Student’s mathematical thinking has three aspects, they are mathematical attitudes, mathematical methods, and mathematical contents.
I. Mathematical Attitudes
1. Attempting to grasp one’s own problems or objectives or substance clearly, by oneself
(1) Attempting to have questions
(2) Attempting to maintain a problem consciousness
(3) Attempting to discover mathematical problems in phenomena
2. Attempting to take logical actions
(1) Attempting to take actions that match the objectives
(2) Attempting to establish a perspective
(3) Attempting to think based on the data that can be used, previously learned items, and assumptions
3. Attempting to express matters clearly and succinctly
(1) Attempting to record and communicate problems and results clearly and succinctly
(2) Attempting to sort and organize objects when expressing them
4. Attempting to seek better things
(1) Attempting to raise thinking from the concrete level to the abstract level
(2) Attempting to evaluate thinking both objectively and subjectively, and to refine thinking
(3) Attempting to economize thought and effort
II. Mathematical Thinking Related to Mathematical Methods
1. Inductive thinking
2. Analogical thinking
3. Deductive thinking
4. Integrative thinking (including expansive thinking)
5. Developmental thinking
6. Abstract thinking (thinking that abstracts, concretizes, idealizes, and thinking that clarifies conditions)
7. Thinking that simplifies
8. Thinking that generalizes
8. Thinking that specializes
9. Thinking that symbolize
10. Thinking that express with numbers, quantifies, and figures
III. Mathematical Thinking Related to Mathematical Contents
1. Clarifying sets of objects for consideration and objects excluded from sets, and clarifying conditions for inclusion (Idea of sets)
2. Focusing on constituent elements (units) and their sizes and relationships (Idea of units)
3. Attempting to think based on the fundamental principles of expressions (Idea of expression)
4. Clarifying and extending the meaning of things and operations, and attempting to think based on this (Idea of operation)
5. Attempting to formalize operation methods (Idea of algorithm)
6. Attempting to grasp the big picture of objects and operations, and using the result of this understanding (Idea of approximation)
7. Focusing on basic rules and properties (Idea of fundamental properties)
8. Attempting to focus on what is determined by one’s decisions, finding rules of relationships between variables, and to use the same (Functional Thinking)
9. Attempting to express propositions and relationships as formulas, and to read their meaning (Idea of formulas)
(Mathematical Thinking and How to Teach It?, http://pbmmatmarsigit.blogspot.com/)
Topic: Linear Equation System with Two Variables
Aim : Knowing about student’s learning linear equation system.
I asked to student at third grade junior high school about linear equation systems. I make an example with the variable is books and pencils. If I bought three pencils and two books, the cost is Rp12.000 and if I bought two pencils and three books, the cost is Rp13.000. How the cost of each book and pencil?
She can answer that book’s cost is Rp3.000 and pencil’s cost is Rp2.000. To solve that problem, she makes idealization that pencils are same and books, too. She makes assuming that each book has a same cost and each pencil has a same cost, because if each cost is different she cannot solve that problem.
I asked her, how is the color? Are you use that to solve? She said nope because the important thing is the cost.
She makes abstraction by changed pencil with variable x and by changed book with variable y. It makes her easy to solve the problem. She can easily solve the problem with variable x and y. It makes her use elimination or substation easily.
Conclusion:
She use mathematical thinking to solve the problems, because she makes an idealization and abstraction. Idealization and abstraction including a mathematical attitudes, mathematical methods, and mathematical contents.
0 komentar:
Posting Komentar