“Mathematics” or “Mathematizing”

Wah, lama ga update blog ni. Minggu ini, kami mahasiswa IMPoME Utrecht 2012 sedang disibukkan dengan sederetan aktivitas perkuliahan yang melelahkan ditemani sederetan kisah sedih, forum diskusi yang memanas dan berimbas di facebook, pengalaman pertama kali bersepeda di Belanda, tugas yang menumpuk, hingga hal-hal menggelikan yang selalu saja ditanggapi dengan tawa. Masih ditemani oleh dinginnya udara musim dingin, saya mencoba berbagi beberapa tasks yang saya telah kerjakan di mata kuliah Introduction in Realistic Mathematics Education (RME) yang diasuh oleh Mieke Abels ditemani oleh Martin Dolk.

Sedikit deskripsi tentang perkuliahan ini, mata kuliah ini seharusnya diasuh oleh Jaap De Hertog, seorang ahli RME. Nah, dikarenakan Jaap sedang mengalami proses penyembuhan pasca operasi kanker, oleh karena itu Mieke lah yang mengisi kekosongan itu. Semoga cepat sembuh ya Jaap, we miss you. Pada pertemuan pertama kita mempelajari beberapa video hasil riset yang terdapat di TIMSSVideo, kemudian dilanjutkkan dengan memganalisis dan mencoba membuat “Didactical Triangular” dari video-video tersebut. Selanjutnya, diakhir pembelajaran, kita diminta uuntuk membaca sebuah literatur yaitu chapter 1 dari buku Young Mathematician At Work (2001) karya C.T. Fosnot & M.L.A.M. Dolk. Sebagai evaluasi dari kegiatan membaca ini, kita diminta untuk membuat list kata-kata, kalimat, penting, dan summary nya. Berikut hasil resume saya.






innumeracy without a basic knowledge of mathematics and arithmetic


truism a statement that is obviously true and says nothing new or interesting


preoccupied (of a matter or subject) dominate or engross the mind of (someone) to the exclusion of other thoughts


indignation anger or annoyance provoked by what is perceived as unfair treatment:


framework an essential supporting structure of a building, vehicle, or object: a basic structure underlying a system, concept, or text:


nod lower and raise one’s head slightly and briefly, especially in greeting, assent, or understanding, or to give someone a signa


genuine truly what something is said to be; authentic


empathetic the ability to understand and share the feelings of another.


ponder think about (something) carefully, especially before making a decision or reaching a conclusion:


flair a special or instinctive aptitude or ability for doing something well:


logico-mathematical thinking a mathematics process reqiured logica thinking


unitizing form into a unit; unite into a whole:


infer deduce or conclude (something) from evidence and reasoning rather than from explicit statements:


glimpse a momentary or partial view:


quantifiable express or measure the quantity of:  Logic define the application of (a term or proposition) by the use of all, some, etc., e.g. ‘for all x if x is A then x is B’.


akin of similar character:


fait accompli a thing that has already happened or been decided before those affected hear about it, leaving them with no option but to accept it:


underneath situated directly below (something else):


embedded fix (an object) firmly and deeply in a surrounding mass


intrigued arouse the curiosity or interest of; fascinate:


inherent existing in something as a permanent, essential, or characteristic attribute:


progressive happening or developing gradually or in stages:


schemazatice arrange or represent in a schematic form:


  • “When teaching and learning are closely related, they will be integrated in learning/teaching framework: teaching will be seen as closely related to learning, not only in language and thought but also in action.”

As I experience during observing in SD Negeri 119 Palembang, and also based on my own experience in the school, teaching and learning process seems to be something separated. There is a big gap between teachers and students. Teaching and learning process must be two different activities. Teaching is perceived as a lecturing and giving such a long boring speech by teacher, while learning is interpreted as a discussion or doing some tasks by students.

  • … rather than focusing on their answer, Terry wants to keep them grounded in the context as she explores their strategy.

This is one of unusual and rare things that we can find in the learning process. In general, teachers tend to directly judge a student answer without considering whether their methods or strategy used. This brilliant way will make the students experience mathematics as their daily activity, and let them to explore and build their well understanding to the material or concept

  • Most of students in mathematics classrooms did not see mathematics as a creative but instead as something to be explained by their teacher, then practiced and applied.

This sentence refers to term name traditional approach school mathematics, which is one of an effect of misconception of interpreting teaching/learning as separated activities. This wrong paradigm should be changed.

  • Creativity is at the core of what mathematician do.

All this time, people judge that mathematics is only a subject without any progress. They judge that there is no changing since 2+2 must be 4 all the time. This perception is totally wrong. There are a lot of progress and changing process in mathematics especially in numerical approximation. Even, people also judge that there is no place for creativity in mathematician world. That is something to be clarify that there are a lot of approximation can be used to get something.


Basically, teaching and learning mathematics process are related activity, but the different approach of students and teachers make a different interpretation. Instead of creative, progressive, and alive, traditional approach school mathematics mislead people in judge that mathematics is something dead. This condition let people especially students perceived mathematics as something that to be explained by teacher.

Changing student paradigm through mathematics is not an easy way. However, we can outwit it by a different approach. The idea of mathematics as a human activity is one of the answer of this problem. By letting student to use their own strategy in beginning without considering their answer will help student to make their own progressive schematization of thinking, which is an important inherent characteristic of learning.

Let our students use their critical thinking to build up a big idea. By having an idea, they will learn how to reasoning and answer the questions appropriately. Every student has their own mathematical way to solve a problem, by letting them use and criticize it we unwittingly develop their ability in analyzing a problem, thinking mathematically, and reasoning.

Nevertheless, using a model also can help them to investigate further about a problem. It is not only help student in reaching the goal, but also make the learning process become interactive and interesting activity by choosing an appropriate model. However, something that is much more important is the way teachers and students communicate each other and the context used. Different contexts have the potential to generate different models, strategies, and big ideas, while without a good communication or framework will lead student to the traditional approach of school mathematics.

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