A Summary of Designing A Mathematics Curriculum by Lee Peng Yee
The development of curriculum in Indonesia has changed many times through the ages. Relating to the issue of mathematics curriculum reform, the government of Indonesia has implemented at least six different mathematics curriculums since the 1970s. These curriculum reforms are Curriculum before 1975, curriculum 1975, curriculum 1984, curriculum 1994, curriculum 1994 revised and Competence based curriculum. Generally speaking, curriculum is defined as the package of a syllabus together with the implementation tools such as textbooks and other resource materials for teacher training. In Indonesian context, although the mathematics syllabus did not change, the mathematics curriculum has changed by the movement of PMRI. Normally, the next interested topic is the design of mathematics curriculum embracing PMRI.
The discussion in this summary was based upon Lee Peng Yee’s article with the same title. The summary covers several important factors in designing curriculum, some practices and the most recent trends.
DESCRIPTIVE VERSUS PRESCRIPTIVE
Typically, there are two types of syllabuses. The first is descriptive and the other is prescriptive. Descriptive means that the syllabus is brief and there is available space for teachers to interpret them so that they were not to be dictated by designers. The other type of syllabus is prescriptive in which items to be excluded would be clearly stated in that syllabus and the outline of topics covered.
It is already known that some of these descriptive and prescriptive syllabuses are moving closer together. Specifically, the descriptive syllabuses that tried to go for subject-specific content, that is, to be more prescriptive. On the other hand, the prescriptive syllabuses went in the opposite direction is to be more descriptive. In the other worlds, they are moving toward the same goal from two opposite ends.
In the syllabus, there are several kinds of strands. Strands such as numbers, algebra, geometry and statistics are commonly happen in the syllabus. Some syllabuses may have more than four strands. Most of syllabuses are spiral in which a topic may be introduced at a lower grade, but it will be revisited again and again at a higher level. There are also countries that adopted non-spiral approach in order to making it easier for teacher training. A syllabus describes about what to teach, and sometimes how to teach, but never why we teach what we teach.
A major event in the history of mathematics education in the past 50 years was the Maths Reforms in the 60s and 70s. Then it was followed by another 20 years of recovery and the era of problem solving. The Maths Reforms has been generally regarded as a failure. However, it is also undeniable that it helped to bring the changes for some developed countries in teacher training and locally-produced textbooks.
There is a known fact that a reform can move only as fast as teachers can move. Therefore, training of teachers becomes an important factor in the implementation of a curriculum. It was a common practice to conduct workshops for in-service teachers and seems to be the only way to train teachers to acquire new knowledge in the short period of time. Generally speaking, teachers tend to keep their original way of teaching even though they have been trained to conduct a new approach in their classroom. Intervention seems to be effective way to change the teachers’ habits. Sometimes it works. But, when it does not, it just ends up as a fashion without lasting effect.
Student profile has changed as society changed. The environment definitely affects their learning. Therefore, it is very important to know our students when designing a curriculum. Teaching mathematics is not just teaching mathematics alone. It is also a part of training for students to deal with work place.
One of difficult concepts to be explained is negative numbers. In the 70s, there is a great effort was made by textbook writers and teachers to differentiate the negative symbol from the minus sign. But, finally, they gave up. The other example is teaching fractions. Presently, we still teach simple fractions, move on rapidly to decimals, and then come back to fractions again. This is because of the fact that students use calculators nowadays. Because the habit of students has changed, the design of curriculum should also change.
It is already known that student profile is not a top priority in designing curriculum. Understanding the learning habit of our students is as important as selecting the topics to be included in a syllabus.
The essence of issue of Mathematics for All was that all students should study mathematics and up to a certain level. The questions were and still are how to help them and whether they really need it. Every country has its own way in dealing with this problem. For example, Japanese syllabus is a minimum syllabus in the sense that every teacher goes beyond it. Likewise, the U.S. standard is a maximum syllabus in the sense that nobody reaches it. Many other countries adopted differentiated syllabus, in one way or another. It seems that confidence, belief and commitment play an important role in learning, particularly in the Asian culture. Assuming that every students need to learn mathematics; a solution could be differentiated syllabus or differentiated curricula when designing a curriculum.
Firstly, assessment was meant as assessment of learning means we assess what is learned. Later on, people started advocating assessment for learning means we learn from what is learned. In the past two years, people invented the other new term, that is, assessment as learning means assessing is a way of learning.
There is nothing wrong to teach for examination. What is wrong is to teach for examination only. As far as we can see, examination will stay longer at least in the near future. If examination can lead to learning, it can also lead to the change in learning. Simply, examination plays an important role in designing a curriculum.
The latest change in the classroom is to teach in context and to emphasize on the process. Geometry with proofs and mechanics were two essential subjects in school mathematics before the Maths Reforms. Now Algebra dominates the school mathematics. We lost two rich training grounds to teach thinking process and to teach applications. Unfortunately, there is no replacement so far.
One way to compensate this situation is to incorporate modeling into curriculum. Many countries such as Australia and Germany have done with it. The success of the modeling project depends on how the participants play it.
A curriculum is good curriculum only when we have implemented it successfully. In order to be successful, it has to be considered in connection with teachers, students and many other determining factors. When we review our syllabus, we look around among other countries and compare with them. PMRI with activity-based teaching may have made in-roads into the classroom in Indonesia. The design of locally-produced curriculum will lead the movement of PMRI to become a main stream in the reform of mathematics teaching in particular, and education in general, in Indonesia.
Lee, P. Y. (2010). Designing A Mathematics Curriculum. Journal on Mathematics Education IndoMS-JME Volume 1 No. 1. ISSN: 2087-8885.