Difficulty: Medium

Average Score: 57%

A graduate student in curriculum development is designing a proficiency scale for the following standard: CCSS Math Content HSA APR A.1:
'Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication, add, subtract, and multiply polynomial?' (Common Core Standards Initiative, 2021).

Which proficiency scale statement measures procedure knowledge at advanced level 4.0 proficiency for the given standard?

Rationale

The student will analyze and explain how a system is analogous to integers and create examples of closed integers.

This statement demonstrates advanced proficiency as it requires the student to not only understand but also articulate the relationship between polynomials and integers. It involves higher-order thinking skills, including analysis and explanation, which are essential for mastering the concept of closure in mathematical operations.

A (The student will define mathematical terms, including analogous, polynomials, and integers.) YOUR ANSWER

Defining terms indicates a basic level of understanding but does not demonstrate the ability to apply or analyze concepts. This statement falls short of measuring advanced proficiency, as it lacks the complexity and depth required for a level 4.0.

B (The student will create a report in which they define all the mathematical terms related to polynomials and integers and provide examples.) YOUR ANSWER

While this choice involves some level of application, it primarily focuses on definitions and examples rather than analysis. Reporting on definitions is more aligned with foundational knowledge than with advanced proficiency in conceptual understanding and application.

D (The student will perform mathematical operations with integers and polynomials.) YOUR ANSWER

Performing operations reflects procedural knowledge but does not encompass the analytical skills needed to connect the concepts of polynomials and integers. This statement addresses basic procedural skills rather than the advanced analytical thinking required at level 4.0.

Conclusion

To achieve advanced proficiency in understanding the relationship between polynomials and integers, students must analyze and explain the analogous nature of these systems. Choice C requires the integration of higher-order thinking skills, making it the only statement that effectively measures advanced proficiency according to the specified standard. The focus on analysis and the creation of examples ensures a deep understanding of the concept of closure within this mathematical context.

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