Elementary Teachers and Research in MathematicsEducation1

Robert E. KeysUniversity of Missouri�Columbia, Columbia, Missouri

and

Theresa YeagerWest Junior High School, Columbia, Missouri

Although much research is published each year, classroom practicesreflect few current research findings. One of the reasons for thisis the "communication gap" that seems to exist between researchersand classroom teachers. This article focuses on several issues thathave contributed to this existing "gap" and that must be alleviatedif research in mathematics education is going to make a differencein classroom practices.Do elementary teachers read research? Do they look to research

for answers to classroom problems? Are undergraduate preparatoryprograms geared to prepare elementary classroom teachers to beconsumers of research? What are some ways of disseminating researchfindings directly to elementary teachers? In an effort to answer theseand other related questions, the authors personally interviewed 40elementary teachers. These subjects were randomly selected from75 elementary teachers in one school district located in a mid-westerncommunity of approximately 20,000. At least three teachers fromeach grade level (K-6) were included in the sample.When these inservice elementary teachers were asked how often

they read research flavored articles, 87.5 per cent of them responded"Seldom or Never." On the other hand, 97.5 per cent said theyread general education journals "Always or Frequently." This suggeststhat these teachers were reading professional journals, but not devotingmuch of their effort toward material that was research oriented.Why do teachers not read research oriented articles? There are

at least two good reasons. First, most published research lacksrelevance for classroom teachers. Since they are primarily concernedwith the current day to day problems encountered in teaching, itis little wonder that most of their professional reading is limited tothe "Hints to Heloise" kind of articles. In fact, when these teacherswere asked to rank eight possible reasons for preferring one type

1. This article is based on a presentation "The Involvement of Preservice and Inservice Teachers in Mathematics

Education Research" at an Annual American Educational Research Association meeting. It is presented in hopesof promoting discussion which will ultimately lead to an improvement of existing means of implementing researchfindings into the classroom.

431

432School Science and Mathematics

of journal to another, nearly 90 per cent of them ranked "generalinterest" articles and "suggestions for classroom practices" as theirfirst, second, or third choice. This suggests they are looking for ideasand information that have immediate payoff in the classroom. Thisis not to be condemned, but it does not inculcate an interest forreading research articles in their traditional format.The stimulus to read research articles is further hindered by the

way in which most of it is reported. Published research often seemsfar removed from the elementary classroom. Whereas teachers arelooking for clear cut and widely applicable findings, most researchis characterized by carefully stated limitations and detailed descriptionsof oftentimes atypical conditions; also, it may be couched in termswhich generally requires the reader to interpret and derive classroomimplications. This is not necessarily bad, but few elementary teachersare either willing or able to read this kind of report.The subjects were asked to rank the following six reasons as to

"why teachers shy away from reading research articles?"

1. Availability of articles2. Statistical jargon3. Stereotype format4. Excess of charts, graphs and tables5. Lack of direct classroom applications6. Lack of time

Eighty per cent of them identified "Lack of time" or "Lack of directclassroom implications" as their first or second reason. Teacherswere then asked to rank the four criticisms identified in Table 1with respect to the readability of research articles. Table 1 showsthe criticism with the highest overall ranking was that’ ’research articlestake too long to express ideas." If you combine this criticism withteachers’ lack of time, as was suggested earlier, it becomes moreclear why few teachers read research articles.

TABLE 1: HOW TEACHERS RANKED CRITICISMS RELATED TO READABILITY OF RESEARCHARTICLES

(N = 40, PERCENTS REPORTED)

Statement

Took too long to express ideas

Words too Technical

Too many references to charts, graphs, andtables

Sentences too long

Rank1234

30

30

35

5

40

25

25

10

25

32

12

30

5

13

28

55

Elementary Teachers and Research 433

A second reason is the lack of exposure to research in most preservicepreparatory programs for elementary teachers. For one thing, theelementary undergraduate program of studies is already crowded.Content courses taught in the mathematics department rarely reflectresearch findings. The focus in most methodology classes in mathe-matics education is on curriculum, learning theories, and instructionalstrategies. Each of these areas contribute toward the preparation ofan effective teacher, yet they do not allow time for much else. Thusit comes as no surprise that little if any time is devoted to actualdiscussion or involvement in research in most undergraduate programs.The teachers were asked to assess the extent to which their under-

graduate program prepared them for two aspects of research. Thefirst question concerned provisions for learning of findings and thesecond was related to classroom implications of research findings.The teachers were then asked to what extent their undergraduateprogram should have provided for these two items. As shown by theresults in Table 2, 70 per cent of the teachers felt that their under-graduate program provided for "little" or "no" learning of researchfindings; and over two thirds of the teachers indicated that theirundergraduate program should have provided this learning to "much"or "great" extent. (The shaded portions of Table 2 calls attentionto the marked trends.) Also, 75 per cent of the teachers felt that

