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Mathematics Goals: What Does the Public Want?1Martin Hershkowitz2Operations Research, Inc.Silver Spring, Maryland
Mohammad A. A. Shami3Maryland State Department of Education
Baltimore, Maryland
Thomas E. Rowan4Montgomery County Public Schools
Rockville, Maryland 20850
For a number of years mathematics educators and those in otherdisciplines have been wrestling with the question of objectives. Oneof the foggiest areas in the discussions surrounding this issue is thebasis upon which the objectives are identified. Mathematicians wouldselect their objectives based upon the content and structure ofmathematics�when they are willing to select them at all. Educatorswould place considerably more emphasis upon learning theory�theway children learn. Politicians would accept either view so long assuccess could be "accounted" for and a dollar figure could be attachedto it. Although it might not be a popular idea with mathematiciansor educators, one way of establishing a framework within whichobjectives could be designed is by determining what is importantto most people in the general public. This should be a central concernof the schools since the schools exist because of and for that group.Goals which are important to the general public could be used togive direction to the more specific level of goal development whichwould be carried out by mathematics educators.During the 1971-72 school year the Maryland State Department
of Education conducted a needs assessment study (Maryland StateDepartment of Education, 1972; Hershkowitz, 1972).5’6 The studyconcerned itself with a wide range of goal types, but two of the
1. This article is based on a paper by Shami and Hershkowitz (1973) discussing selected findings from theMaryland Goals Validation and Needs Assessment Study.Shami, M. A. A., and Hershkowitz, M. Relative Importance of "Knowledge of Mathematical Concepts"and "Mastery of Computational Skills" as Goals of Public Education. Silver Spring, MD: Operations Research,Inc., 1973.2. Senior Scientist of the Resource Analysis Division; was Project Director of the Maryland Goals Validation
and Needs Assessment Study.3. Consultant in Research (Curriculum), Division of Research, Evaluation and Information Systems; was Project
Monitor of the Maryland Goals Validation and Needs Assessment Study.4. Mathematics Supervisor, Division of Curriculum and Instruction.5. Maryland State Department of Education. Goals and Needs of Maryland Public Education. Baltimore, MD:
1972. (Prepared by M. A. A. Shami and M. Hershkowitz.)6. Hershkowitz, M. A Study to Validate Goals for Public Education and to Assess Educational Needs in the
State of Maryland. Vitro Laboratories Technical Report 01722.01-1. Silver Spring, Md: 1972.
723
724 School Science and Mathematics
goals were directly concerned with mathematics and others wereindirectly concerned with mathematics. The purpose of the studywas to identify valid goals which were related to needs as determinedby a wide variety of respondent groups. The study focused on goalswhich were specific enough to communicate their intention to mostpersons, but not so specific as to be termed behavioral objectives.Table 1 displays the 37 goal statements which were developed forthe study. The eighth and twenty-second goal statements are the tworelated directly to mathematics:
� Knowledge of mathematical concepts� Mastery of computational skills.
In order to provide the desired validation of the 37 goals the studysought the opinions of a large number of people from the generalpublic and various private and educational groups. Table 2 displaysthe respondent groups and the sample size selected for each. Randomselection procedures were used to identify respondents in each group.Each respondent was asked to indicate his or her opinion about theimportance of each of the 37 goals on a five-point scale from "veryimportant" (scale value 5) to "not at all important" (scale value 1).A mean importance score was then computed for each goal. Goalswere ranked by their mean importance scores and then grouped intofive cardinal ranks from "Most Important" to "Least Important."Table 1 presents the mean importance scores assigned to the 37 goalstatements by each of the ten respondent groups. Table 2 revealshow the ten respondent groups ranked the two mathematics goals.Note that the concepts goal was ranked between 16th and 27th byall respondent groups while the skills goal fell even lower, between27th and 35th. These rankings caused "Mastery of computationalskills" to fall in the cardinal rank "Least Important" and "Knowledgeof mathematical concepts" to fall in the cardinal rank "Less Impor-tant." Both of the mathematics goals had overall mean importancescores greater than 3.0, which indicates general acceptance that theyare valid goals, but their rankings relative to other goals were quitelow.These data could lead to the interpretation that the respondents
generally considered the mathematics goals to be of rather lowimportance. If such an interpretation were taken as the final conclusion,this would certainly not be in the best interest of mathematics education.However, these results can be considered together with the resultsconcerning the fourteenth goal statement in the list with a very differentinterpretation. The fourteenth goal states, "Ability to apply knowledgeand skills to the solution of real life problems." Table 1 reveals thatthis goal was ranked very high by all respondent groups. Its mean
Mathematics Goals 725
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Mathematics Goals 727
TABLE 2: SAMPLE SIZE, MEAN IMPORTANCE AND RANK BY DIFFERENT RESPONDENT GROUPS,AS RELATED TO THE EDUCATIONAL GOALS "KNOWLEDGE OF MATHEMATICAL CONCEPTS" AND
"MASTERY OF COMPUTATIONAL SKILLS"
Knowledge ofMathematical Concepts
Mastery ofComputational Skills
Respondent Groups
StudentsSchool StaffCentral Staff of
School SystemParentsBoards of EducationBusiness /IndustryGeneral PublicElected & Appointed
OfficialsMSDE StaffPostsecondary Educators
Sample ISize 1
8,4322,316
5124,557
1571,2045,933
379129371
<lean Impor;ance Score ^
4.14.1
3.94.34.23.84.0
4.03.84.0
I} Rank 1
2022.5
2717.516.521.524.5
19.52721
Viean Impor:ance Score’
3.63.9
3.93.73.83.43.6
3.43.73.7
8 Rank
32.532
2734.53128.535
343129.5
8 The minimum mean importance score of 2.6 was awarded by the Business/Industryrespondent group to the goal "Knowledge of fine arts concepts"; the maximum meanimportance score of 4.8 was awarded by nearly all the respondent groups to the goal"Mastery of reading skills."
