* Conceptual understanding: Grasping the meaning of mathematical concepts, not just memorizing procedures. For example, understanding what multiplication *means* rather than just knowing the multiplication tables.
* Procedural fluency: Carrying out mathematical procedures accurately and efficiently. This includes things like correctly performing calculations, solving equations, and using algorithms.
* Problem-solving: Applying mathematical knowledge and skills to solve real-world or abstract problems. This often involves choosing appropriate strategies, analyzing information, and justifying solutions.
* Reasoning and proof: Making mathematical arguments and justifying conclusions using logical reasoning. This involves explaining why a solution is correct and understanding underlying principles.
* Communication: Clearly and effectively conveying mathematical ideas using language, symbols, diagrams, and other representations.
Specific examples of math competencies might include:
* Solving linear equations: A competency demonstrating procedural fluency and problem-solving skills.
* Understanding fractions and decimals: A competency showcasing conceptual understanding.
* Using geometry to calculate area and volume: A competency integrating conceptual understanding and procedural fluency.
* Interpreting data from graphs and charts: A competency highlighting problem-solving and communication skills.
* Formulating and solving word problems: A competency requiring all the above skills.
Therefore, a competency isn't just a single piece of mathematical knowledge, but rather a demonstrable ability to use that knowledge effectively in various contexts.