Why ABE Math Assessment Practices Must Change

by Tricia Donovan
Franklin Hampshire Employment and Training Constortium,
Greenfield, MA

Editor's Note: This article is reprinted from The Problem Solver, a publication jointly funded by SABES and the Massachusetts Department of Education. The edition from which this article was taken was designed to introduce and reinforce changes in mathematical assessment practices as encouraged by the Massachusetts Curriculum Frameworks document (primarily the ABE portions). The Problem Solver pages include materials developed by the three Frameworks Math Assessment Study Groups from the Boston, Northeast and West SABES regions. Much of the edition focused on potential assessment tasks and actual Frameworks-based assessments performed as part of the study group exploration.

Assessment is a key component of curriculum. It initiates the academic teacher-student relationship and guides instructional decisions in the best of circumstances. Currently, the Massachusetts Curriculum Frameworks, encompassing the Mass. ABE Math Standards and the NCTM Math Standards, calls for teachers to heighten their awareness of curriculum decisions which may have become or can become automatic, almost unconscious and too often homogenized to serve institutional needs, not student needs. Teachers are asked in the Frameworks to reform their mathematical teaching practices, including their assessment methodologies.

The Frameworks and Standards beg teachers to open up their questions, integrate academic skills and pique critical/creative thinking in their courses, their teaching. And all these changes are urged in the belief that students can be better served by teachers familiar with the nuances, ambiguities and potentials of mathematics. However, the Frameworks recognize that it is impossible to illuminate a course of study without accurate, informed and comprehensive assessment of student knowledge and learning which by rights should drive the curriculum.

A teacher must know what mathematics each student understands in order to serve well that student. To figure out what is known and what is not, how a person learns and what blocks his or her learning, requires assessment of a sort far different from that which has traditionally been practiced; it requires an 'assessment mindset' that, yes, utilizes new tools, but more importantly is exercised diligently/insightfully, regardless of the problem, test or task used. The evolution in assessment asks teachers to think deeply about mathematics and about students all the time.

"Every mathematical activity can become an opportunity for assessment," note teachers engaged in exploration of Frameworks-based assessment.

Both the Frameworks and the NCTM Standards champion an evolution in assessment practices, an evolution in which careful, criteria-based analysis and collections (portfolios) of students' work, not just a compilation of their percentages or positions on the bell curve, becomes the standard procedure used to determine what a student knows, at what level (s)he comprehends what is known and what scholastic attitudes or intellectual behaviors are exhibited. This evolution assumes an awareness of lesson objectives and an investigation of students' meeting, exceeding or confusion with these objectives in order to inform subsequent instruction.

Frameworks-based assessment requires teachers to know what it is they expect students to learn from or demonstrate via a particular lesson. Random selection of activities, whether to keep students busy or to entertain them, is viewed as counterproductive. A clear vision of students' knowledge base and direction for future development is required. That is, the teacher must know the student and the subject in order to develop or locate appropriate materials for instruction and assessment.

When assessing students, teachers are advised to ask:

What skills, knowledge, and academic behaviors do I want my students to
express, and what tasks will provide evidence of these?

The emphasis here is on establishing criteria to prove mastery. Does the student understand concepts, techniques, algorithms, etc., and can (s)he apply this knowledge flexibly and appropriately, and, finally, what criteria will establish for teachers valid proof that a student knows the concepts, techniques, algorithms, etc. or possesses academic habits of thinking?

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Documentation of investigation results is necessary, just as recording numbers and case notes has been. Only now what is recorded is information relative to specific curriculum objectives, especially as articulated in the Frameworks and the Standards. Is the student a flexible problem solver? Can the student coherently communicate the mathematics embedded in a problem? Does the student apply previous knowledge to a new situation? The answers to these questions, as demonstrated on particular tasks or in exploration projects or in portfolios, are the informational foundations of Frameworks-based academic assessment. (It must be noted that academic assessment always operates within the larger gestalt of assessment which for devoted teachers involves assessment of students' physical, psychological and spiritual statuses as well as mental or academic status.) These informational foundations are built to help teachers better serve the academic needs of their students.

