Rethinking basic mathematics

By Hendra Gunawan

BANDUNG (JP): Pupils at primary schools are facing psychological problems learning mathematics due to misconceptions about teaching materials.

In a mathematics test, for example, a question was set which asked for the answer to 2 + 3 + 5. Most pupils wrote 10, which is correct. But the teacher crossed it out. He wanted his students to write 2 + 3 + 5 = (2 + 3) + 5 = 5 + 5 = 10 or 2 + 3 + 5 = 2 + (3 + 5) = 2 + 8 = 10. And this happens in the very first year at primary school.

Some problems can be clearly identified here. The first is the learning material, which is not suitable for first grade students. Even if it is only arithmetics, it is too formal and abstract. Do we really want our first grade students to learn arithmetics that way?

The second problem concerns the teacher, who may not realize what concepts are involved and how complicated they are for seven-year-old children.

But this is partly because first grade teachers are all-round teachers, who are not specialized in one particular subject. They probably just follow what is written in the syllabus or the textbook.

Hence the third problem is the curriculum designers and textbook writers, who might be too ambitious, or just do not understand mathematics.

As a result, mathematics becomes students' worst nightmare. No wonder students hate mathematics so much and perform poorly in the subject. Later, when these students go to university, they try to avoid mathematics whenever they can (even though they actually need mathematics for their studies).

Now, how can these problems be fixed? First, teachers, curriculum designers and textbook writers must realize that mathematics is not merely numbers and symbols, but a concise language to solve problems. Students are taught mathematics because they are expected to be able to solve problems, not only deal with numbers.

Second, children at primary schools are concrete thinkers. Thus, for primary school students, mathematics, as well as other subjects, are better taught through concrete daily problems, not by using abstract symbols and notations. Marbles, stones or bamboo sticks (not their pictures) can be used as teaching aids, as in the old days.

Later, when students have had enough experience with concrete problems, teachers can pose "semi-concrete" problems. For example, Ani has two apples, Budi has three and Coki has five. They put all their apples in a basket. How many apples are there in the basket? Surely students will answer 10. The teacher can, of course, ask how they come to the answer, but do not expect them to write it down symbolically. Oral explanation is adequate here.

Through concrete problem solving, students will find mathematics useful. Then, formal symbols, notations and terminology may be introduced and mathematics can be taught in an abstract way.

Thus what we need now is change in the curriculum, textbooks and teaching practice in schools. The current curriculum is just too ambitious. We are not in a "sprint" competition (with other countries), but in a "marathon". So there is no use speeding up in the early stages.

Moreover, knowledge grows exponentially and so does mathematics. This means that we can never finish studying the subject material. So, instead of emphasizing the material, it is much better to focus on the development of students' learning abilities (curiosity, critical thinking, creativity, etc.). They need these abilities for their future career, much more than the knowledge of the subject material itself.

There is one more thing that we need to pay attention to -- the written examination practice in the first four grades at primary schools. First, who has the heart to watch students aged seven to 10 face an exam paper consisting of a bunch of questions that they individually have to answer in a quiet room under a teacher's supervision?

Second, is a written examination really necessary for them? Can't we wait until they get to the fifth or sixth grades? For first to fourth grade students, can't evaluation be carried out in other forms? I guess we all should rethink what is the purpose of the evaluation, especially for the first four graders at primary school.

The writer is a staff lecturer at the Mathematics Department of the Bandung Institute of Technology in Bandung.