Massachusetts Adult Basic Education
Curriculum Framework
For
Mathematics and Numeracy
Massachusetts Department of Education
Adult and Community Learning Services
October, 2005
Acknowledgments 3
Introduction 4
How to use This Document (Teacher's Guide) 8
Connecting Curriculum, Instruction, and Assessment 10
Core Concepts 13
Guiding Principles 16
Habits of Mind 17
Content Strands and Learning Standards 18
Outline of Learning Levels 24
Appendices 118
Acknowledgments
Special thanks are due to the team who have contributed to the development of the Massachusetts ABE Curriculum Framework for Mathematics and Numeracy over the past number of years:
Patricia Donovan*
Barbara Goodridge*
Robert Foreman
Roberta Froelich*
Esther D. Leonelli*
Andrea (Drey) Martone
Marilyn Moses*
Jenifer Mullen*
Mary Jane Schmitt*
Jane Schwerdtfeger
Ruth Schwendeman*
Judith Titzel
* Denotes members of the original Math Curriculum Framework Development Team
I
Massachusetts Adult Basic Education Curriculum Framework for Mathematics and Numeracy 4
Massachusetts Department of Education, Adult and Community Learning Services, October 2005
n addition, we would like to recognize the ABE practitioners, students, business representatives, and other stakeholders from across the Commonwealth who shared their valuable time and talent through developmental working groups, field trials, and revisions that were essential in bringing the ABE Curriculum Framework for Mathematics and Numeracy to the level of quality that is reflected in this edition.
Introduction
for Mathematics and Numeracy
Over the past number of years, several initiatives have set the stage for writing the Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy.
The First Version: Changing the Way We Teach Math
In 1989, the National Council of Teachers of Mathematics (NCTM) published the Curriculum and Evaluation Standards for School Mathematics, a document that served as a template for reforming and improving K12 mathematics education across the nation. In 1994, sixteen Massachusetts ABE/GED teachers formed a team and studied the Massachusetts K12 standards to see how some of the ideas might play out in their adult education classrooms. After a year of action research in their classes, these teachers published two documents: a set of adult education math standards and stories of what changes looked like in their classrooms. Their adult math standards were incorporated into the Massachusetts ABE Math Standards (1995) and were the first set of ABE frameworks to hit the press. As such, they served as an early template for the Massachusetts ABE Curriculum Frameworks in other subjects that were subsequently developed.
In 1996, in the wake of education reform and a national science and math initiative in the state (which included Adult Basic Education), the Massachusetts ABE Math Standards were subsumed into the document, Massachusetts Curriculum Frameworks: Achieving Mathematical Power (1996). This state curriculum framework was to be used for both grades K12 and for Adult Basic Education. In 2000, when the Massachusetts K12 frameworks were revised, it was decided that the adult education math framework should be rewritten and revised, and developed as a separate document. This current version of the Massachusetts ABE Mathematics Curriculum Frameworks is a second revision of that first framework, but it is heavily influenced by developments in the adult education field since then, both nationally and internationally.
National Influences: The Adult Numeracy Frameworks and Equipped for the Future
In March 1994, the first national Conference on Adult Mathematical Numeracy, cosponsored by the National Council of Teachers, the National Center on Adult Literacy (NCAL), and the U.S. Department of Education/Office of Vocation and Adult Education, brought policy makers, researchers, publishers, and practitioners together to discuss the issues of adult numeracy needs and mathematical education. Out of this conference came at least two significant events: the formation of the Adult Numeracy Network (ANN), a national network of practitioners, and the development of the “honest list: what math we should be teaching adults.”
In October 1995, the ANN was granted one of eight planning grants for system reform and improvement, funded by the National Institute for Literacy as part of the Equipped for the Future (EFF) project. Over the course of a year, through teacherled focus groups of learners, business, and other state policy stakeholders in five states (including Massachusetts), and an online virtual study group, the ANN expanded upon the “honest list” developed from the conference. The teacher teams studied, among other documents, the teacherdeveloped Massachusetts ABE math standards, the report of the Secretary’s Commission on Achieving Necessary Skills (SCANS, 1991), and Equipped for the Future. Out of their research and focus groups, the teams developed seven themes which serve as the foundation for adult numeracy standards: Relevance/Connections, ProblemSolving/Reasoning/DecisionMaking, Communication, Number and Number Sense, Data, Geometry: Spatial Sense and Measurement, Algebra: Patterns and Functions. In 1996, they published A Framework for Adult Numeracy Standards: The Mathematical Skills and Abilities Adults Need to be Equipped for the Future (1996).
As a result of this work, mathematics was included in the Equipped for the Future Content Standards: What Adults Need to Know for the 21^{st} Century (Stein, 2000), a framework for adult instruction that is grounded in data gathered from adults on their roles as workers, parents, and community members. Of the sixteen EFF standards, one specifically addresses numeracy or mathematics: listed under DecisionMaking Skills, it is Use Math to Solve Problems and Communicate.
International Influences: Looking at Adult Numeracy
In addition to studying state and national mathematics curriculum frameworks, the ABE Math Frameworks 2001 Development Team considered several numeracy frameworks from other countries, including Australia, the United Kingdom, and the Netherlands, as well as the numeracy framework developed for the Adult Literacy and Lifeskills Survey (ALL), an international, largescale comparative survey of basic skills in the adult populations of participating countries.
The term numeracy is a word that was first used in 1959 in Great Britain and is used more often internationally than in this country. Numeracy has been described as the mirror image of literacy (Crowther Report, 1959) and is often thought to deal just with “numbers.” But since the 1980’s, work by adult educators in Australia, the UK, and other countries, has expanded the notion that numeracy refers just to the ability to perform basic calculations. For example, in the Australian curriculum frameworks, numeracy denotes the ability to perform a wider range of math skills, such as measuring and designing, interpreting statistical information, and giving and following directions, as well as using formulas and other advanced topics to pursue further knowledge. Moreover, numeracy and literacy are presented as interconnected and on an equal footing. The frameworks are written so as to address the purposes for learning mathematics and do not proceed from a schoolbased mathematics curriculum model so much as looking at the mathematics that is used in the context of adult lives. The Massachusetts ABE Curriculum Frameworks for Mathematics and Numeracy incorporate some of these ideas in the current revision.
