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One Point of view: Mathematics in Urban SchoolsAuthor(s): Paul R. Trafton and Virginia R. MorganSource: The Arithmetic Teacher, Vol. 26, No. 4 (December 1978), pp. 3-4Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41191547 .

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ONE POINT OF VIEW

Mathematics in Urban Schools By Paul R. Trafton, Chairman, Editorial Panel of the Arithmetic Teacher and Virginia R. Morgan, Director of Title I, Dougherty County School

System, Albany, Georgia

The limited achievement of many students in the schools of our nation's cities is a major concern today. The National Council of Teachers of Mathematics has made urban education a major priority and has estab- lished a Task Force on Mathematics in Urban Schools to focus on mathematics programs in these schools and to provide impetus to efforts to improve mathematics instruction and learning.

The problems of urban education transcend the learning of subject mat- ter content; yet, many of these problems are directly influenced by instruction and the resulting amount of student learning in the classrooms. Al- though overall problems such as student attendance and discipline, parent concerns, and staff unrest must be ad- dressed and resolved, it is imperative that we closely examine constructive ways of improving the quality of edu- cational programs in the basic skill areas. In fact, more effective instructional programs can be a factor in re- solving the broader questions.

December 1978

Components of effective instruction and learning in mathematics are appli- cable to all students, including those from poverty backgrounds. Although it is not the intent of this editorial to reiterate these components, three points of particular relevance to urban schools are discussed.

1 . Mathematics needs to be taught. The strong, necessary emphasis on reading in urban schools in many cases has resulted in little or no time being devoted to mathematics, particularly in the primary grades. Basic mathematical concepts and skills must be carefully developed over a period of time if students are to master them and estab- lish a base for future learning. Cer- tainly, it is possible for both reading and mathematics to receive the time and attention they require in each school day.

2. Curriculum content needs to be carefully selected. There are many important aspects to a well-rounded curriculum for all students. Nonetheless, in order for essential aspects of number

ideas, operations on numbers, compu- tational skills, and real-world appli- cations of number ideas to be learned well, they need careful attention and extended instructional time. This means that painful decisions need to be made regarding curriculum content and the temporary deferral of many desirable and important mathematical topics. A good basic program for all students is quite comprehensive. Em- bedded in that basic program are those skills that are critical for managing one's personal affairs and being em- ployable in the marketplace. The time spent on inappropriate, peripheral, and recreational content in thé school program is distressing. Despite the many values of the study of the associative property of addition, prime numbers, tessellations, and tangrams at the appropriate time, these topics are hardly of the same order of magnitude as the ability to write a multiplication sen- tence for a model, the knowledge of basic facts, the ability to apply the cor- rect operation to a real-world situation, and the knowledge of fundamental

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measurement concepts. The continuing emphasis on multiplication with 3-digit factors, dividing by 3-digit divisors, and adding long columns of multidigit addends are similarly hard to defend.

3 . Instructional time and materials must be used purposefully. Recent evidence suggests that only a small por- tion of the time allotted to instruction is time on task; that is, time spent on learning. For instruction to be effective students need to be engaged in the task at hand. This is particularly important for students who may miss the critical element of a learning task unless their attention is directed explicitly to that task. Other critical components involve careful analysis of what is to be learned and how this learning is most effec- tively acquired. Curriculum materials have an important role to play. They need to be learning materials; they must not be limited to drill-and-practice. Carefully sequenced materials serve as valuable aids to teachers by helping them focus on effective imple- mentation and student-learning. Paral- lel, back-up materials are necessary to provide the additional experience and practice needed. Unfortunately, many commercially-prepared and locally-developed materials lack the careful focus and extended development needed to ensure student mastery.

Special Programs A major force in education, and in urban schools in particular, is the funding of programs for underachieving, dis- advantaged students. Many of these programs are federally funded. This funding can be a vehicle for sub- stantially changing the achievement of students for whom the learning of mathematics has been unsuccessful. Despite the existence of several exem- plary programs, these efforts have too often fallen far short of their potential. Often large sums of money have been spent with little evidence of changes in overall achievement patterns. Pro- grams sometimes have become entan- gled in political and administrative machinations. It is incumbent upon the education profession to be good stew- ards of outside funds; to do all possible to insure that the wealth of federal support truly benefits students in learning in the classroom. Several consid-

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erations for successful programs for the low achiever are presented.

1 . The central administration of school districts must have serious commitment to the programs and provide strong support for them to make a real difference in student achievement.

2. Students must be viewed as ca- pable of learning if appropriate conditions for individual achievement are provided. Many of these students are untaught rather than unlearned.

3. Careful assessment and mon- itoring of students' academic weak- nesses and achievements are essential in an instructional program that fo- cuses on each individual's needs.

4. Program design must include a management system and materials designed to allow teachers to teach effec- tively. Many well-meaning, individ- ualized programs have buried teachers in paperwork with the result that students learned less well than in the regular class setting.

5. Materials must be designed for student-learning. We know that the regular instructional system has been ineffective with these students. Cer- tainly, more of the same is not likely to solve their problems.

6. Intensive, ongoing teacher train- ing is vital in developing programs for both teacher-professional growth and program maintenance and support.

7. Programs need to be accountable in terms of student achievement of well-defined, critical, content objec- tives. Too often we reason as follows: (1) Approach X is hypothesized to be effective; (2) Program Y is an attempt to implement X; (3) therefore, Y is an acceptable program.

8. Program evaluation is best as- sessed in tçrms of the percent of students who have mastered content as measured by thoughtful criterion-refer- enced instruments. The survey nature of most normative tests causes them to be too broad in design to measure ac- curately the critical skills which must be a major focus of such programs. Certainly we must develop high stan- dards for program evaluation of which the cornerstone needs to be pupil-mastery of content studied.

9. The cost-effectiveness of programs needs to be carefully examined.

Programs are sometimes termed successful in terms of criterion gain; but when they are closely examined, the number of students treated per teacher is so low as to have no significant im- pact on the total number of students needing help within a district. Another dimension of cost-effeciveness is the assessment of program cost per in- crement of student gain as measured against cost of such gain in a regular classroom.

Summary Times of great challenge and great problems can be viewed as new oppor- tunities to do the job well and achieve great success. All need to be involved. Teachers need to rededicate themselves to overcoming obstacles and using their resourcefulness to be successful; administrators need to commit themselves to a significant investment of budgeted time and resources in order to insure that programs will work; and, mathematics education specialists need to be willing to come to grips pragmati- cally with the real problems existing in schools. It is intellectually satisfying to speculate upon the ideal programs of the future, to engage in strenuous de- bate regarding the relative merits of various "good" approaches to mathematics instruction, or to ponder the is- sues of the day. Yet, our future influ- ence on schooling may, in large part, be determined by how well we address the pressing needs of city schools and the students that they serve. We need to help implement in a pragmatic way the sound knowledge about instruction and learning that we possess. We need to be willing to test our ideas against the criteria of student-mastery rather than how well they conform to philo- sophical positions. We need to direct research-and-development efforts to the creation and validation of curriculum materials that have well-defined content outcomes. Certainly with the talent available, the knowledge we possess about instruction and learning of specific content, and the commitment to make mathematics learning a successful experience for all, the problem can be solved. It is heartening to note that while many students have not learned, few cannot learn and almost none will not learn when sound programs are provided. D

Arithmetic Teacher

