teacher reflection (A reflection to paper)

hmm.. sorry to give false alarm. here, i give you a reflection to paper
title: Games for Enhancing Sustainability of Year 7 Maths Classes in Indonesia: Theory-Driven Development, Testing and Analyses of Lessons, and of Students’ Outcomes
by Christa Kaune, Edyta Nowinska, Annika Paetau, Mathilde Griep

http://fairfieldmathadvocates.com

there are several parts of this paper that quite interesting in my opinion. those parts showed in the aim of the paper, examples given, inferred result from the examples, and the conclusion of the paper.
First,
when the aim was written, the author purposely state that the paper mean to argue that manipulative that we as teacher used to use  is not a proper way bridging the knowledge students know and the lesson in classroom. the author state that the example that students already know and the manipulative teacher use have a substantial difference in the students' understanding. furthermore, lots of students think that lesson taught in the classroom differ from the prior knowledge they know.
the example given in this paper actually can enlighten teacher that the manipulative is not really effective because there is a different mathematics understanding between teacher (as an expert) and students (as novice). teachers need to not only make connection students' prior knowledge but also help students to built their undertanding.
you can read the complete examples in http://jims-b.org/ (find the correct paper)

as far as i am concern, this paper show us that not all manipulative is as effective as what we assume. teachers including me tend to create manipulative was made by our point of view, sometimes we forget that students can see what we teach (using those manipulative) is just a demonstration and rarely bridge it to the knowledge they already know. therefore, i think it's very important to use students knowledge to scaffold the new knowledge they learn in the classroom.

alternative way teaching percentage (reflection paper)

title: Solving Problems with The Percentage Bar
by Frans van Galen, Dolly van Eerde
 

it's been a while, i am not writing anything here. hereby, here i share an interesting reflection paper about percentage.i hope it will give some help.

source: http://www.oncalc.com

This paper in general informs the reader how the result of percentage lesson should be concerned. At first, Frans and Dolly gave result of their study in grade 7 in understanding percentage. Those result showed that most of the students tend do make some error when doing discount problem despite it should be easy to be solved. Later on, they show other result when percentage bar help those students solving the percentage problems. Furthermore, it is also explained how percentage bar help students to understand the problem. 
At the introduction part, the writer illustrated that from the results of their study in fourteen 7^th graders. First, most of the students failed to find the correct answer. To be precise only 4 out of 14 that can solve the problem. this paper present the alternative way to teach percentage using percentage bar, or percentage table.


the percentage bar used as a tool to bridging the percentage and the amount its present. it can be seen as the picture below

the percentage bar can be divided into 2, so the students can get 50%, or they can divide into 10%, or even 1%. when the students can use this bar effectively, they will not have any difficulties in solving percentage problems.

for the further inquiry about this method of teaching percentage please read by downloading  the actual paper in http://jims-b.org/

example of contextual problems

hi everyone..it's been a while that i didn't  write in this blog. i won't say that it was because i was too busy, sometimes it's just because some internet connection problems, sometimes i can say that i am lazy to upload t because there were no internet connections in my room, to the point it frustrated me.
so, here i give you some example of contextual using my hometown context. i already post the indonesian version of it in previous post.


this first question is about one of traditional cake (if i could say that) in my hometown. actually, when you are look up for this cake in the internet it will directly connect to my hometown. the name of the cake is kamir.

    1.       Ms. Ani has been selling Kamir (a trsditional cake from pemalang) for 10 years. She always packs the cake into a cartoon box. However, this year she tried something new in the kamir packaging. She tried to use a transparent box, instead of cartoon box. Therefore, anyone can see through the box, the cakes packed.

Mr Bambang, 5^th grade teacher in SD N 02 Banjardawa, bought a box of kamir from ms. Ani. Later on, he showed the students this box and asked the student to guess how much kamir which is stored in the box. However, Mr Bambang gave limitation to student and prohibited the students to open the box. He just allowed the students to observe the box.

The picture below show the Dika’ s observation result (he is one of the students there).

Front view

Side view

 

Top  view

 

Using dika’s picture, could you guess how much kamir inside the transparent box?

the next problem related to one of annual festival in Pemalang. actually, i did not really remember about it, because i just went to see this festival once, years ago. actually, this festival is kind of traditional ceremony which is showing gratefulness and hope. there are lots of this festival akin in Indonesia. even in some places the festivals have the same name.

   2.       Every Tuesday or Friday (kliwon) in Muharram month each year, in Pemalang there is a festival called Baritan. The aim of this festival is to show gratefulness to God by giving sacrifice in the sea. Each year, there are lots of boats joining this festival, even though not all of them are going to the sea to do the procession. 

   
          Pemalang Tourism Department has been listing the number of boats participating each year. The number of the boats participating in this festival could be seen in table below

Boats’ participation in Baritan festival

Pemalang tourism Department

(not actual data)

year	The number of boats participating in the festival	The Number of Boats went to the sea in the festival
2008	20	15
2009	25	22
2010	29	21
2011	28	20
2012	27	19

According data above, find:

a.       The average of the number of boats participating in the festival in 2008-2012

b.      The average of the number of boats went to the sea in the festival in 2008-2012

c.       In which year, the number of the boats participating reach the highest

    
    this last problem is about one of traditional clothes made in pemalang. even if there are lurik in Jogja or Solo, however both the motif and the color are kind of different. there are many people in my hometown that make this clothes are using non-machine weaver, they weave the clothes manually, using a manual weaver. the weaver itself is unique, it's my own opinion especially when the weavers use it. it's kind of complicated though. however, it's all paid off when the we got the clothes in the end. it is very beautiful and colorful, one of trademarks from north part of java (pantura).

    3.       To make a lurik cloth, weaver should weave thread in certain sequence to get a certain motif.

Look at the picture in the right.

The picture shows a part of lurik cloth. According to the picture, find the color of thread in line

      a.       90^th

      b.      253^rd

 





i hope it's helpful. ^_^

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