutions in the body affects the healthy condition of our body. When the glucose in our body exceeding the normal size, then our health would be affected. When a less glucose (very low concentration) is present in our body then obviously the balance of our body also affected. This situation encourages the

Data in the **Figure 1**, represent the result of health lab test of the first author of this chapter (health of Turmudi's lab test) which was conducted in February 25th, 2014 in the Pramita Lab of Bandung. Suppose the number 130 mg/dl for triglycerides showed that as many as 130 mg of triglycerides in 1 dl solution, a healthy person is when she/he has less than 150 mg/dl (<150

Learning mathematics using mathematician framework usually takes place when introduc‐ ing the concept of sets and functions and then the "set approach" is used. Therefore, the func‐ tion is understood without using illustration. Function concept is understood as verbatim. Most mathematics teachers in Indonesia usually introduce relationship or function concepts using arrow diagram. Relating two sets of quantities, such as group of students in one hand, and their shoes number size in the other hand. He/she used arrows to link among two sets of

**Figure 2** represents the relationships among two quantities such as name of persons in set A and numbers of their shoes in set B. The research team, however, prefers to take advantage of this phenomenon by associating two specific situations. Rather than using data without

research team to take advantage of this phenomenon in mathematics.

meaning (meaningless), the research team prefers to observe variety of sugar solution concen‐ tration, and checking the time sneaking by an object at any percentage of sugar solution. The research team chose some phenomena by conducting experiments for each of these phenom‐ ena, and all served in front of students in the classroom. The result is quite amazing because students turned out to have an awareness of the usefulness of the relationship between a quantity and other quantities in the phenomenon.

Sugar solution is prepared with varying concentrations of 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50% by the researcher team (**Figures 3** and **11**). Then an object in this case is a small sphere like "ball" made of plasticine dipped in each solution. Here, we have two quantities when a dipping clay ball, i.e., concentrations of the solution expressed in percent and time crept from plasticine ball measured using stopwatch and expressed in seconds. We note the plasticine ball sneaked time in different percentage of sugar solution, so we have ordered pair numbers,

**Figure 3.** Solutions of sugar cane in percents.

that is the number percentage of sugar solution and sedimentation time of "ball" on each of these solutions.

**Figure 3** represents various concentrations of solutions. Practically, we used more details of sugar solutions by inserting 15, 25, 35, and 45% of sugar solution. Instructional design of mathematics based on the science using didactical phenomenology approaches was pre‐ sented to the students, so that the students have a sense of the relationship between two quan‐ tities. Students have the ability to represent it in a variety of mathematical representations. Furthermore, numbers obtained are processed and then packaged in various forms of math‐ ematical representations. Using this reflective thinking, students can think mathematically and scientifically to instill their awareness to be able to live in a healthy life and harmony.

The chapter presents the results of this study synergically involving scientific activities. Didactical phenomena of instructional design of mathematics were designed by the team in the laboratory activities, recorded using video camera, transferred to the power point presen‐ tation. The student tasks in the classroom were to make mathematical model or mathematical graph related to the data as the result of observation was recorded in video camera and power point presentation. These data were presented in the form of table. The pair numbers in the table as coordinates were then be plotted in the Cartesian coordinates. By graphing this phe‐ nomenon, the students were asked to interpret the phenomena.

As a design proposed by Verschaffel, Greer, and De Corte (2002, cited by Turmudi et al. [2], **Figure 4**), the process of learning mathematics that involves the modeling process includes the observation of phenomena (reading), understand the situation, modeling, analyzing the model, formulate the results, interpretation, and then make a communication:

The teaching materials of mathematics in this study used the didactical phenomenon in the form of a natural situation or similar situations that conditioned the models created in the science laboratory. The students in the classroom are faced with these instructional materials and the materials were manipulated in the form of power point presentation.

**Figure 4.** Diagram of mathematical modeling process.
