39. Which proficiency scale statement measures procedure knowledge at advanced level 4.0 proficiency for the given standard?
Answer: C
The student will analyze and explain how a system is analogous to integers and create examples of closed integers.
This statement effectively measures advanced level 4.0 proficiency by requiring the student to not only analyze the concept of analogy between polynomials and integers but also to provide examples that demonstrate their understanding of the closure property.
A) The student will define mathematical terms, including analogous, polynomials, and integers.
While this statement involves defining key terms, it primarily assesses basic knowledge rather than advanced understanding. It does not require the student to engage in higher-level thinking or application of the concepts related to the standard.
B) The student will create a report in which they define all the mathematical terms related to polynomials and integers and provide examples.
This option involves creating a report that includes definitions and examples, which indicates a solid understanding; however, it does not specifically focus on analyzing the analogy between systems or demonstrating advanced procedural knowledge related to the concept of closure.
C) The student will analyze and explain how a system is analogous to integers and create examples of closed integers.
This statement is the most appropriate for measuring advanced procedure knowledge at level 4.0. It requires the student to not only analyze and explain the analogy but also to apply their understanding by creating relevant examples, which aligns perfectly with the expectations of the standard.
D) The student will perform mathematical operations with integers and polynomials.
This statement focuses on the execution of mathematical operations, which is more aligned with procedural knowledge at a lower level. While necessary, it does not encompass the analytical and explanatory skills needed for advanced proficiency concerning the analogy and the closure properties of polynomials.
Conclusion
Option C stands out as the most comprehensive measure of advanced procedural knowledge, as it combines analysis, explanation, and application through examples. The other options, while they assess important skills, do not fully encapsulate the advanced level of understanding required by the standard, making them insufficient for measuring proficiency at the level 4.0 benchmark.