Assessment criteria: Specific standards used to evaluate student performance on problem-solving tasks.
Evaluation rubric: A scoring tool that defines levels of performance for different aspects of a task.
Problem solving skills: The cognitive abilities required to analyze and solve mathematical problems.
- Understanding: Did the student comprehend the problem?
- Strategy: Did the student select an appropriate approach?
- Execution: Did the student carry out the plan correctly?
- Accuracy: Are the final answers correct?
- Communication: Did the student explain their thinking clearly?
Student correctly identifies this as a pattern problem looking for the next terms.
Student recognizes the pattern: add 3 to each term.
Student correctly calculates: 12 + 3 = 15, 15 + 3 = 18.
Answers 15 and 18 are correct.
Student explains: "I noticed each number goes up by 3, so I kept adding 3."
Understanding: ✓, Strategy: ✓, Execution: ✓, Accuracy: ✓, Communication: ✓
• Clear criteria: Define expectations before evaluating
• Objective scoring: Use consistent standards across all students
• Constructive feedback: Provide specific guidance for improvement
Rubric: A scoring guide that breaks down a task into specific components with defined performance levels.
Performance levels: Descriptive categories indicating quality of work (e.g., Excellent, Proficient, Developing, Beginning).
Scoring guide: A tool that assigns points based on specific criteria.
Method, Accuracy, Explanation are essential for factor identification.
Four levels allow for nuanced assessment of student understanding.
Each level has clear, observable behaviors for objective scoring.
Total of 15 points allows for meaningful differentiation of performance.
Systematic approach to factor identification with clear performance indicators for each component.
• Specificity: Clear, observable behaviors for each level
• Balance: Equitable point distribution across components
• Clarity: Students understand expectations
Error analysis: Systematic examination of mistakes to understand student thinking and misconceptions.
Diagnostic assessment: Evaluation designed to identify specific areas of difficulty.
Learning gaps: Areas where student understanding is incomplete or incorrect.
First 5 multiples of 6: 6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30
Student wrote 32 instead of 30 for the 5th multiple
Computational error: 6×5=30, not 32
Student understands the concept of multiples but made a calculation mistake
Review multiplication facts and emphasize checking work
Conceptual error: None, Computational error: 6×5=32 instead of 30, Instructional focus: Basic multiplication facts
• Separate conceptual from computational errors
• Understand the thinking behind mistakes
• Use errors to inform instruction
Assessment: The systematic process of gathering information about student learning and performance. Example: Evaluating how students solve mathematical problems.
Problem solving assessment: Evaluation focused specifically on a student's ability to analyze and solve mathematical problems. Example: Scoring a student's approach to finding factors of a number.
Performance criteria: Specific standards used to judge the quality of student work. Example: Correctness of calculations, clarity of explanation, appropriateness of strategy.
Diagnostic assessment: Assessment designed to identify specific strengths and weaknesses. Example: Finding out if a student struggles with multiplication facts or pattern recognition.
Formative assessment: Ongoing assessment used to guide instruction. Example: Observing students during problem-solving activities.
Summative assessment: Assessment used to evaluate learning at the end of a unit. Example: End-of-chapter test on factors and multiples.
Self-assessment: Students evaluating their own work and understanding. Example: Students checking their own work using different methods.
- Plan the assessment: Define learning objectives and success criteria
- Select appropriate methods: Choose assessment types that match the learning goals
- Create assessment tools: Develop rubrics, scoring guides, and evaluation forms
- Administer assessment: Implement the assessment fairly and consistently
- Collect evidence: Gather data on student performance and understanding
- Analyze results: Examine patterns in student responses and errors
- Provide feedback: Give specific, actionable feedback to students
- Inform instruction: Use assessment results to guide future teaching
• Validity: Assessment measures what it claims to measure
• Reliability: Consistent results across different evaluators
• Authenticity: Tasks reflect real-world problem-solving
• Transparency: Students understand expectations
• Equity: Fair assessment for all learners
• Utility: Information guides instruction and learning
Problem Solving Assessment Framework
🛠️ STRATEGY: Selects appropriate approach
⚙️ EXECUTION: Carries out the plan correctly
✅ ACCURACY: Results are correct
💬 COMMUNICATION: Explains thinking clearly
🗣️ Oral explanations: Verbal problem-solving processes
📊 Observation: Watch problem-solving strategies
🔄 Self-reflection: Student evaluates own work
🤝 Peer review: Students assess each other
🎯 Address specific improvements
📈 Connect to learning goals
🔄 Encourage self-reflection
🏆 Focus on growth mindset
Performance levels: Descriptive categories indicating the quality of student work.
