Nebraska

The standards are well presented and easy to read. They are divided by topic, though, logically, not every topic appears in each grade. For example, there are no standards about probability in the early grades.

Many standards are succinct and clear, such as:

Count by multiples of 5 up to 100 (grade 1)
Compare and order whole numbers 0-1,000 (grade 2)
Estimate and measure length using customary (nearest 1/2 inch) and metric (nearest centimeter) units (grade 4)

Some, however, are not clear, such as:

Compare different models to represent mathematical situations (grade 5)
Justify the classification of three-dimensional objects (grade 6)
Explain how statistics are used or misused in the world (grade 12)

In these examples, the reader is left with no idea what students are supposed to know or what kinds of problems they should be able to solve. Moreover, as the twelfth-grade standard above illustrates, the high school material tends to be particularly broadly stated and subject to interpretation. Another example of this is the following, which is one of the few standards that mentions quadratic equations but does not make clear what students should know, specifically, about quadratic equations:

Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value) (grade 12)

In addition, some standards are confusing such as:

Show equivalence among common fractions and non-repeating decimals and percents (grade 6)
Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square) (grade 12)

In regards to the first example, 1/3, a common fraction, gives a repeating decimal. Moreover, technically, non-repeating decimals are never equivalent to fractions. The second one just makes no sense.

Nebraska’s standards are generally well presented and easy to read. However, there are some standards that are too broadly stated to interpret. They “do not quite provide a complete guide to users” and receive a Clarity and Specificity score of two points out of three. (See Common Grading Metric.)

Content Priorities

While the state does not explicitly set priorities, the number of standards devoted to particular content areas communicates implicit priorities. Accordingly, arithmetic is only moderately well prioritized—almost 40 percent of the standards in appropriate grades deal with its development.

Content Strengths

The structure of arithmetic—commutativity, associativity, distributivity, and the inverse nature of addition and subtraction and of multiplication and division—are all well covered.

The number line starts early and is carried through the years, for example:

Show equivalence among common fractions and non-repeating decimals and percents (grade 6)
Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square) (grade 12)

In the development of fractions, common denominators are explicitly included:

Identify and name fractions in their simplest form and find common denominators for fractions (grade 5)

In addition, the standards include the important skill of conversion between measurement systems:

Convert between metric and standard units of measurement, given conversion factors (e.g., meters to yards) (grade 8)

In high school, while some standards are too vague to determine the intent, we also find some very strong standards. In geometry, for example, proofs of some major theorems and explicit mention of postulates are both included:

State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles) (grade 12)
Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true (grade 12)

In addition, important high school algebra skills are included, for example:

Add, subtract, and simplify rational expressions (grade 12)
Multiply, divide, and simplify rational expressions (grade 12)

Content Weaknesses

The development of whole-number arithmetic is inadequate. One illustration of this is the fact that the phrase “place value” does not even appear in the standards.

Instant recall of number facts is not required, but is replaced with the less stringent:

Fluently add whole number facts with sums to 20 (grade 2) Compute whole-number multiplication facts 0-10 fluently (grade 3)

In the continued development of whole-number arithmetic, fluency and standard algorithms are not required. There are some clear statements that students are expected to know how to do basic arithmetic, but methods and procedures are not specified.

The development of formulas for area is not specifically included in the standards. Students are expected to “determine” area, but the development of the requisite formulas is not made explicit:

Determine the area of rectangles and squares (grade 5) Determine the area of parallelograms and triangles (grade 6)

The high school standards are missing much essential content.

The coverage of linear functions is missing some basic content such as point-slope form and finding the equation of a line through two points.

Quadratic equations are not well covered. They are mentioned specifically only a few times, and the theory is not developed. Solving quadratic equations is in the following standard, but it does not adequately specify particular content expectations:

Solve quadratic equations (e.g., factoring, graphing, quadratic formula) (grade 12)

Missing content for quadratics includes the technique of completing the square, vertex form, and max/min problems.

In addition, most of the STEM-ready material is not covered. There is almost no trigonometry after the basic definitions. Other missing content includes logarithms and polar coordinates.

Though slightly prioritized, the development of whole-number arithmetic is not adequate. The high school material is missing much of the essential content. These “serious problems” result in a Content and Rigor score of three points out of seven. (See Common Grading Metric.)