The teacher must know the student and the subject in order to develop or locate appropriate materials for instruction and assessment.

And it is assumed that every ABE (Adult Basic Education) teacher wants to serve her or his students in the best manner possible. Every adult educator wants his or her students to be successful, to get what "they came for" and to feel better about themselves as they become more confident in their abilities. These are the ABE teacher's rewards. Moreover, all ABE instructors know the bottom line for many funding sources and the basic goal of most students is attainment of the GED certificate. The GED certificate is accepted as recognition of general academic achievement. But for too many stuoents achievement of the GED with a minimum score in mathematics leads to educational and economic stagnation. It is not sufficient preparation for what comes later. Minimum competency is not enough; it is not serving students in the best manner possible.

By aligning itself with the K-12 teachers and administrators who are developing Curriculum Frameworks and Alternative Assessment Practices, the Massachusetts Adult Education community seeks to dream a bigger dream for ABE students, one which unlocks the prison of poverty and social disenfranchisement. It seeks to clear paths to economic, social and personal growth which formerly opened only for those Prepared by a college-prep or advanced technological prep high school program. It says getting by by the skin of your teeth is not enough. It says, "We can help you learn to solve problems, imagine problems and discuss them with others."

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The purpose of ABE is not only to teach students a few tricks to get past the 'academic guards' in the GED Testing Office; it is to awaken learners who are alienated from the unavoidable world of academic ideals, and arouse those beginning to see the value of and power in the ability to read all genres, write coherently, calculate and problem solve with mathematics. To awaken and arouse learners requires ongoing, informed, documented assessment of learning. Armed with such assessment information, every teacher becomes capable of leading students down their various paths to success.

The paths to achievement, economic equality and personal development are being widened by efforts like the Frameworks so people of all backgrounds can walk down them. Across the State, teachers and administrators seek ways to better prepare all students for the challenges known to lie ahead. These educational leaders realize that successful citizens are able to reason, solve problems, communicate and make connections throughout their lives. They know that when a student's creative intelligence and curiosity are allowed to flourish, that student plants her/his feet firmly on the paths to fulfillment and success. The determination of the Massachusetts Curriculum Frameworks and the development of Frameworks-based assessment practices are efforts to help us all become better skilled, sharper thinking citizens who are able to question and develop solutions to problems.

Teacher and student reflection upon classroom work is integral to the process of improvement. The quality of thinking, the quality of interaction, the quality of expression of each student must be considered and then evaluated in order for learning to take place. In this process of observation, examination, active reflection, consideration and evaluation which The Frameworks terms assessment, the intention is to better serve the individuals involved in educational development. Percentages, bell curve positions and vague intuitions are not enough to prepare adult students of basic education for the demands of the 21st century. Teachers need to know what students truly understand and how they came to understand it if they, the teachers, desire to nourish the students' intellectual capacities and free them from the constraints of a limited education.

To awaken and arouse learners requires ongoing, informed, documented assessment of learning. Armed with such assessment information, every teacher becomes capable of leading students down their various paths to success.

To improve students' abilities to maneuver in a fast-changing world, to broaden their horizons and stimulate the desire to understand more about themselves and that world which surrounds and influences them, teachers have to listen and look deeply, discerningly, at students' mathematical utilizations and inventions. This is what Frameworks-based assessment advocates. This Frameworks-based assessment process is neither easy nor simple, but it promises to clarify teachers' perceptions of student and to lead to more accurate and useful evaluations of students' accomplishments and needs.

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Originally published in Adventures in Assessment, Volume 9 (December 1996),
SABES/World Education, Boston, MA, Copyright 1996.

Funding support for the publication of this document on the Web provided in part by the Ohio State Literacy Resource Center as part of the LINCS Assessment Special Collection.