The Research Base for Use Math to Solve Problems and Communicate

The descriptions of performance at each level of the Use Math to Solve Problems and Communicate Performance Continuum are anchored in analysis of data on adult learner performance collected by teacher researchers working with adult learners in adult basic education programs (including adult literacy, adult ESOL, family literacy, and adult secondary education). Teachers in five field research states developed performance tasks and measured learner performance on the tasks as part of a rigorous three-year field development process. The aim was to generate rich descriptions of adult performance on the standards that grew out of adult learners' expressed needs and goals related to the use of mathematics. This evidence of learner performance on the standard went through extensive analysis by research staff and was reviewed and amended by a panel of content experts. At each step in this process, cognitive science and math theory and research was used to guide and refine the definition of performance criteria.

While research in adults' mathematics learning still is limited, the development of the Use Math to Solve Problems and Communicate Standard and Performance Continuum builds upon the extensive cognitive research on children's learning of mathematics, parallel standards development for the K-12 system, and the input of the business community. This research shows that people learn mathematics that is useful to them in many settings outside of the classroom. Frequently the ways adults perform mathematical tasks are predicated on strategies that make sense in the environment in which they were developed, and demonstrate a flexibility and conceptual basis that is closely tied to the context in which they are used. However, these procedures and strategies are often quite different from the decontextualized procedures and strategies that are taught in formal schooling. For some, the informal strategies and procedures were developed and are used alongside existing school-based strategies and procedures. For others who did not attend school, informal strategies and procedures were developed to meet real-world needs. To fill the gaps in adults' conceptual understanding and to address the limitations of their informal and formal mathematics knowledge, the Use Math to Solve Problems and Communicate Standard and Performance Continuum emphasize the following:

  • the development of facility with multiple representations of mathematical concepts,
  • movement from the familiar and meaningful to the less familiar,
  • connections within and across mathematical procedures, and
  • the reality of multiple effective strategies to achieve the same ends.

By embedding the mathematics in realistic contexts, the boundaries and limitations between formal and informal mathematics are lessened, reducing the difficulty of transferring knowledge from decontextualized instruction to application within real world contexts.

Adults' needs for 'just-in-time' learning do not match the type of mathematics instruction found in most adult education (as well as K-12) programs. This traditional instruction is based on a linear sequencing of mathematics learning: numerical computation procedures in sequence (addition, subtraction, multiplication, division, fractions, decimals, percents), then algebra, then geometry, and then data and statistics. Research in K-12 education has shown that mathematics learning benefits from the simultaneous development of algebraic reasoning, measurement and shape, and understanding of data throughout the course of instruction. This simultaneous development is called the parallel strands approach to instruction (National Council of Teachers of Mathematics).

We now know that the development of expertise in mathematics involves the increasing ability to organize information around important concepts and ideas rather than surface features (conceptual understanding), the knowledge of how to apply that conceptual understanding to practice (procedural knowledge), and the ability to chose the most effective strategies appropriate for the task at hand (strategic competence).The Performance Continuum for the standard provides guidance concerning the kinds of procedural knowledge, conceptual understanding, and strategic competence that are the appropriate focus for instruction at each EFF level. (The Use Math to Solve Problems and Communicate Resources section of the EFF Assessment Resource Collection library contains a more detailed description of this research and a bibliography.)

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