Forward To Basics

Forward To Basics

Ross Taylor

Consultant in Mathematics K - 12807 Northeast Broadway

Minneapolis Public SchoolsMinneapolis, Minnesota 55413

BASIC SKILLS IN TODAY’S EDUCATION ENVIRONMENT

The School, Science and Mathematics Association is to be commendedfor publishing this special issue of "School Science and Mathematics"devoted to basic skills. At this time when there is great public demand formore emphasis on basic skills, professional educators need to address thecritical issues associated with basic skills instruction. We have to resistpressures to go back to basics of yesteryear. We have a professional re-sponsibility to direct attention forward to the basic skills our studentswill need as adults. Each of us in mathematics and science educationshould be addressing the question of what can be done to improve theteaching and learning of basic skills in mathematics and science. In parti-cular, each reader of this issue should be asking, "What does this articlecontain that will help me improve instruction in basic skills in mathe-matics and science?" A prominent finding from the National ScienceFoundation (NSF) sponsored Studies in Science Education report is thatthe teacher is key to the type of mathematics and science education a stu-dent receives in a given year. (CIRCE and CCC, 1978, p. 19:2). Becauseof the time needed to develop curriculum that reflects current needs, thegreatest immediate benefit to students will come if the teachers are ableto take ideas such as those appearing in this issue of "School Science andMathematics" and apply them directly in their classrooms.The current demand by the public for accountability by the schools for

the learning of basic skills comes at a time when the financial resourcesavailable to the schools are severely restricted. Today, schools are hardhit by inflation. Furthermore, many school systems with stable or de-clining enrollments are faced with higher salary costs each year as theirmaturing faculties move up on the salary scale. The passage of Proposi-tion i3 in California in June of 1978 was symbolic of the public resis-tance to higher taxation that is being felt throughout the country. In ef-fect, the schools are being asked to do better with less. They are beingasked to establish priorities and then be held accountable for studentachievement with respect to these priorities.The public pressure has potential for promise or for peril. There is

promise in the focus on learning. However, a narrow concentration onlow level skills or an attempt to apply simplistic solutions to complexproblems could prove to be oerilous.

547

548 School Science and Mathematics

The last time that mathematics and science education were faced witha strong influential external force was in the aftermath of the launchingof Sputnik in 1957. At that time, the public demanded better educationto produce more scientists, mathematicians and engineers to insure a fav-orable position in technological competition with the Russians. Theprincipal response to this national concern came through the funding bythe National Science Foundation of curriculum development projectsand staff development programs. The curriculum development programswere national in scope and they were aimed at bringing the influence ofcontemporary science and mathematics into the school curriculum. Thestaff development programs were conducted by the colleges and universi-ties with the primary purpose of improving the competence of teachers inthe disciplines of science and mathematics.Today the back-to-the-basics force is being felt most strongly at the

state and local levels where many legislatures and school boards are es-tablishing minimum competency requirements in basic skills. In most

cases these requirements include reading and mathematics, while rarely,if ever, do they include science. (Pipho, 1978, pp. 587-8) There is strongopposition to the imposition of federal requirements. In some cases, re-

quirements are being set at the state level and in others at the local level.Considerable reinventing of the wheel appears to be occurring as thestates and local school systems establish their own objectives, tests andinstructional programs.

There are some striking contrasts between the influences that resultedfrom Sputnik and the basic skills influences that are being felt today. Forexample, the post-Sputnik emphasis was on science and mathematics,whereas today the focus is on communication skills and mathematicalskills. The previous emphasis was on working with the more talented stu-

dents, while today attention is directed to the least talented. The involve-ment of higher education was essential to the previous effort. NSF proj-ects were funded through higher education, but never directly throughthe schools. Today, many basic skills efforts are proceeding with little or

only peripheral involvement by higher education. NSF has not yet be-come significantly involved in basic skills. The Office of Education (OE)is virtually devoid of mathematics and science educators. Of the over

three billion dollars that OE spends annually for Title I programs for dis-

advantaged students, perhaps 20% is spent for mathematics instruction.

However, there are no stipulations that anyone with expertise in mathe-

matics education should have any influence concerning this expenditureof over a half a billion dollars annually. Clearly, professional mathe-matics and science educators need to exert more influence at the federallevel.

