A Report of Minilesson from Addition and Subtraction Minilessons the part up to related problems CD ROM
The minilesson is more guided and more explisit. It designed to be used at the start of mathematical workshop and to last for ten to fifteen minutes. Each day, no matter what other unit or materials are used, I might choose a minilesson from this resource to provide my students with experiences to develop efficient computation. I can also use the lessons with small groups of student as my differentiate instruction.
To really understand addition and subtraction, student must understand how they are related. Student must have a generalized model of quantity, and understand how a whole is made up of parts, parts which may be “rearranged” (for example added in different order). By composing and decomposing parts of a whole, student become able to understand and represent the operations of addition and subtraction.
This observation is needed to analyze in generalizing of the development mathematical models in addition and subtraction. From the CD, Michael Galland, a third grade teacher in New Rochelle, New York, in the midst of a minilesson. His minilesson is comprised of a string of related problems. The first three problems are 146 – 12, 272 – 14, and 283 – 275.
B. Observational Question
What strategies do they use? What mathematical ideas are they constructing?
C. Purpose of the Observation
The purpose of this observation is to figure out what is going on during learning process, the goal of Michael’s interventions, and the differences occurred among children.
D. Description of Activity
Firstly, Michael give the problem of “146 – 12”. One boy with the yellow jacket answered it “134” without need a long time to think. It seems that he has count instantly in his thinking – subitizing. We can see in the figure 1, Michael writes the answer. Then Michael continues to ask what the process of this answer. Almost all students raise their hand including the boy who gave the answer. But Michael did not choose that boy, he choose another student, Maria, to give the reason. She precisely said “I have 146. I took away 10 then I got 136. I took away 2 then I got 134”. Maria’s strategies are splitting and removal. Michael directly writes Maria’s reason in the blackboard using open number line in order to guide student to get the meaning of open number line model. It looks success because no one of student gives any comment about the model.
For the second problem, Michael chooses Samantha to answer it and to give the reason also. It is a little bit different, Michael seems increase the difficulty. Samantha has to solve the problem by herself whereas in the first problem needed two students to solve it. She done it well with removal and splitting strategies (272 – 14 = 258) even though one time when she give the reason she rather difficulty to determine that 262 take away by 4 is 258 (figure 3). After that, Michael asks all students if they are agree or disagree with Samantha’s answer. There is one student who came up with 254 as the answer. So Michael asks further reason for that because it seems interesting. While Michael guides him to the right understanding, he lets other students to check it if it is true or not. In fact, he comes up with 256 as the answer. One of students feels peculiar about it and says it is wrong answer because it is not the answer of 272 – 14 but 272 – 16 (figure 4). From here, Michael’s strategy is success giving the right answer without says it directly. Why I said like that, because another student can repair wrong reason before to the right reason with adding 2.
In this video, Michael seems want to give a fact that not all subtraction problem is easy to overcome with removal strategy. Michael asked three different students and expected that each student give different reasons. First student, Ian, he came up with different strategy (figure 5). He used adding on strategy “275 added by 5 equal to 280. Then, added by 3 equal to 283. So the answer is 8” (figure 6). It looks like he has realized that comparing with removal strategy, adding on strategy with splitting strategy is easier for this problem. Second student said that he has the same reason with previous student (figure 7). However, for compare two strategies, Michael needs one student to give the reason with removal strategy. So Michael asked again and got one student who can explain her reason precisely with removal strategy. It needs a long time to solve this problem with removal strategy and also splitting strategy (figure 8). I think other student will realize what problem that suit for removal strategy or adding on strategy depend on the difference between two numbers (far or close).
There are some strategies that student used to overcome the problem, such as removal strategy, adding on strategy, splitting, and counting on. From above explanation, I can conclude that removal and adding on strategies are used separately depend on the kind of problems. The problems are distinguished based on close or far the distance between two numbers. If the distance is close, it will easier to overcome it with adding on. Then, if the distance is far, it will easier to overcome it with removal strategy. To come up with the understanding like that, student has to get the idea of generalizing between addition and subtraction in open number line. If they can construct the idea, they will come up to understanding that subtraction is a reverse from addition in number line.
By Ekasatya Aldila Afriansyah