The EM2 Cognitive Diagnostic Assessment System targets three rational number sub-domains: 1) fractions, 2) decimals, and 3) operations with rational numbers. These sub domains are further delineated into 12 focus areas shown in the table below.

Each assessment targets one or more research-based misconceptions. Example misconceptions are listed below:

  • ●   A fraction is two separate whole numbers: Students with this misconception do not perceive a fraction as a single quantity, but rather see it as a pair of whole numbers and apply whole number thinking by comparing the size of the numbers in the denominators or numerators or both. For example, they will conclude that 4/7 is larger than 3/5 because 7 is larger than 5.
  • ●   Incorrect direct substitution to convert a fraction to a decimal: Students with this misconception incorrectly use direct substitution in which they replace the fraction bar with a decimal point while using the same numbers. For example, students incorrectly think 1/7 is equivalent to 1.7.
  • ●   Count interval hash marks to locate a fraction on a number line: Students with this misconception overgeneralize from whole number reasoning to locate a number on a number line by simply counting the number of hash marks or points. For example, they will place 2/5 at the 2nd hash mark on a number line regardless of the interval size between hash marks.
  • ●   Estimate the sum of two fractions by adding the numerators and the denominators: Students with this misconception estimate the sum of two fractions by adding across the numerators and denominators rather than considering the size of each of the fractions. For example, to estimate the sum of 2/3 + 4/5 students will add 2 + 4 and 3 + 5 to arrive at 6/15, then provide the benchmark estimate for 6/15, which is about 1/2.
  • ●   Multiplication always makes bigger: Students with this misconception incorrectly assume that the product will always be larger than the factors when multiplying, regardless of the factors’ sizes. For example, when asked which expression results in a larger answer, 2/3 × 3/5 or 2/3 ÷ 3/5, students with this misconception choose the multiplication expression.