MINIMAL SKILLS, BASIC SKILLS AND EXPANDED SKILLS

If we maintain a clear distinction between the terms "basic skills" and

Forward to Basics 549

"minimum competence," we will avoid a great deal of confusion. Wecan establish a reasonable consensus (at least within the education pro-fession) of which basic skills in mathematics and science everyone oughtto have in order to function effectively in our technological society.However, an attempt to establish consensus on a minimum level ofcompetence for all would be fruitless, frustrating and futile. "Minimumcompetence" is useful only as a relative term with specific meaning in aspecific context. For example, it is possible (though not necessarily desir-able) to define a minimum level of competence necessary for graduationfrom a particular high school. The establishment of minimum compe-tence requirements for high school graduation or for grade level pro-motion presents a dilemma. If the objectives are as broad and the re-quirements as high as many would desire, then a politically unacceptablenumber of students would fail. However, narrowing the objectives andlowering the requirements could seriously restrict teacher expectationsand student aspirations.The term "basic skills" most frequently is used to mean the basic skills

needed by all in order to function effectively in society. In this context,the basic skills needed by all are clearly a subset of the expanded skillsneeded by practicing scientists or by persons in other fields. The curricu-lum should be designed to guarantee that by the time they leave highschool all students will have ample opportunity to learn the basic skillsthey will need as adults. In addition, students must have the opportunityto learn those expanded skills that they will need for various careers or asprerequisite skills for further learning in post-secondary education.Counselors as well as teachers of mathematics and science have a respon-sibility to inform students that by continuing to take courses where theywill learn expanded skills in mathematics and science, they will be keep-ing their options open. Special efforts are needed at this time to counter-act the avoidance of mathematics and science courses by young womenand by minorities. The stereotype that mathematics and science are thedomain of the "pale and male" must be overcome.

For the remainder of this article, we shall be concerned with the basicskills needed by all citizens in order to function effectively in adult so-ciety. The reader should have no difficulty maintaining the distinctionbetween "basic skills" for all, "minimal skills" for a specific purposeand "expanded skills" needed for various careers.

WHAT ARE THE BASIC MATHEMATICAL SKILLS?

Any discussion of basic skills inevitably brings up the question, "Whatare the basic skills?" Within the mathematics education profession, thereis almost universal agreement with the concept of basic skills as set forthin the National Council of Supervisors of Mathematics Position Paper


on Basic Mathematical Skills (which accompanies this article). In thespring of 1976, the National Council of Supervisors of Mathematics(NCSM) established a task force to prepare a position paper to respondto pressures to emphasize computation to the exclusion of other im-portant mathematical skills. The paper was developed with financial sup-port from the National Institute of Education (NIE). It lists ten vitalbasic mathematical skills areas:

Problem SolvingApplying Mathematics to Everyday SituationsAlertness to the Reasonableness of ResultsEstimation and ApproximationAppropriate Computational SkillsGeometryMeasurementReading, Interpreting, and Constructing Tables, Charts, and GraphsUsing Mathematics to PredictComputer Literacy

The NCSM position has been endorsed by the National Council ofTeachers of Mathematics (NCTM) Board of Directors and by the NCTMDelegate Assembly. It has been widely disseminated within the educationprofession.The NCSM list of basic skills corresponds closely with the basic skills

set forth in the report of the NIE sponsored conference on Basic Mathe-matical Skills and Learning held in Euclid, Ohio, in October, 1975.(NIE, Vol. II, 1975, pp. 17-20) The list also corresponds closely to thetitles of chapters in this issue of "School Science and Mathematics."This issue is timely because with the exception of a publication by theVirginia Council of Teachers of Mathematics (V.C.T.M., 1978) little hasbeen written giving specific ideas for teaching many of those basic skills.Due to factors such as the universal availability of hand-held calcu-

lators, the increasing use of computers and the forthcoming conversionto the metric system, there is a changing emphasis on which skills are im-portant. For example, the importance of computation is decreasing,while the importance of estimation and approximation is increasing. TheNCSM list stresses applications of mathematics in everyday life. All tenof the mathematics skill areas have important applications in science.This is appropriate because these are skills that students will need to livein a highly technological society. Furthermore, there is considerableoverlap between those mathematical skills and the important skills ofscience both with respect to content and to desirable teaching ap-proaches. Hence, an interrelated approach to the teaching of the basicskills of mathematics and science has great potential for improved learn-ing in both disciplines.The Case Studies in Science Education report found that science


education currently has a low priority in the schools, with overwhelmingattention being given to "The Basic Two�Reading and Arithmetic."(CIRCE and CCC, 1978, p. 19:2) The NCSM position has been found tobe useful by many supervisors in expanding the emphasis in mathematicsto the other nine skill areas in addition to computation. Mathematicseducators have found that when they establish a dialog with adminis-trators, school board members and the public they can gain agreementthat the emphasis in basic mathematical skills needs to go well beyond anarrow focus on computation. This dialog can be extended further tostress the importance of the basic skills of science. Mathematics andscience educators must strengthen their communication links with theeducational decision makers at all levels to insure that the concept ofbasic skills is sufficiently broad. Then students will receive instruction inthe full range of skills they need today and that they can be expected toneed as adults.

