Measured Progress Maryland Mathematics Performance Task Unstructured Answers

Maryland's Mathematics Performance Task (MPT) is a crucial component of the state's assessment system, designed to evaluate students' mathematical understanding, problem-solving skills, and ability to apply mathematical concepts in real-world contexts. One of the most challenging—yet potentially insightful—aspects of the MPT is the inclusion of unstructured answers. These open-ended responses demand more than simple calculations; they require students to articulate their reasoning, justify their solutions, and demonstrate a comprehensive grasp of the underlying mathematical principles. Understanding how to effectively assess and interpret these unstructured answers is paramount for educators seeking to improve student learning and overall mathematics performance in Maryland.

Understanding the Maryland Mathematics Performance Task (MPT)

The MPT is not just another standardized test; it represents a shift towards more authentic assessment methods. Its primary goal is to measure students' ability to think critically, analyze complex problems, and communicate mathematical ideas effectively. Unlike traditional multiple-choice tests, the MPT presents students with multi-step problems that often require them to integrate multiple mathematical concepts.

Key Features of the MPT:

• Real-World Context: MPT problems are often situated in realistic scenarios, making the mathematics more relevant and engaging for students.
• Multi-Step Problems: Students must navigate through multiple steps to arrive at a solution, requiring them to plan, execute, and evaluate their approach.
• Open-Ended Responses: A significant portion of the MPT relies on unstructured answers, where students must explain their reasoning, justify their solutions, and demonstrate their mathematical thinking.
• Emphasis on Mathematical Practices: The MPT assesses not only students' knowledge of mathematical content but also their proficiency in the Standards for Mathematical Practice, such as making sense of problems, reasoning abstractly, and constructing viable arguments.

The Significance of Unstructured Answers

Unstructured answers are the cornerstone of the MPT's assessment of higher-order thinking skills. They provide a window into students' mathematical reasoning, allowing educators to gauge their understanding beyond mere procedural fluency.

Why Unstructured Answers Matter:

• Reveal Conceptual Understanding: Unstructured answers can reveal whether students truly understand the underlying concepts or are simply applying rote procedures.
• Assess Problem-Solving Strategies: By examining students' explanations, educators can gain insights into the problem-solving strategies they employ, their ability to adapt those strategies, and their resilience in the face of challenges.
• Promote Mathematical Communication: Requiring students to articulate their reasoning encourages them to develop their mathematical communication skills, which are essential for success in advanced mathematics and STEM fields.
• Inform Instruction: Analyzing patterns in students' unstructured answers can provide valuable feedback to teachers, informing their instructional decisions and helping them address common misconceptions.

Challenges in Assessing Unstructured Answers

While unstructured answers offer rich insights into student thinking, they also present significant challenges in assessment. Unlike multiple-choice questions, which can be scored objectively, unstructured answers require subjective judgment and careful consideration of multiple factors.

Common Challenges:

• Subjectivity: Evaluating unstructured answers inevitably involves some degree of subjectivity, as different raters may interpret student responses differently.
• Rater Reliability: Ensuring consistency among raters is crucial for maintaining the validity and reliability of the assessment.
• Time Consumption: Assessing unstructured answers can be time-consuming, especially when dealing with large numbers of students.
• Developing Rubrics: Creating clear and comprehensive rubrics that capture the full range of possible responses can be challenging.
• Providing Feedback: Giving meaningful feedback on unstructured answers requires careful analysis of student work and thoughtful articulation of areas for improvement.

Strategies for Effectively Assessing Unstructured Answers

To overcome these challenges, educators need to adopt systematic and well-defined strategies for assessing unstructured answers. These strategies should focus on promoting rater reliability, streamlining the assessment process, and providing actionable feedback to students.

1. Developing Clear and Comprehensive Rubrics:

A well-designed rubric is the foundation of effective assessment of unstructured answers. The rubric should clearly define the criteria for evaluating student responses and provide specific examples of what constitutes different levels of performance.

