Komponen Algebraic Thinking

Algebraic thinking terbahagi kepada dua komponen utama; pembangunan alat pemikiran Matematik dan juga kajian kepada idea asas algebraic. Alat pemikiran Matematik adalah berkait dengan perlakuan minda yang analitikal. Ia disusun kepada tiga topik: kemahiran penyelesaian masalah, kemahiran perwakilan dan kemahiran penaakulan kuantitatif. Idea asas algebraic pula mewakili domain di mana alat pemikiran Matematik berkembang. Ia diterokai melalui tiga lensa, algebra sebagai generalisasi arithmetik, algebra sebagai bahasa serta algebra sebagai alat untuk fungsi dan permodelan Matematik. Rajah 1 menyimpulkan komponen-komponen tersebut yang dipetik daripada 2006 California Mathematics Content Standards (California Board of Education, 2006).


Components of Algebraic Thinking
(with illustrative citations from the 2006 Mathematics Framework for California Public Schools, Kindergarten Through Grade Twelve)


Mathematical Thinking Tools

Problem solving skills
• Using problem solving strategies
• Exploring multiple approaches/multiple solutions

Representation skills
• Displaying relationships visually, symbolically,
numerically, verbally
• Translating among different representations
• Interpreting information within representations

Quantitative reasoning skills
• Analyzing problems to extract and quantify essential
features
• Inductive and deductive reasoning



Fundamental Algebraic Ideas

Algebra as generalized arithmetic
• Conceptually based computational strategies
• Ratio and proportion
• Estimation

Algebra as the language of mathematics
• Meaning of variables and variable expressions
• Meaning of solutions
• Understanding and using properties of the number
system
• Reading, writing, manipulating numbers and symbols
using algebraic conventions
• Using equivalent symbolic representations to
manipulate formulas, expressions, equations,
inequalities

Algebra as a tool for functions and mathematical modeling
• Seeking, expressing, generalizing patterns and rules
in real-world contexts
• Representing mathematical ideas using equations,
tables, graphs, or words
• Working with input/output patterns
• Developing coordinate graphing skills