**7. Innovative perspectives**

The views of this innovative approach affect how the teacher in the classroom and how teachers evaluate students learn mathematics. This is related to the questions of the students related to mathematical ideas, the introduction of mathematical concepts, encourage and pro‐ mote discussion and group work. The Minister of Education and Culture of Indonesia in the era of 1990s reminds us through his views on mathematics and science "Most schools and teachers treat students as a 'vessel' or something to be filled with knowledge." Another well‐known example is the tendency toward right‐wrong answer/fact‐based learning. School and teachers focus on getting the right answer from the students at the cost of developing the processes that generate the answer [41]. Furthermore, he argued "I would like to challenge you to create greater understanding on how students learn as prerequisite for improving our teaching methods in mathematics and science, and improving the education of teachers for these subjects" (p. 36). These challenges need to be captured and acted wisely, of course. Similar challenges also presented by the President of the National Council of the Teacher of Mathematics (NCTM), Glenda Lappan "Throughout the more recent mathematics education research literature, there have been expressions of growing dissatisfaction with the limita‐ tions of the traditionally formal ways of teaching mathematics." Suppose, Lappan (1999, cited by [16]) provides arguments "We have had the longest running experiment in human history about whether rote memorization of facts and skills works." And it does not. Students are coming to universities and to the work place for not understanding mathematics. Why would not I want to try something new?

Challenges like that should be welcomed "Why we do not want to try something new?" After Lappan [16] we had a long trial of the history of humanity, about whether rote memorization of facts and skills can take place either? Challenges of Minister of Education and Culture, to (1) create a better understanding and to create a method of learning in mathematics and sci‐ ence [41], and (2) the growing dissatisfaction with the limited ways of teaching mathematics is traditionally formal (Glenda Lappan in Ref. [16]), gave rise to the urge to try something new, for example learning by using didactical phenomenon. Lappan (in Refs. [16, 41]) was one of international proponents who are very concerned for better innovative changes.

The underlying issue is how do we support the desire of teachers to improve learning in the classroom and how to provide examples and ideas that can be utilized in a practical way by the teacher in the classroom.
