Getting to Know the Dimensions of Performance for Use Math to Solve Problems and Communicate

Take a minute now to look over the performance continuum for Use Math to Solve Problems and Communicate . Each of the five levels is on a separate page. You may use this version to create customized tools for your program.

Section 1 — The Components of Performance

The continuum begins with the definition of the standard, one that remains the same for each level of performance. Including the definition as the starting point for each performance level description reminds us that the definition of the standard as an integrated skill process is consistent across the continuum.

Section 2 — Knowledge, Skills and Strategies

The second section is a list of the key knowledge, skills, and cognitive and metacognitive strategies to be mastered for proficient performance at each level. These are the primary behavioral indicators (or benchmarks) of proficient performance at each level.

Bullet 1 focuses on the reading, writing, and interpretation of different types of mathematical information. Within this bullet parallel content strands include numbers and number sense (such as whole numbers, monetary values, fractions and decimals); patterns, functions and algebraic thinking (from commonly-used patterns to increasingly complex formulas); data and statistics (from simple ways to represent data in check sheets and graphs to more complex representations and interpretations of data); and measurement and spatial sense (from high frequency standard units of measurement and shapes to more complex units of measurement, shapes and models and their interpretation and representation).
Bullet 2 deals with recalling and using mathematical procedures. Students move from using simple procedures such as counting, addition, ordering and basic measurement to the use of complex multi-step concepts and procedures. They move from more familiar to less familiar procedures within the parallel content strands of numbers and number sense, algebraic thinking, data and statistics, and measurement and spatial sense.
Bullet 3 deals with the student's evaluation of the degree of precision needed for the solution. Although this bullet is the same across levels it is applied in increasingly complex ways.
Bullets 4 addresses the student's selection, definition, and organization of the information presented and use of available tools in order to solve the problem and verify his or her solution.
Bullets 5 deals with the student's ability to communicate the solution to the problem in a variety of ways. As students become more proficient, they are expected to be able to communicate their solution using representations (such as pictures, charts, graphs, and statistics) to a variety of audiences.

Section 3 — Fluency, Independence and Range

This section is a description of the fluency, independence, and ability to perform in a range of settings expected for proficient performance on the standard at each level.

  • Fluency of performance refers to the level of effort or ease required for an adult to retrieve and apply what he or she knows in order to solve a particular mathematical problem.
  • Independence of performance reflects the extent to which the person needs direction or guidance in organizing, solving, and communicating the solution to a mathematical problem.
  • Range of performance refers both to how well a person can use mathematical skills and whether the person can transfer learning from one context to another. This includes both a range of kinds and complexity of mathematical tasks, and a range of contexts and audiences for tasks.

Section 4 — Examples of Proficient Performance

This section has examples of the kinds of purposeful applications of the standard that can be accomplished by an adult who is proficient at each level. These examples represent only a few of many mathematical activities that could be developed in adult education settings.

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