• Define Scoring Categories: Identify the key aspects of student responses that will be evaluated, such as accuracy, reasoning, communication, and strategy.
• Develop Performance Levels: Create detailed descriptions of what performance looks like at each level (e.g., advanced, proficient, basic, below basic).
• Provide Anchor Papers: Include sample student responses that exemplify each performance level. These anchor papers serve as benchmarks for raters and help ensure consistency in scoring.
• Use Holistic and Analytic Scoring: Consider using a combination of holistic and analytic scoring. Holistic scoring provides an overall judgment of the quality of the response, while analytic scoring evaluates specific aspects of the response in more detail.

2. Training and Calibration of Raters:

Even with a well-designed rubric, it is essential to train raters on how to apply it consistently. Rater training should include:

• Review of the Rubric: Ensure that all raters have a thorough understanding of the rubric and its criteria.
• Practice Scoring: Provide raters with opportunities to practice scoring sample student responses and discuss their ratings with experienced raters.
• Calibration Exercises: Conduct calibration exercises where raters score the same set of responses and compare their ratings. Discuss any discrepancies and resolve them through consensus.
• Ongoing Monitoring: Continuously monitor rater agreement and provide ongoing feedback to raters to ensure consistency over time.

3. Implementing a Systematic Scoring Process:

To streamline the assessment process and reduce subjectivity, implement a systematic scoring process that includes:

• Blind Scoring: Whenever possible, score student responses without knowing the student's identity. This helps to minimize bias.
• Multiple Ratings: Have each response scored by at least two independent raters. If the ratings differ significantly, have a third rater score the response and resolve the discrepancy through discussion.
• Data Analysis: Analyze the ratings to identify patterns in student performance and areas where students are struggling. Use this data to inform instructional decisions.
• Technology Integration: Utilize technology to streamline the scoring process. Online scoring platforms can facilitate blind scoring, multiple ratings, and data analysis.

4. Providing Meaningful Feedback to Students:

The ultimate goal of assessment is to improve student learning. To achieve this goal, it is essential to provide students with meaningful feedback on their unstructured answers.

• Focus on Strengths and Weaknesses: Highlight both the strengths and weaknesses of the student's response.
• Be Specific: Provide specific examples of what the student did well and what they need to improve.
• Offer Suggestions for Improvement: Provide concrete suggestions for how the student can improve their reasoning, communication, or problem-solving skills.
• Encourage Reflection: Encourage students to reflect on their performance and identify areas where they need to focus their efforts.
• Timely Feedback: Provide feedback in a timely manner so that students can use it to improve their future performance.

Examples of Unstructured Answer Assessment

To illustrate the assessment of unstructured answers, let's consider a hypothetical MPT problem and examine how a rubric might be used to evaluate student responses.

Hypothetical MPT Problem:

A local bakery is planning to introduce a new type of cake. They need to determine the optimal price for the cake to maximize their profit. They have collected data on the number of cakes sold at different prices:

• Part 1: Develop a mathematical model to represent the relationship between the price of the cake and the number of cakes sold. Explain your reasoning.
• Part 2: Use your model to determine the price that will maximize the bakery's revenue. Show your work.
• Part 3: Discuss any limitations of your model and suggest ways to improve it.

Sample Rubric:

Sample Student Responses and Scoring:

• Student A (Advanced): "I developed a quadratic model to represent the relationship between price and sales: Sales = -2.5(Price)^2 + 70(Price) - 375. This model fits the data points well and captures the decreasing trend in sales as the price increases. To maximize revenue, I took the derivative of the revenue function (Revenue = Price * Sales) and set it equal to zero. Solving for price, I found that the optimal price is approximately $14. The main limitation of this model is that it assumes a continuous relationship between price and sales, which may not be realistic. In reality, the bakery might only be able to set prices in increments of $0.50 or $1. To improve the model, I could collect more data points at different price levels and use a more sophisticated regression technique." (Score: 4, 4, 4)
• Student B (Proficient): "I used a linear model to represent the relationship between price and sales: Sales = -5(Price) + 100. This model is easy to understand and works reasonably well for the given data points. To maximize revenue, I calculated the revenue for each price point and found that the revenue is highest when the price is $14. One limitation of this model is that it doesn't account for the fact that sales might drop off more sharply at higher prices. To improve the model, I could try using a different type of function, like a quadratic." (Score: 3, 3, 3)
• Student C (Basic): "I think the price should be $14 because that's when they sell the most cakes. I don't know how to make a model. One problem is that people might not like the cake." (Score: 2, 2, 2)
• Student D (Below Basic): "I don't know how to do this problem." (Score: 1, 1, 1)

