Massachusetts Department of Education
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What is Numeracy? A Definition of Numerate BehaviorFor purposes of this framework, the following definition is incorporated for describing numeracy and what it means to be a numerate adult:
How to use This Document (Teacher's Guide)The Mathematics Frameworks presents four learning strands: Number Sense; Patterns, Functions, and Algebra; Statistics and Probability; Geometry and Measurement which are described beginning on page 16 (in the Section on Content Strands and Learning Standards.) In order to present a document that makes sense practically, as well as theoretically, the Outline of Learning Levels on page 21 presents each of the strands and their standards at six performance levels:
At each level the strands are given in a chart, as shown below. Level ÞLevel 1: Beginning Adult Numeracy Strand Þ Number Sense Learners engage in problem solving within adult contextual situations by communicating, reasoning, and connecting to:
Benchmark Column (e.g. At this level an adult will be expected to:) Benchmarks describe the set of skills learners need to develop and achieve in order to meet the more broadly stated standards. By providing more detailed information on the specific skills and contexts for learners to meet the standard, benchmarks show teachers and learners what a standard “looks like” at each of the six levels. The strands and standards are arranged by performance levels so that each level can build on the previous ones. At each level, the four strands and their standards are outlined with the skills appropriate for that level. The skills defined at each level are ones to be achieved while working through the level. The teacher can use the frameworks as a curriculum guide. Each level builds on the previous levels, so it is recommended that teachers familiarize themselves not only with the level of their own class, but with the preceding levels as well. Enabling Knowledge and Skills Column The study of mathematics is developmental, but many adult learners have gaps in their learning of math. At times a learner may struggle with a skill because he or she has not grasped an enabling skill on which it is based. To present problems and practice with a skill, we must first lay the proper groundwork. Since not all adult education teachers have experience teaching math at an elementary level, the skills needed for the development of each performance skill are outlined. Examples of Where Adults Use It Column Teaching mathematics to adults is different than teaching it to children. As stated in the Common Chapters for the Massachusetts Adult Basic Education Curriculum Frameworks, “Adult learners value education and the power it has, but they rarely see it as an end in and of itself. Rather, education is seen as a means to other kinds of opportunities and achievements.”1 Adult learners need to know that what they are learning in the classroom is relevant to the lives and goals outside of the classroom. For this reason, we have included an application for each skill by giving an example of using the skill in an adult context. It is our expectation that this format will be a useful tool for:
The standards and benchmarks for each level are ambitious. They set the bar to be reached by learners, not the expectation of what is covered in a given class in a given year. However, the Framework does assume that the teaching of numeracy and mathematics be given a significant amount of time and attention in a program’s class offerings and curriculum. Mathematical understanding progresses from the concrete (counting two groups of blocks) to the representative (adding numbers presented in pictorial or verbal problems) to the abstract (using symbols and graphs). Presenting adults with problems or situations that allow them to develop their own approach to an inquiry model gives learners opportunities to talk about, write about, and represent math situations. During such inquiry, a learner can experience this progression in his or her own thinking. This affords an opportunity to see interconnections within math and between math and other disciplines. The numbering system used with the Standards and benchmarks was developed so the specific benchmarks or enabling skills can be referred to (e.g. in a lesson plan, curriculum, or scope and sequence). In the number 2P-3.4.1, for example, the system is as follows:
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