my first experience PMRI teaching

here i will give you one of my experiences in teaching PMRI. though this design may be not perfect, i hope it will help teachers to have alternative way in teaching factor and prime number.

Background

For some students mathematics becomes something that very frightening and frustrating. They thought mathematics not only was very hard to understand but also need to be memorized so that they can get a better mark.

Prime and factor of a number were one of materials that student could not grasp the real meaning behind it. Even months after they were taught this material, they easily forget about the prime numbers or the factor of a number. 

Characteristic of RME

There are 5 characteristics which have to be consulted when one design the instructional activities in teaching and learning. Those characteristic are:

    1.      The use of context in phenomenological exploration

As prime numbers and factors are hardly seen in daily life except for their application in cryptography, the concept of these materials should be brought to mathematics land. Of course the concept should be close and quite realistic for students. In this case, the concept of those two come from multiple, a material that students already know and I believe they know the meaning of that material.

   2.      The use of models for progressive mathematization

Models are used as a bridge from concrete level to a more formal level. In this case the students will be brought to understand the concept of the material by experienced the multiplying numbers. Then in the end of this process student will be able to understand the notion of prime numbers and factor of a number.

  3.      The use of students own construction and production

In the activity, the students are given the opportunity to solve some problems by themselves. They have the chance to solve the problem in their own strategies. In the end of this activity, there will be a class discussion to choose what the most efficient way to solve the problems is.

   4.      The interactivity in teaching process

The activities in the teaching process are designed so that students can take a part in solving a problems or finding the meaning of the materials. Teacher in the class will be a facilitator that will support and help the students to understand. 

    5.      The intertwining of various mathematics strands or units

The sequence of instructional activities not only emphasizes the meaning of factor and prime and strategy to solve the problems, but also stress the relation between factor and prime number and to multiple numbers.

 HLT

There will be a sequenced of activities that designed in a way to reach the aim of the lesson. The activities will be describe in table below

Activity	Goal	Description of activity	Conjecture
Working with multiple	-    Student can relate factor of a number and the multiplication -    Students understand the prime number is the number which have exactly two factors	-   Teacher provides a teaching aid (related to multiplication of a number) where the student will use that. -   Teacher provides a student worksheets to guide the students understand about the materials	-     Some student will easily find the multiplication using their memory of it -     Some student will count the boxes in teaching aid so that they can get the multiplication product -     Some student will use a paper and a pencil to count the multiplication
Working with prime number	-    Student can find a strategy to determine whether a given number is a prime number	-   teacher will provides a problem where students should solve related to determine a number whether it is prime or not -   two groups will present their solutions	-     Some students will try to find a multiplication to get the number. -     Some students will get the answer by divide the questioned number by numbers that they guess

Result and analysis

In this part of report, there will be a comparison between HLT and the actual teaching learning process.

Activity 1

In this first activity, the teacher presented a teaching aid that will help the students to grasp the meaning of factor and prime numbers.

The teacher let the students to stick the sticker in the board in terms they should stick it in the multiplication of the number in the sticker. Students do this activity until all of the stickers run out.

Every time students stuck a number, teacher reminded the students what is the multiplication of that number.

In this activity, most of students did not have any problems with multiplication of numbers under 11. Most of them can easily find which number is a multiplication of a particular number. However, some of students are still have a difficulty in multiplication fact. This quite became obstruction in the teaching learning process.

 

For numbers more than 12 most of students counted the number of the boxes in the teaching aid. However, some student tended to be incorrect when they counted the boxes, so there were some stickers which were misplaced.

After finishing the teaching aid, teacher asked the students to look at the stickers as those stickers have a particular name that is factors of number in the box. Then teacher asked the students what is the meaning of those. There are some idea came from students one of them even see that if the two of numbered sticker multiplied then the product will be the number in the box.

As for the prime numbers, teacher give hints to the students that the number which has only 2 stickers. And students have no difficulty to see which number is prime number and which one is not. And they could see that factor of prime numbers consist of 1 and other number.

It is believed that students can distinguish which number is prime and not. Even, the students understand that 1 is not prime and they also can mention numbers within 1-42 that are include in prime numbers.

Unfortunately, the second activity is not done yet. Because the time is ended before all the activities were done.

Conclusion

Most of the students can distinguish a number whether prime number and not. However, for the numbers higher than 42, it can be known yet. The evaluation should be assessing first so that the result could be assured.

for the pdf version (english-indonesia) could be found  here