Improving Mathematics Performance in Maryland

The assessment of unstructured answers on the MPT is not just about assigning grades; it is about improving mathematics performance in Maryland. By analyzing student responses, educators can identify areas where students are struggling and tailor their instruction to meet students' needs.

Strategies for Improvement:

• Focus on Conceptual Understanding: Emphasize the underlying concepts and principles rather than rote memorization of procedures.
• Promote Problem-Solving Skills: Provide students with opportunities to solve complex, multi-step problems and encourage them to develop their own problem-solving strategies.
• Develop Mathematical Communication: Encourage students to articulate their reasoning, justify their solutions, and communicate mathematical ideas effectively.
• Use Real-World Contexts: Present mathematics in realistic contexts that are relevant and engaging for students.
• Provide Targeted Feedback: Give students specific and actionable feedback on their work, focusing on both strengths and weaknesses.
• Collaborate with Colleagues: Share best practices with other teachers and collaborate on the development of instructional materials and assessment tools.
• Professional Development: Participate in professional development opportunities to enhance your knowledge of mathematics content, pedagogy, and assessment.
• Utilize Technology: Use technology to enhance instruction, provide personalized learning experiences, and streamline the assessment process.
• Parental Involvement: Engage parents in their children's mathematics education by providing them with resources and support.
• Data-Driven Instruction: Use data from the MPT and other assessments to inform instructional decisions and monitor student progress.

Frequently Asked Questions (FAQ)

Q: What is the purpose of the Maryland Mathematics Performance Task (MPT)?

A: The MPT is designed to assess students' mathematical understanding, problem-solving skills, and ability to apply mathematical concepts in real-world contexts. It goes beyond traditional multiple-choice tests to measure higher-order thinking skills.

Q: Why are unstructured answers important on the MPT?

A: Unstructured answers provide insights into students' mathematical reasoning, conceptual understanding, and problem-solving strategies. They allow educators to gauge students' understanding beyond mere procedural fluency.

Q: What are the challenges in assessing unstructured answers?

A: Common challenges include subjectivity, rater reliability, time consumption, developing rubrics, and providing feedback.

Q: How can educators improve the assessment of unstructured answers?

A: Strategies include developing clear rubrics, training raters, implementing a systematic scoring process, and providing meaningful feedback to students.

Q: How can the MPT data be used to improve mathematics performance in Maryland?

A: By analyzing student responses, educators can identify areas where students are struggling and tailor their instruction to meet students' needs. Data-driven instruction, professional development, and collaboration among educators are crucial for improvement.

Q: What role does technology play in assessing unstructured answers?

A: Technology can streamline the scoring process through online platforms, facilitate blind scoring, enable multiple ratings, and assist in data analysis.

Conclusion

Assessing unstructured answers on the Maryland Mathematics Performance Task is a complex but essential task. By implementing systematic strategies, educators can ensure that the assessment is fair, reliable, and informative. The insights gained from analyzing student responses can be used to improve instruction, promote conceptual understanding, and ultimately enhance mathematics performance in Maryland. The MPT, with its emphasis on unstructured answers, represents a valuable tool for fostering deeper mathematical thinking and preparing students for success in the 21st century. Continuous improvement in assessment practices, coupled with targeted instructional strategies, will pave the way for a brighter future in mathematics education in Maryland.