EVALUATION OF ACHIEVEMENT IN BASIC SKILLS

With the current public pressures for accountability by the schools forstudent achievement in basic skills, evaluation is playing an increasinglyimportant role. These pressures can result in a tendency to emphasizeskills such as computation which are easily measured by machine-scoredmultiple-choice paper and pencil tests. In the process, other importantbasic skills can be neglected. Furthermore, the standardized norm-ref-erenced tests which are widely used today for assessing and reporting stu-dent achievement are not completely appropriate for evaluating achieve-ment of basic skills. The norm-referenced testing model was developed inthe first half of this century when a principal function of testing was tosort students. (Tyier, 1978) Tests were used to determine which studentswere most deserving of the limited number of spaces for higher oppor-tunities in education. Today, the emphasis is on educating all studentsrather than on sorting out and pushing out the least promising. In basicskills testing the principal information sought is knowledge of whichskills have been mastered and which have not. On the basis of this in-formation, students can be provided with instruction suitable to theirneeds. Basic skills programs are usually designed with the expectationthat ultimately most of the students will achieve most of the skills. How-ever, for norm-referenced tests to perform the sorting function, theymust contain a large number of items which half or more of the studentswill miss.

Another problem with current standardized tests is that they must bekept secret. However, in basic skills instruction, the students, theteachers, the parents and the public should have a clear idea of what thestudents are expected to learn. Moreover, there should be opportunities


for decisions about which skills are to be learned to be made at the localor state levels. If standardized tests are used, then there is a very limitednumber of tests from which to select.

Clearly, there is a need for assessment techniques and reporting proce-dures that are appropriate for contemporary basic skills programs. Theneeded research and development are not likely to be financed by the testpublishers. The local systems and the states have limited resources.Therefore, we must look to national agencies such as NSF, NIE and OEfor support of the needed development. There is a reluctance to involvethe federal government in testing because of the fear of federal control.However, testing models can be developed that will encourage greater lo-cal control. For example, school systems that use the "piggyback" con-cept in relation to the National Assessment of Educational Progress pro-gram can select only the objectives they wish to test for their local pro-grams.

CURRICULUM DEVELOPMENT

Today, the public is demanding that the schools produce high schoolgraduates who are competent in basic skills. However, the federallyfunded efforts in curriculum development have not as yet zeroed in onthe basic skills needs at the high school level. For example, during thetime that the National Science Foundation was in the curriculum de-velopment business, it didn’t fund any curriculum projects for basicmathematical skills instruction at the senior high level. There are nosecondary mathematics or science basic skills programs listed in the 1977edition of "Educational Programs That Work," a publication whichlists validated exemplary federal programs. Curriculum development inbasic mathematics and science skills for high school has been donelargely through the commercial publishers and through fragmented localefforts. At this time, comprehensive and coordinated research and de-velopment efforts are needed if we are to provide suitable basic skillscurricula for poorly motivated high school students with a range of prob-lems which affect their learning. For now, a major resource is the in-dividual effort of the creative teacher. Such a teacher should find thisissue of "School Science and Mathematics" to be a valuable source ofideas.

STAFF DEVELOPMENT

A key factor in the improvement of basic skills instruction is the train-ing of teachers. Today, relatively few new teachers are coming into theprofession so preservice training will not have a large impact on instruc-tion in the immediate future. Therefore, at least for the near term, weshall have to look to inservice training. The needs of teachers are quitedifferent at the elementary and secondary levels.


Many elementary teachers need to upgrade their knowledge of mathe-matics and science. Anxieties concerning mathematics and science can re-sult in their avoidance by elementary teachers. Many elementary teachersnever seem to have enough time to teach science. With the current em-phasis on basic skills, they usually have time for computation, but manynever get to the other mathematical skills. Elementary teachers need tohave inservice opportunities in mathematics and science that are designedto increase teacher knowledge of the disciplines and how children learnthem. Inservice must also give teachers practical ideas that are directlyuseful in their classrooms.At the secondary level, most mathematics and science teachers have

