MATH first page

For additional information about the New York State Adult Education Resource Guide and Learning Standards (AERG), see    http://www.nysed.gov   or contact Linda Headley-Walker.

MATH MATRIX

Across the top of the Math Matrix (below) are the basic Mathematics Topics.  Down the side of the matrix are the Foundation Skills- concepts of operations, and the thinking and communication skills needed to deal effectively with the mathematics topics. The Math Matrix therefore, is an graphic illustration of the inter-relationship of foundation skills and the basic mathematics topics.

The horizontal sequencing of the Mathematics Topics across the top of the matrix is not intended to imply an order in which the topics are to be taught but represents a continuum of linked and related subjects rather than a disjointed series of compartmentalized skills. The vertical Foundation Skills, include the concepts of operations and computation, along with the thinking, problem-solving and communication skills referred to in the SCANS (Department of Labor Secretary's Commission on Achieving Necessary Skills). Unlike the listing of mathematics topics however, the order in which these foundation skills are listed is purposeful since problem-solving and communication are the apex of these skills. The chart also demonstrates that though computation skills are a basic necessity, they are not an isolated end in themselves, but rather one set of the tools needed for problem-solving and communication in mathematics. Also, the introduction of each new mathematics topic for instruction implies the reintroduction, review and/or practice of the math concepts, as well as, thinking and communication skills.

Throughout all the Mathematics Topics an important consideration in planning instructional activities is the development of students' understanding of the concepts underlying the mathematics operations, and of the use of reasoning skills to apply that knowledge to problem-solving and to communicating mathematical ideas. For example, looking at the matrix, if an instructional goal is to prepare students to solve a work-related problem involving ratio/proportion (indicated by the X in the matrix) some students may first need to review their understanding of the underlying concepts behind the operations involved (Why cross-multiply and divide?) before they are able to estimate an answer, perform the computation, recognize the inherent patterns, see relationships, make connection to similar problems; all of which lead to effective problem solving.

The teacher is strongly encouraged to select and sequence those aspects of instruction that are most relevant to the needs of his/her students on an individualized and group basis. For initial assessment, an analysis of Tests of Adult Basic Education (TABE) or other testing instrument may provide a starting point for instruction by identifying learners' basic strength/weaknesses. However caution is advised in using only the results of these tests for instruction, since they may not identify gaps in understanding of basic concepts of mathematics. Research has shown that activities designed to facilitate recall of concepts and aid in the synthesis and application of reasoning skills are most effective if a team approach is used.  

A team approach can entail:

• -Embedding math topics and computation skills in problem solving/decision making processes
• -Learner-centered activities as vehicles for instruction, since they aid in the synthesis and application of concepts through
• communication
• -Students working in pairs/triads or teams, which allows opportunities for questioning and discussion, justification of thinking and content integration.
• -Concrete hands-on materials, rather than pencil and paper alone.
• -Calculator use at all levels of teamwork.

Mathematics (NCTM) and the recommendations of the Adult Numeracy Practitioners Network Framework for Adult Numeracy Standards. Note that there is an overlap of skills and examples in some cases.