Analyze. Create a list of test items...

 

 analyze. Create a list of test items. Research the literature regarding inter dependencies of each item and the impact of the l-n scores. 

 

Based on my analysis of the provided image and research into elementary mathematics, here is a breakdown of the test items, their interdependencies, and the scoring.

Analysis of the Report

The image provided is a "MATH: PROCEDURES" report for Marlinton Elementary. It lists specific math skills and compares the school's local performance ("LOC") against a national standard ("NAT").

• NAT (National): This likely represents the National Percentile Rank (NPR). It compares the local students' performance on a skill to a large, representative sample of students across the nation.

• LOC (Local): This represents the Local Percentile Rank (LPR), which compares the students' performance to their peers within the same school or district (Marlinton Elem).

• L-N (Local-National): This score is the difference between the Local and National percentiles (LOC - NAT). This score is the key indicator of relative performance.

  • A positive L-N score means the school is performing better than the national average on that specific skill.

  • A negative L-N score would mean the school is performing below the national average.

  • An L-N score near zero means the school's performance is in line with the national norm.

For example, on the item "Subtraction," Marlinton Elementary's local rank (94) is 14 points higher than the national rank (80), resulting in an L-N score of 14. This indicates a significant area of strength. The largest positive gaps are seen in "Two-digit addition" and "Two-digit subtraction" (both +22).

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List of Test Items

As extracted from the report:

• Three-digit addition

• Addition

• Missing addend

• Two-digit addition with regrouping

• Subtraction

• Two-digit addition

• Two-digit subtraction

• Two-digit subtraction with regrouping

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Skill Interdependencies in Elementary Math

These skills are not learned in isolation. They form a distinct pedagogical ladder, where mastery of one skill is a prerequisite for the next. The order below represents a more typical learning progression.

1. Foundational Skills (Addition & Subtraction)

The items "Addition" and "Subtraction" represent the foundation. This is a student's ability to fluently add and subtract, typically with single-digit numbers (e.g., $5+7$, $9-4$). This also involves understanding what addition (joining groups) and subtraction (taking away, finding a difference) mean.

2. Conceptual Understanding (Missing Addend)

The "Missing addend" item (e.g., $8+?=13$) is a critical cognitive leap. It directly measures a student's understanding of the inverse relationship between addition and subtraction.

• Dependency: A student who truly understands this concept knows that to find the missing part, they can use subtraction ($13-8=5$).

• Impact: This skill moves a student from rote memorization to flexible, algebraic thinking. It is a key indicator of deep number sense and is foundational for solving word problems and, later, equations.

3. Multi-Digit Procedures (Without Regrouping)

The items "Two-digit addition," "Two-digit subtraction," and "Three-digit addition" (assuming they are without regrouping) are the next step.

• Dependency: These skills depend on place value (understanding that the '2' in '25' means 20, not 2) and basic fact fluency.

• Process: Students learn to add or subtract vertically, column by column (ones with ones, tens with tens), without any "carrying" or "borrowing." For example, $25+41$.

4. Multi-Digit Procedures (With Regrouping)

This is the most complex set of skills on the list: "Two-digit addition with regrouping" and "Two-digit subtraction with regrouping."

• Dependency: These skills depend on all the previous steps: basic facts, place value, and the simple multi-digit procedure.

• Addition with Regrouping ("Carrying"): This is required when the sum of a column is 10 or more. For example, in $47+25$, the ones column ($7+5$) equals 12. The student must understand that this 12 is '1 ten and 2 ones', writing the '2' in the ones place and "carrying" the '1' (which is actually a 10) to the tens column. * Subtraction with Regrouping ("Borrowing"): This is required when a digit in the top number is smaller than the digit below it. For example, in $52-17$, the student cannot take 7 from 2. They must "borrow" 1 ten from the '5' (making it a '4') and add that 10 to the ones place (making it '12'). The problem becomes $12-7$. This requires a strong, flexible understanding of place value.

 Nat=WV Experimental