While there are smart student characteristics that are common to all disciplines and all grade levels, there are some characteristics that indicate strength in a given discipline. In math, for example, there are a number of variables that determine whether or not a student will develop as a “proficient” mathematics student. A brief summary of these characteristics is included in the chart below:
Characteristics Required for Proficiency in Mathematics | Current Tools Available | Usable in Regular School Setting | Usable in VI or NTI Setting | Priority |
A positive attitude about mathematic study |
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Mastery of the reading and writing skills required on state mathematics assessments |
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A work ethic that includes maintained high-level engagement in tasks |
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A positive perception of self as mathematician |
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Arithmetic fluency (e.g., number fact fluency) |
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Mastery of course-appropriate concepts |
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Successful real-world applications of arithmetic |
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Mastery of the arithmetic formats and venues |
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Mastery of arithmetic operations |
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Mastery of grade level algebraic concepts |
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Mastery of grade level algebraic operations |
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Mastery of grade level algebraic thinking and problem-solving |
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Successful real-world applications of algebra |
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Mastery of algebraic assessment formats and venues |
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Mastery of grade level geometric concepts |
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Mastery of grade level geometric operations |
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Mastery of grade level geometric thinking and problem-solving |
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Successful real-world applications of geometry |
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Mastery of grade level geometry assessment formats and venues |
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Mastery of calculus concepts |
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Mastery of calculus operations |
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Mastery of calculus thinking and problem-solving |
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Successful real-world applications of calculus |
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This development goes on to include statistics, mathematical operations from other disciplines, etc. in a standards-based world. It is inappropriate for a teacher to say a student is a bad math student without identifying the competency area listed above and the specific element(s) within the competency area that undermine that student’s proficiency.
It is important to note that many of the characteristics of a proficient math student fall outside of the taught curriculum area. During the second semester, it is critical for math teachers to attend to both the taught and the experienced curriculum and to monitor student growth in competency areas that were previously seen as “not proficient.”
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