Mathematics Proficiency Score Standards 1997-2002

Proficiency Level

Proficiency Descriptors

• Demonstrates all the characteristics of proficient performance; consistently exhibits superior performance, especially in problem solving and mathematical communication.
• In data analysis, draws information from multiple sources and infers solutions, providing data-based conclusions.
• When solving real-world, non-routine problems, employs multiple strategies, where applicable, as well as shows in-depth reasoning.
• Displays a highly developed sense of number and number relations and an understanding of number theory and the properties of numbers and operations.

(scale scores 659 and above)

• Consistently exhibits mastery of basic conceptual knowledge, skills, and problem solving.
• Applies the four fundamental operations with whole numbers, adds and subtracts decimals and fractions, and determines the reasonableness of answers.
• In geometry identifies two-and three-dimensional figures, congruence of figures; uses physical models to examine relationships.
• Analyzes data from visual displays and applies it to solve problems.
• Uses appropriate tools, understands appropriate units, and measures length to a specified degree of accuracy.

(scale scores 623 to 658)

• Demonstrates a good portion of expected conceptual knowledge and skills but may not be as proficient in applying them to problem solving situations.
• Solves simple one-step story problems,
• Mathematical computation is limited to addition and subtraction of whole numbers, simple basic multiplication facts, and addition of decimals without regrouping.
• Recognizes, fills-in and extends numerical and geometric patterns. Reads a ruler and a thermometer.

(scale scores 581 to 622)

Proficiency Level

Proficiency Descriptors

• Consistently demonstrates very high levels of conceptual understanding, numerical, geometric and measurement skills, and problem solving ability.
• Accurately applies computational skills with whole numbers, fractions, decimals, percents and integers to the solution of non-routine problems.
• Uses knowledge of statistical techniques and theory of probability to establish conclusions and infer future events.
• Communicates in a thorough and logical manner about solution strategies, the validity of their own conjectures, and the inferences of others.

(scale scores 750 and above)

• Demonstrates mastery of computational and estimation skills with decimals, fractions, and integers and applies these skills to the solution of two-step problems.
• Shows ability to work with various kinds of visual displays of data, using them to support conclusions.
• Applies measurement skills to determine perimeter and area in both customary and metric units.
• Demonstrates competent analysis, solving, and evaluation of solutions to real world problems by using appropriate symbols, tables, graphs, and algebraic expressions.

(scale scores 718 to 749)

• Demonstrates somewhat competent conceptual knowledge and skills.
• Performs basic operations on whole numbers, decimals, and some fractions. In data analysis, works with bar and line graphs and determines possible outcomes of given events.
• In geometry and measurement, recognizes most two-and three-dimensional figures, identifies congruence and similarity, and solves simple indirect measurement problems with physical models.
• Works backward and uses guess-and-check as techniques to solve problems.

(scale scores 674 to 717)

Proficiency Level

Proficiency Descriptors

• Consistently demonstrates in-depth understanding of conceptual knowledge, problem solving skills and ability to communicate in a thorough, logical, and articulate fashion.
• Utilizes tools of data analysis, probability, and statistics to thoroughly examine data, make inferences, and draw conclusions.
• Demonstrates use of a wide variety of high level algebraic, geometric and measurement skills.
• Uses direct and indirect reasoning, gives examples while solving problems, makes conjectures, and/or judges the validity of the inferences of other persons.

(scale scores 782 and above)

• Consistently demonstrates the ability to apply conceptual knowledge and skills to a variety of problems.
• Shows mastery of computation with and without calculators and estimates computations in real-life situations.
• Other numerical skills include working with patterns, ratio and proportion, formulas, and translating amongst equivalent forms such as exponents, fractions, decimals, percents, and scientific notation.
• Uses data presented in graphical form to rationalize and support arguments, inferences or conclusions.
• Works with probability of simple events, communicating about it with fractions, decimals and percents.
• Competent demonstration of measurement skills, including facility with scale drawings, are well developed.

(scale scores 744 to 781)

• Demonstrates somewhat competent success with most conceptual knowledge and skills, although level of mastery is less than that of proficient performance.
• Supports conclusions with some clarity.
• Somewhat competent with the basic operations with whole numbers, decimals, fractions, and percents.
• Uses appropriate measuring tools to obtain direct measurements, and ratio and proportion for indirect measurements.
• Algebraic skills include pattern recognition, substitution to solve equations and formulas, interpretation and use of expressions, and solution of one-step equations.
• Works backwards and uses guess-and-check to solve problems.

(scale scores 716 to 743)