Report of CD-ROM Exploring Playgrounds
Unitizing, using numbers to counts group of objects rather than single object, is one of the big idea that important to understand multiplication and also to understand equivalence. It is happened through the process of learning classroom. In this process, there is model, representations of mathematical relationships used by student to organize their activity and solve problems, which can facilitate student to construct their thinking creatively. For example, an array, a rectangular arrangement of rows and columns, is a model that can represent multiplicative relations and student can use it as a tool to organize and explore quadratic relations.
This present observation has been done in Greenwich Village Middle School, Region 9 of New York in the West Village area of Manhattan. The class is seventh grade math class of 22 students, Kara Imm is the teacher. She teach student about multiplication of fractions with the context, a real and imaginable situation used by a teacher to solve mathematizing. She wants to know what strategies student use and what mathematical idea are they constructing.
Kara start from real life problem, the area problem as context, “There are two parks, Carol and Flatbush, in Brooklyn that have empty slot with width 50 yards and length 100 yards. Each park will be built playground with blacktop, a place for playing kickball and basketball In Carol Park, of lot is playground and of playground is blacktop. While in Flatbush Park, of lot is playground and of playground is blacktop. So, where in which park would you have more space for blacktop?”. This is a really good question for getting the meaning of fraction in area problem. It seems that a reverse of fraction numbers in different park is intended to make student compare between two parks and found what the idea is.
Student began to do the problem in pairs and asked them to write down the result in a poster. It seems for me that Kara want to make all of student thinking the solution by himself and also share the idea what he think with his friend. Sharing and discussing is important to achieve things in broader idea. In this part of activity, I see Kara has to support many pairs because students are looked feeling difficult to get the meaning of the problem above. Sometimes they do not concern of what part of the fraction it is. For example, they defined of lot is playground and of lot is blacktop also. It made a misconception and would not get the right answer. Therefore, Kara gave a support for the student who is faced up with these kinds of cases.
In the next meetings, Kara did a math congress, student come together as a larger group to present, question, and prove their solutions to each other after they have investigated, and four groups of pairs have been chosen to represent their result. I think the order of the group has been arranged in such a way according to Kara’s thinking. Therefore, it will be rather easy for Kara to guide the student in constructing the idea of unitizing in a right concept. In the first and second presentation, there is only a slightly different drawing model. I could say that the second drawing presentation is better than the first because the second drawing model is precisely right not only in the answer of the number rectangular of blacktop space but also in the answer of the number rectangular of remaining space. The third drawing model built the idea of “doubling strategy” I could say it equivalent concept – unitizing. The last presentation is rather same with second presentation. Many students said that the rectangular is flipped but I think it is not like that. It only seems like that but, in fact, if student aware of rectangular form in each park is different, the student would not say the rectangular is flipped.
From the process and the result of activities, I get some strategies and mathematical ideas that student used. The strategies are existed, such as: doubling and halving, splitting the rectangular (horizontal or vertical ways), comparing each rectangular, and recognizing the pattern. For the mathematical ideas, student came up with some ideas, such as multiplicative operation, unitizing, numerator (the top number in a fraction) and denominator (the bottom in a fraction). So, Kara has done her job with a good way of teaching using a mini-lesson, an investigation, and a math congress to emphasize the active nature of investigation – Math Workshop.
By Ekasatya Aldila Afriansyah