importance score ranged from 4.4 to 4.8, placing it in the cardinalrank "Most Important" for all respondent groups.When the data on the mathematics goals are considered with the
data on application of skills in real life they can be interpreted tomean that, in the views of the respondents, imparting mathematicsconcepts and skills in and of themselves is of relatively low importance;but if those concepts and skills are presented so that they can beapplied to the solution of real life problems, then they become ofhighest importance. To put it in another way, people want to seemore relevance built into the curriculum. It is only logical thatmathematics in a public school organization should serve the needsof the individual, the needs of the community and the needs of thesociety at large.What is the implication of this interpretation of the study data?
One possibility would be to take a close look at the present curriculumto determine the extent to which it meets these needs and to makerevisions to the curriculum which would bring it closer to meetingthem. Such analyses and recommendations could probably best beaccomplished by interdisciplinary teams working closely with students,parents and other members of the community. Perhaps the present
728 School Science and Mathematics
interest in career education could be expanded and given clearerdirection toward accomplishing such an aim. Even if approachesthrough interdisciplinary teams or an expanded view of career educa-tion are not considered to be the most reasonable the results of theMaryland survey indicate a need for mathematics curriculum develop-ers to pay close attention to the question of relevance. Mathematicsfor mathematics’ sake is not, relatively speaking, important to thepublic.A great deal more emphasis can be placed upon mathematical
applications than is presently the case. This can be done with noreduction in the quality of the mathematics programs. It would likelyrequire in-service training of mathematics teachers and perhaps somecross-discipline teaming within schools. Certainly the problems shouldbe studied by curriculum developers, as well as those in teachereducation institutions, where the implications of such a change wouldbe quite extensive.
REFERENCES
HERSHKOWITZ, M. A Study to Validate Goals for Public Education and to AssessEducational Needs in the State of Maryland. Vitro Laboratories Technical Report01722.01-1. Silver Spring, MD: 1972.
Maryland State Department of Education. Goals and Needs of Maryland PublicEducation. Baltimore, MD: 1972. (Prepared by M. A. A. Shami and M. Hershkowitz.)
SHAMI, M. A. A., and HERSHKOWITZ, M. Relative Importance of "Knowledge ofMathematical Concepts" and "Mastery of Computational Skills" as Goals of PublicEducation. Silver Spring, MD: Operations Research, Inc., 1973.
MARINE GEOPHYSICAL DATA CATALOG�1975
NOAA Environmental Data Service’s National Geophysical and Solar-Ter-restrial Data Center has just released Marine Geophysical Data Catalog�1975,Key to Geophysical Records Documentation No. 4, which includes all bathy-metric, magnetic, gravimetric, seismic profile, and navigation informationavailable from the Center. It also indicates types of data formats, identifiesspecific cruises or surveys, depicts geographical distribution of the data byarea index charts, and includes a trackline sketch for each cruise or survey.The 1975 catalog updates (and supersedes) Key to Geophysical Records
Documentation No. 1 (published in June 1972), and includes 58 marinegeophysical data sets that have become available since 1972. It also givesavailability of other complementary data, including map plots, charts, etc.A pocket insert map, "Multitrackline Plots," includes bathymetric, magnetic,gravimetric, and seismic reflection data collected worldwide along 2-1/4 millionnautical miles of tracklines.The catalog may be purchased from: Superintendent of Documents, U.S.
Government Printing Office, Washington, D.C. 20402 for $5.25 (Stock No.003-017-00292).
