1. Problem Solving Skill
1.1. Understanding the Problem:
1.1.1. Ability to interpret and comprehend the problem requirements, including identifying key information and constraints.
1.2. Modeling/Formulating
1.2.1. Representing real-world problems mathematically, such as through equations, graphs, or diagrams.
1.3. Visualization and Representation
1.3.1. Drawing or creating diagrams, graphs, or tables to represent information. Understanding and manipulating shapes, quantities, and spatial relationships when needed
1.4. Estimation and Approximation
1.4.1. Approximating answers to check if results seem reasonable.
1.5. Validating/Evaluation Solutions
1.5.1. Reviewing answers for accuracy, completeness, and alignment with the problem requirements.
1.6. Computational skills
1.6.1. Utilizing mathematical methods, formulas, or computational tools relevant to the problem.
1.7. Creativity in Approaching Mathematical Problems
1.7.1. Being able to try alternative strategies if the initial approach doesn’t work or if unexpected challenges arise.
1.8. Strategic Thinking -Selecting Strategies
1.8.1. Choosing appropriate methods (like using formulas, algorithms, or heuristics) to approach different types of problems.
1.9. Analytical Thinking
1.9.1. Decomposing complex problems into manageable parts or steps.
2. Data Interpretation
2.1. Data Collection and Organization
2.1.1. Data Collection: Gathering relevant information or measurements for analysis. Data Organization: Arranging collected data systematically for easy interpretation and analysis.
2.2. Data Representation
2.2.1. Data Representation is the process of organizing and displaying information visually, such as through charts, graphs, or tables, to make it easier to understand and interpret.
2.3. Pattern Recognition and Trend Analysis
2.3.1. Pattern Recognition: Identifying recurring sequences, structures, or relationships in data or numbers. Trend Analysis: Observing and interpreting changes over time to predict future outcomes based on past data.
2.4. Comparing Data Sets
2.4.1. Comparing data sets involves analyzing two or more groups of data to identify similarities, differences, and patterns.
2.5. Statistical Reasoning and Inference
2.5.1. Statistical Reasoning: The process of using data to make logical conclusions, identify patterns, and understand relationships between variables. Statistical Inference: Drawing conclusions about a population based on data from a sample, using probability to measure reliability.
3. Mathematical Investigation/Enquiry
3.1. Formulating Questions
3.1.1. Developing clear, specific, and researchable questions to guide an investigation
3.2. Hypothesizing
3.2.1. Making educated guesses or hypotheses about potential relationships, patterns, or outcomes
3.3. Gathering and Organizing Information
3.3.1. Systematically collecting and arranging data or information relevant to the investigation.
3.4. Reflecting on Results
3.4.1. Extending specific observations or results to broader contexts or cases
3.5. Exploring Patterns and Relationships
3.5.1. Systematically collecting and arranging data or information relevant to the investigation.
3.6. Validating
3.6.1. Experimenting with examples, counterexamples, or cases to confirm or refute a hypothesis.
3.7. Generalizing Findings
3.7.1. Analyzing and interpreting outcomes and considering what was learned from the investigation.
4. Mathematical Reasoning
4.1. Comparing and Contrasting
4.1.1. Identifying similarities and differences between objects, numbers, shapes, or concepts.
4.2. Classifying and Sorting
4.2.1. Grouping items or information based on shared attributes or characteristics.
4.3. Inductive Reasoning
4.3.1. Making generalizations based on patterns or specific examples, essential in discovering rules or principles.
4.4. Deductive Reasoning
4.4.1. Drawing conclusions from known facts, definitions, or axioms, such as proving theorems or logical implications.
4.5. Analyzing Relationships
4.5.1. Examining connections and dependencies between concepts or numbers to understand how they influence each other.
4.6. Constructing Proofs
4.6.1. Building formal, logical sequences of statements to demonstrate the truth of mathematical statements.
4.7. Evaluating Arguments
4.7.1. Assessing the validity, logic, and strength of reasoning within a statement or claim.