Design a Mathematics Curicullum
We often refer to syllabus as an official document which describes what to teach in schools. We may refer to curriculum as the package of a syllabus together with the implementation tools such as textbooks and resource materials for teacher training. Then we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. Naturally, the next topic of interest is the design of a mathematics curriculum encompassing PMRI. Sebenarnya dulu sebelum perang dunia kedua, silabus bukanlah apa, hanya sebuah koleksi latihan, but now the syllabus is standards, has the size of a book, spelling out in detail what to teach, and sometimes also how to teach.
In this article, the author put in writing some of the experience gained through the involvement in designing curricula since 1971. This article decided factors in designing a curriculum, some practices, and the latest trends. For convenience, we keep the discussion general, and do not refer to a specific syllabus. And refer to the syllabus of 7-10th grade.
There are two types of syllabuses, descriptive and prescriptive. Descriptive It leaves a lot of room for teachers to interpret the syllabus.So, the techer can be manage and also design how to present the syllabus. And prescriptive syllabus is sometimes to the extent that items to be excluded would be clearly stated in the syllabus.
Actually, lets descriptive and prescriptive syllabuses are moving closer together.
A reform can move only as fast as teachers can move. Hence training of teachers becomes an important component in the implementation of a curriculum. There has been research showing that a better way could be through peer learning within the school environment. However workshop remains a common practice. The production of textbooks became another important component in the successful implementation of a syllabus. In some countries, textbooks are produced officially or semi-officially. Some leave it to the private enterprises. The official syllabus may be the intended syllabus. Textbook should be the interpreted syllabus. Often this is not the case if not done officially with or without official sanction.
A reform can move only as fast as teachers can move. This is a known fact. Hence training of teachers becomes an important component in the implementation of a curriculum. During the Maths Reforms, it was a common practice to conduct workshops for in-service teachers. That seems to be the only way to train teachers to acquire new content knowledge within a short period of time. Somehow this became a standard practice till now without ever questioning whether this is a good way to train teachers. There has been research showing that a better way could be through peer learning within the school environment. However workshop remains a common practice.
The lesson we learn from the past is that we must prepare the teachers before any changes in the curriculum. We cannot afford to rush.
Society has changed. So has the student profile. For example, the older people listen to radio, whereas the younger people watch television. The older people write by hand, whereas the younger people work on the computer. Students are at the receiving end of the teaching process. The environment definitely affects their learning.
Often student profile is not a top priority in designing a curriculum. Knowing the learning habit of our students is as important as selecting the topics to be included in a syllabus. In one sentence, we may wish to pay greater attention to the student profile while designing a curriculum.
The issue of Mathematics for All was discussed extensively at the international conferences in the 90s. The essence was that all students should study mathematics and up to a certain level. This created immerse difficulty for some students. The questions were and still are how to help them and whether they really need it. This is a general problem in education and not mathematics alone. Most countries practise some kind of streaming and some do it more rigorously than others. One consequence of such severe streaming is that after 25 years we may produce a group of students who would never make it anywhere within the existing educational system. Consequently, special schools had to be set up to cater to this group of students.
Assume that every student needs to learn some mathematics. In connection with the design of a curriculum, a solution could be differentiated syllabuses or differentiated curricula.
Initially, assessment was meant to be assessment of learning. Then people started advocating assessment for learning. In the past two years, people invented another new term assessment as learning. Roughly speaking, assessment of learning means “we assess what is learned”. Assessment for learning means “we learn from what is assessed”. Assessment as learning means “assessing is a way of learning”. It is too early to say whether the third version of assessment will work as well as the first two. Teaching must always come before learning.
The latest change in the classroom is to teach in context and to emphasize on the pocesses.
Geometry with proofs and mechanics were the two essential subjects in school mathematics before the Maths Reforms. Both involve processes more so than algebra. Now algebra dominates the school mathematics. We lost two subjects rich in content and rich in exam questions. In other words, we lost two rich training grounds to teach thinking process and to teach applications. So far, there is no replacement.
The success or otherwise of the modelling project depends on how the participants play it. The hope is that learning experience and modelling might help bring back some of the things that we have lost in geometry and mechanics. We can only wait and see.
A curriculum is a good curriculum only when we have implemented it
successfully. To be successful, it has to be considered in connection with teachers,
students, and many other determining factors. A short summary is given below.
- Mathematics is the core and not how to teach it.
- A reform can move only as fast as teachers can move.
- We train our students for the work place different from our own.
- We need to cater to students of different abilities.
- We should explore the positive aspect of the examination system.
- Make explicit in a syllabus teaching in context and emphasis on processes.
It is common to take a generation or 25 years to find out whether we have
made a correct decision on a major educational policy. Further, it would take another 25 years to correct it if the decision was found to be wrong. We can give a few examples. Perhaps designing a curriculum is not so serious. The fact that it takes time to find out right or wrong is the same.
When we review our syllabus, we look around among other countries and compare with them. Perhaps we should also look back in time. Find out what we have done right and what we have done wrong. In order to do that, we need good documentation of the past events. In other words, we must have institutional memory. Activity-based teaching of PMRI may have made in-roads into the classroom in Indonesia. It will be the design of a locally-produced curriculum that 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.
Written by : Lee Ping Yee