Authors: Lynda Ginsburg, Myrna Manly, Mary Jane Schmitt

Institutional affiliation/Agency/Program: NCSALL

Publication date: December 2006

Number of pages: 70

Website URL: http://www.ncsall.net/fileadmin/resources/research/op_numeracy.pdf

Abstract: The research article examines the nature of numeracy. After a thorough review of curricular and assessment frameworks and standards documents from adult education, K-12, and community college the authors discuss the definitions of numeracy and its difference from mathematics. Basically numeracy means math in real context with real purposes or uses, woven into the context of work, community, and personal life. Their analysis identified three major components of numeracy:

• Context - the use and purpose for which an adult takes on a task with mathematical demands (family or personal, workplace, community, further learning).
• Content - the mathematical knowledge that is necessary for the tasks confronted (Number and Operation Sense; Patterns, Functions and Algebra; Measurement and Shape; and Data, Statistics and Probability).
• Cognitive and Affective-the processes that enable an individual to solve problems and link the content with the context (Conceptual Understanding, Adaptive Reasoning, Strategic Competence, Procedural Fluency, and Productive Disposition).

All three components of adult numeracy, Context, Content, and Cognitive and Affective, are necessary to be numerate, act numerate, and acquire numeracy skills. One component without the other is insufficient.

The article also discusses implications for practice. Numeracy practitioners are encouraged to reexamine their practice to "include context in curriculum and instruction." In addition, the sequence of math instruction should be reexamined, so all content strands are included at all levels. Math instruction needs to include more than computation, focusing on conceptual understanding and mathematical relationships. To facilitate problem-solving, numeracy practitioners need to develop classrooms where students can interact and discuss mathematics in a social setting. The document discusses the importance of the development comprehensive numeracy assessments and supporting teachers to address all the components of numeracy.

Finally, the document suggests research that is needed in the field of adult numeracy.

Content Expert Reviewer Feedback: The Components of Numeracy should be required reading for all stakeholders in adult education: educators, curriculum designers, assessment experts, program directors, policymakers, and professional developers. The document is important because such stakeholders need a full understanding of numeracy in order to provide adults the tools and learning experiences with which to meet their goals.

Additional Remarks:

• Within the chapter on "The Context Component", there is an important discussion of the difference between "realistic" and "real" tasks and contexts.
• This resource could be used as the basis for an on-going professional development activity/discussion among staff members at learning sites. Activities could be explored and developed around the major components of numeracy (as described in this resource) of context, content, and cognitive/affective processes-or the difference between realistic" and "real"-see above.
• The document includes valuable information about frameworks and standards document, helpfully displayed in a useful table format:
  *Components and Subcomponents of Numeracy
  *Appendix B: Context in Adult-focused Documents
  *Appendix C: Mathematical Content Strands in Selected Frameworks
  *Appendix D: Cognitive and Affective References in Selected Frameworks