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

## A Concept Map of Developing Mathematical Models

**A Concept Map**

consept map

**Definitions**:

*Developing Mathematical Model:* the development of human activity of organizing and interpreting reality mathematically in addition and subtraction. Development of modeling usually proceeds from the modeling of a situation or strategy, to the use of a model as a tool – a model to think with.
*Facilitating:* give something that can useful for learning material (e.g. give a context)
*Context:* a real and imaginable situation for the children used in learning classroom. In this text, the context is some problems. There are two kinds of problems, such as removal problem (working with different amount of number from one object) and comparison problem (involving two different objects but related each other).
*Difficulty: *A condition that student cannot get *model for *or* *big idea in addition and subtraction
*Supporting: *guiding student with give some clues in order to achieve the goal of learning
*Big Idea: *A mathematical idea that often requires puzzlement, reflection, and discourse. It is important in mathematics, but also it is a developmental leap, sometimes a new perspective, for children. In this text, there are some ideas such as: cardinality (knowing that the number you end on when counting tells how many objects there are in the set), part/whole relationship (knowing ), hierarchical inclusion (understanding that whole numbers grow by one each time, and therefore that numbers nest inside each other: six is inside seven by removing one, etc.), and relationship between addition and subtraction (understanding that there are a connection of this generalizing across problems, across models, and across operations in which subtraction and addition are reversed on the number line)
*Strategy:* An organized pattern of behavior, a scheme for solving a problem. I found some strategies in this text, such as: counting on (for example when adding 9 + 7, rather than counting from one, the student start with nine and say, “10,11,12,13,14,15,16”), adding up vs. removal (when subtracting one can add on or remove, e.g. 32 – 3 is best solved by removing three, but 32 – 28 is more easily solved by adding 4on, rather than removing 28), doubles +/- (using doubles to solve problems that are near doubles, e.g. 6 + 7 = 6 + 6 + 1), and splitting (a decomposing strategy for addition and/or for subtraction, e.g. 38 + 26 = 30 + 8 + 20 + 6. Both numbers has been split, making use of expanded notation).
*Model: *Representations of mathematical relationships used by mathematicians to organize their activity and solve problems. For example the number line is a model that represents “number space” and mathematicians can use it as a tool to organize and explore number relation.
*Model of: *Representation of action and situation
*Model for: *Representation of symbolic. In this text, there is one *model for* open number line (a number line without specific numbers marked, except as added by student and/or the teacher to represent a computation strategy, or to explore number relations. This model is used to represent the jumps taken and landmark numbers used by student as they perform operations, like adding and subtracting, but student may use it as a tool to think with).

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