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Pusat Penelitian dan Pengembangan Pendidikan Matematika Realistik Indonesia Sekolah Tinggi Keguruan dan Ilmu Pendidikan

Analysis of six choosing figures between 5.3 and 5.9 in Young Mathematicians at Work in Chapter 5


Analysis of six choosing figures between 5.3 and 5.9


Figure 5.3

figure5.3

Analysis:

Based on my analysis toward this drawing, I think the first and the second picture we can call it two examples of model of – representations of action and situation. However, both of them are different in level of student’ understanding. The first drawing seems easier than second one because there are many notes providing it, such as bus, letter stop, and numbers of people who get in and off from the bus. In the second picture, the student are only draw in minimal record changing the bus and letter stop with square and arrow – to represent the result of the action. Meanwhile, the third drawing is different with others, indeed. It is an open number line as a representation of symbolic – model for. This is general model for addition and subtraction and it expected that student can understand the relationship between three pictures above.

 

Figure 5.4a

figure5.4a

Analysis:

Based on my analysis toward this drawing, I think the first think that came up in Steven’s head is the information given by his teacher, that the houses which Shaun has to pass through was started from no.16 which is his own house until number 34 which is Mica’s house, his destination. So that’s why, I think the first drawing that he made was not the first row “he walked 18 blocks” but the second one “the tallies between 16 and 34”, as he imagine number 16 as the starting point then he imagine each house and represent it with vertical line, he start counting from 17, 18, and so on until he arrived in no 33, then he know that the destination is the house number 34, that’s why he wrote 34. Then he didn’t know how many vertical line he made already??so then he steps to 3rd row where he repeated to draw exactly like his work in 2nd row, this time a little bit smaller writing, maybe he just consider this as his checking to see how many house so that’s why he draw in smaller size, he put number starting from one consecutively until the last lines I guess so that he knows exactly how may vertical lines was it. After he got the number then he put it at the top or I called it as 1st row, he try to recheck his drawing by writing the addition that 16 + 18 = 34. So he concludes that Shaun needs to walk 18 blocks as written on the 1st row.

 

Figure 5.4b

figure5.4b

Analysis:

Based on my analysis toward this drawing, I think Breton started to write number 16 because he know Shaun house is number 16 and it’s the starting point, then the destination was number 34 that’s why he started his counting by drawing each number consecutively 16 to 34. After writing the numbers then he started his counting by drawing curve lines starting from above number 16 continuously connecting each of numbers 16 until 34. At the bottom it seems Breton wants to conclude that his calculation for how many blocks that Shaun needs to cover was 80, but there was something wrong with his writing because as we can see from his picture that the number of curve lines that he made was only 18, in this case maybe Breton still struggling between his answer 18 and the way he write 18 as 80.

 

Figure 5.4c

figure5.4c

Analysis:

Based on my analysis toward this drawing, I think Josh start his idea by drawing a line with number 16 and 34 on each edge of the line respectively because he imagines the line as the path along the blocks that Shaun has to take, number 16 is Shaun’s house and number 34 is Macy’s house. Then he makes a curve line to indicate each of the block, at first he’s not sure yet how many blocks that Shaun has to cover that’s why he draw a normal size of curve line (not too big or to small) but then as he moves along the line he didn’t reach 34 yet while he already close enough with the edge so that’s why he reduce the size of the curve line in order to make enough space until he reach 34 on the edge. He writes his counting above each curve line in order to recheck his counting, he write the next number after 16 which is 17 until 33, then to figure out how many curve line he made he write above the curve line a number from 1 until 18 based on the number of the curves line. He also give number to every end point of each curve line starting from 1 until 15, actually there are some endpoint left that he didn’t label yet, maybe he sure enough with his previous counting so he think not necessary to continue the labeling. At the last part I think he try to make conclusion on his work that along the line between 16 and 34 he got 18 curve line so that’s why he writes: 16 + 18 = 24

 

Figure 5.5a

figure5.5a

Analysis:

Based on my analysis toward this drawing, I think Eve works based on the strategy of splitting, she doesn’t start the counting from 16 but the closest number to the tens and it goes to 20 so that’s why she started from 20 to the next tens which is 30 on her 1st number line and between 20 and 30 she writes 10 on the curve line it means she understand that there are 10 steps  in between 20 and 30 then he makes another number line, starting from 30 to 34 because she knows that the last destination is number 34 so that why she can choose the next tens. She writes 4 above curve line between number 30 and 34 as she knows that there are 4 steps in between 30 and 34, then she came back again to her starting number which is 16, because she works from 20 to 34 already then she needs to find the step from 16 to 20 so that’s why she draws the number line from 16 to 20, she also writes 4 above curve line between number 16 and 20 as she knows that there are 4 steps in between 16 and 20.

On the right side she works downward her calculation starting from her 1st number line when she got 10 steps then she add it with 4 as the result from her 2nd number line, she add those two number and she got 14 then she add it again with 4 as the result of her 3rd number line. she add 14 and 4 then she got 18, she put thicker line below 18, maybe as a sign that 18 was the result.

 

Figure 5.5b

figure5.5b

Analysis:

Based on my analysis toward this drawing, I think  Daniel works based on group of ten as he started it with drawing a number line with number 16 on the left edge then he made 4 small curve line, he made this drawing in order to get 2 tens which is 20. He put 1 and symbol ‘+’ on each of 4 small curves line one to get 20. Then from the other edge he draw curve line and label it with 10, in his mind he has 20 and 10 already so it means she has 4 left to get 34 so that’s why she draws curve line in between the first 4 small curves and last curve and label it with 4. He calculate all the number above the curve lines then he got 18 so he stated “He had to walk 18 blocks”

 

 

By Ekasatya Aldila Afriansyah

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