the subject matter competence necessary for the courses they areteaching. The NSF funded programs over the past 20 years appear tohave been effective in upgrading subject matter competence of secondaryteachers. However, these programs have been focused on providingsecondary teachers with competence to provide instruction for pre-college students. Today, secondary teachers need inservice programs thatconcentrate on the skills needed to teach basic skills of mathematics andscience to students who do not plan to go to college. Teachers need tolearn how to work with poorly motivated, low-achieving students, manyof whom vent their frustrations by being disruptive. The current practiceof mainstreaming special education students increases the need for learn-ing how to teach students with special learning difficulties. The public isdemanding competence in basic skills for all high school graduates. Evenif a goal of a single high standard for all is not realistic, the schools haveto address the basic skills needs of all students. Rather than giving up onhigh school students who are not functioning at an abstract level inmathematics and science, we are going to have to learn to teach them atthe cognitive level at which they are functioning. Secondary teachers willneed to learn new techniques adapted from elementary education. Forexample, the use of manipulatives to teach mathematics is totally un-familiar to most secondary teachers.

CONCLUSION

Today, the schools are in a bind between rising expectations forachievement in basic skills and limited financial resources. The educationprofession has a responsibility to help the schools move forward to thebasic skills that students will need in the future rather than back to thebasics of the past. We in the mathematics and science education pro-fession need to exert our influence with the decision makers at the local,state and national levels, in the school systems, in higher education, andin the publishing industry to bring about improved instruction in basicskills. To provide this instruction, teachers need reasonable class size, as


well as appropriate learning materials, evaluation techniques and inserv-ice training. The ideas in this issue should be helpful to teachers, teachertrainers, curriculum developers and publishers of tests and learning ma-terials. Professional activities, such as the publication of this issue, canserve as a basis from which we can all move forward to the basics.

REFERENCES

Center for Instructional Research and Curriculum Evaluation and Committee on Cultureand Cognition. Case Studies in Science Education. Urbana-Champaign: CIRCE andCCC, January, 1978.

National Advisory Committee on Mathematical Education. Overview and Analysis ofSchool Mathematics, Grades K-12. Washington, D. C.: Conference Board of the Mathe-matical Sciences, 1975.

National Council of Supervisors of Mathematics. Position Paper on Basic MathematicalSkills. NCSM, 1977.

National Institute of Education. Conference on Basic Mathematical Skills and Learning,Euclid, Ohio; Volume II: Working Group Reports. Washington: NIE, October, 1975.

National Institute of Education and National Science Foundation. Report of the Con-ference on Needed Research and Development on Hand-Held Calculators in SchoolMathematics. Washington: NIE and NSF, 1976.

PIPHO, CHRIS. Minimum Competency Testing in 1978: A Look at State Standards. PhiDelta Kappan, Vol. 59, No. 9, May, 1978, pp. 585-588.

TAYLOR, Ross. The Question of Minimum Competency as Viewed from the Schools. TheMathematics Teacher. Vol. 71, No. 2, February, 1978, pp. 88-93.

United States Office of Education. Educational Programs That Work; Volume IV. Wash-ington: USOE, Winter, 1977.

Virginia Council of Teachers of Mathematics. Practical Ways to Teach the Basic Mathe-matical Skills. V.C.T.M., 2332Scarsborough Dr., Richmond, VA 23235; 1978.

SUMMARY OF THE NATIONAL COUNCIL OF SUPERVISORS OF MATHEMATICSPOSITION PAPER ON BASIC MATHEMATICAL SKILLS

Problem Solving: Students should be able to solve problems in situations which arc new to

them.Applying Mathematics to Everyday Situations: Students should be able to use mathematics

to deal with situations they face daily in an everchanging world.Alertness to Reasonableness of Results: Students should learn to check to see that their

answers to problems are "in the ball park."Estimation and Approximation: Students should learn to estimate quantity, length, dis-

tance, weight, etc.

Appropriate Computational Skills: Students should be able to use the four basic operationswith whole numbers and decimals and they should be able to do computations withsimple fractions and percents.

Geometry: Students should know basic properties of simple geometric figures.Measurement: Students should be able to measure in both the metric and customary

systems.Tables, Charts and Graphs: Students should be able to read and make simple tables, charts

and graphs.Using Mathematics to Predict: Students should know how mathematics is used to find the

likelihood of future events.

Computer Literacy: Students should know about the many uses of computers in society andthey should be aware of what computers can do and what they cannot do.

TO OBTAIN THE NCSM POSITION PAPER . . . send a stamped, self-addressed busi-ness envelope to Ross Taylor, NCSM Basic Skills, Minneapolis Public Schools, 807 Broad-way, N. E., Minneapolis, Minnesota 55413.

Documents

Forward To Basics