# >> Behind Good Mathematics Learning – Part 2 : Repersonalization of Mathematics (by Endang Mulyana)

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Mathematics Repersonalization

When we are going to design a learning, the desired picture of learning must be in each of our minds. But it’s not easy. We need a conception of how to engage all students, provide assistance, and organize classroom interactions. In addition, observantly we need to formulate what students should achieve. Is that goal important and beneficial for the next learning? Which sections will be focused and inside and which parts are only discussed at a glance? After that we think about how to achieve it? What’s it going to start with? What’s the situation? How’s the plot? What’s the structure of the task? How did the students respond? How to help students in distress?

To determine the purpose of this learning, teachers need to understand the structure of mathematics, the relationship between the material to be presented, and the previous material that has been studied, as well as the relationship with the material to be studied in the next day. We need to do an in-depth study of the relevant mathematical materials. This is not easy to do because teachers tend to refer to books that students use. Meanwhile, the existing textbooks have not been good and true. This is what may have led to the teachers having limited knowledge of the structure of mathematics. How do we have a good conception of designing math learning?

In 2010 I discovered an algebraic factorization lesson plan created by Masaaki Sato when he was teaching in one of the classes in Indonesia. Its contents are the purpose of learning, a table consisting of two columns, the first column in the form of student activities whose description is the order of student tasks, while the second column is a predictive of the student’s response containing an estimate of various answers in completing the given task.

After learning the lesson plan I tried to imagine the learning process. In my mind I woke up to a picture of problem-based constructivist learning that I had wanted to understand and see for myself the process. Although I didn’t get to see Masaaki Sato’s class firsthand, by trying it out in lectures, I was able to exemplify PBL/constructivist learning about algebraic material.

I previously read Mr. Didi Suryadi’s writings discussing the learning that Masaaki Sato did with the Lesson Plan that I later learned. At first I had trouble reading the article. My mind was a little open after contemplating and doing so. I realized the importance of mapping the conception of teachers and students and managing them well. When I do that and manage to build meaning with students, I feel good. Since then I have been motivated to design algebraic learning in lower classes and discuss it with teachers and students.

In his article, Mr. Didi introduced Didactical Design Research (DDR), a completely foreign term but caught my attention. I had a lot of discussions and he asked me to do what he called repersonalization. He asked me to dig into the material of the line equation with the question: What is the background to the concept of the coordinate system?

Before I reread the various references to analytical geometry, I understood that the coordinate system was created by Descartes to solve geometry issues. It turns out that even vice versa, it completes the summation, multiplication and division of positive real numbers expressed as line segments. The lines used involve two lines that intersect, but do not need to be perpendicular to each other. In addition, grade or paper as a field of coordinates kartesius is already used by artists, especially sculpture artists when coloring it. More than that, it turns out that the first to use the cartesian coordinate field to represent algebraic functions is Newton. (continued)