Standards-based assessment: Evaluation aligned with specific learning standards.
Criterion-referenced: Judged against predetermined criteria rather than compared to peers.
Four levels allow for nuanced evaluation of different aspects of understanding.
Each level has specific behavioral indicators for objective assessment.
Criteria reflect the mathematical concepts being assessed.
Levels are distinct enough to guide instruction and feedback.
Standards-based evaluation with clear performance descriptors for consistent scoring.
• Differentiation: Recognize varying levels of understanding
• Progression: Levels indicate movement toward mastery
• Instructional guidance: Inform targeted support
Effective feedback: Information that helps students improve their learning and performance.
Constructive criticism: Feedback that identifies areas for improvement while acknowledging strengths.
Specific feedback: Detailed comments that target particular aspects of student work.
Effective: "Good job finding the pattern! Your explanation of multiplying by 2 is clear. Next time, check your arithmetic for the last term."
Ineffective: "Good" or "Needs improvement" - too vague to guide learning.
Effective feedback includes: acknowledgment of strengths, specific suggestions, clear expectations.
Specific, actionable feedback promotes growth mindset and continued effort.
Quality feedback helps students apply lessons to new problem-solving situations.
Be specific, actionable, encouraging, and connected to learning goals.
• Timeliness: Provide feedback while learning is fresh
• Specificity: Target particular aspects of work
• Actionability: Give clear directions for improvement
Assessment literacy: Understanding how to design, implement, and interpret assessments effectively. Example: Knowing when to use formative vs summative assessments.
Evidence-based assessment: Evaluation grounded in research and best practices. Example: Using multiple measures to assess problem-solving skills.
Authentic assessment: Tasks that mirror real-world problem-solving. Example: Word problems that connect to students' lives.
Alternative assessment: Non-traditional methods of evaluating learning. Example: Portfolio reviews, project presentations, peer evaluations.
Assessment for learning: Evaluation that guides ongoing instruction. Example: Exit tickets to check daily understanding.
Assessment as learning: Students actively involved in self-assessment. Example: Students tracking their own progress toward learning goals.
- Define learning objectives: Clearly articulate what students should know and be able to do
- Select assessment types: Choose methods that align with learning goals
- Design assessment tasks: Create problems that reveal student thinking
- Establish criteria: Develop clear rubrics and scoring guidelines
- Implement assessment: Administer tasks under fair conditions
- Collect evidence: Gather multiple sources of information about student learning
- Analyze data: Examine patterns in student responses and performance
- Provide feedback: Offer specific, actionable guidance for improvement
- Adjust instruction: Modify teaching based on assessment results
- Monitor progress: Track improvement over time
• Alignment: Assessments match learning objectives and instruction
• Validity: Assessment measures intended learning outcomes
• Reliability: Consistent results across evaluators and occasions
• Authenticity: Tasks reflect real-world applications
• Transparency: Students understand expectations and criteria
• Equity: Fair assessment for all learners regardless of background
• Utility: Information guides instruction and improves learning
• Embedded assessment: Integrate evaluation naturally into instruction
• Self-regulation: Teach students to monitor their own learning
• Collaborative assessment: Use peer evaluation and group reflection
• Data-driven decisions: Use results to inform instructional choices
• Assessment literacy: Ongoing training in effective evaluation practices
• Technology tools: Leveraging digital resources for assessment
• Cultural competence: Understanding diverse learning needs
• Feedback skills: Developing effective communication with students