TABLE 2: PROVISIONS (IN YOUR UNDERGRADUATE PROGRAM) FOR LEARNING ANDIMPLEMENTING RESEARCH FINDINGS(N == 40, PERCENTS REPORTED)

Undergraduate

Evaluation

Great

Much

Little

No

Research Findings

Extent youwere provided

7.5

22.5

SIISagi

Extent youshould havebeen provided

25

7.5

Classroom Implications

Extent youwere provided

10

15

111iii

Extent youshould havebeen provided

22.5

10

their undergraduate program provided for "little" or "no" informationon how research findings could be implemented by the elementaryschool teachers; and over two thirds of the teachers indicated thattheir undergraduate program should have provided this informationto "much" or "great" extent. Most of these teachers felt that moreemphasis should be given to practical aspects of research in theundergraduate program. Such findings are not surprising, yet theydo provide food for thought for those involved in teacher education.

434School Science and Mathematics

For one thing, an assessment of the research emphasis in currentprograms might be quite enlightening, and lead to needed changes.

In order to more effectively disseminate research findings a listof the following alternatives were presented to the elementary teachersinterviewed:

1. Textbook companies supplementing their books with a list of suggestions whichhave been tried in various research projects (i.e. multi-base blocks for teachingdifferent bases), for the various topics in the book. These suggestions wouldbe accompanied with full descriptions on how to carry the project out.

2. Small pamphlet subscriptions (10-15 pages) available to the school library containingnew ideas and suggestions resulting from research. These pamphlets could beplaced in the teachers’ lounge where teachers could easily read one during afree period.

3. Separate subject area journals (mathematics, science) designed primarily to report,in brief, research results without statistical jargon.

4. Teachers participating in periodic in-service courses, or workshops could counttoward graduate credit and deal primarily with reports, demonstrations, andactivities which would relate research findings that have been found effective.

5. Research assistant available to inform teachers of research findings when teachersneed suggestions for new methods, games, teaching aids, media, etc.

6. Classroom teacher with specialized training in research in a particular disciplineresponsible for keeping up with current research in that discipline and disseminatingit to their colleagues.

7. Team teaching approach with different subject area teachers responsible fordisseminating current information in their respective field to colleagues.

The teachers were asked to rank these alternatives in order ofpreference, as to which would help them become better consumersand users of research. Although some trends are discernable thereis a clear lack of consensus. Table 3 reports that three suggestionswere ranked 1, 2 or 3 by over 50 per cent of the teachers. The

TABLE 3: RANKING OF SEVEN SUGGESTIONS FOR HELPING ELEMENTARY TEACHERSBECOME BETTER CONSUMERS AND USERS OF RESEARCH

(N == 40, PERCENTS REPORTED)

StatementNumber

1

2

3

4

5

6

7

Rank1234567

27.5

20

25

12.5

2.5

5

7.5

15

27.5

15

20

12.5

5

5

32.5

7.5

10

15

20

10

5

15

5

12.5

10

32.5

10

17.5

2.5

15

10

20

22.5

15

15

7.5

10

7.5

15

7.5

37.5

15

15

20

7.5

2.5

17.5

35

Elementary Teachers and Research 435

most popular suggestion was for textbook publishers to plug appropriateresearch implications into their materials.2 This was followed byrequests for small pamphlets and bulletins similar to the Interpretivereports. Ironically, none of the teachers reviewed has even heardof the Interpretive Study Bulletin3 This lack of knowledge of theavailability of such information underscores the need for widerdissemination. The third most popular suggestion was the need formore informal reporting of research.These suggestions for disseminating research, in particular the one

that publishers include research findings and implications in theirtextbooks, provides the basis for much speculation. One ever presentdanger of this alternative is that teachers could receive biased reportsof research. Few publishers could afford to provide comprehensivereviews of related research and even fewer would dare to reportanything but favorable results when their materials and methods areinvolved. Furthermore, the lead time required for producing textbookseries would all but prevent publishing "current" research.One other problem inherent in disseminating research findings is

vividly illustrated by the lack of knowledge these elementary teachershave of the Interpretive Study Bulletins. The problem is in actuallyreaching elementary teachers, that is, establishing direct com-munication with classroom teachers. Research information is oftensent to superintendents, principals, and curriculum directors and forone reason or another it rarely gets to the classroom teacher. A realeffort must be made to inform teachers of the fact that various journalsare available within schools and that they have potential value tothe classroom teacher. It is acknowledged that no amount of salesman-ship or extermal pressure will get a teacher to read research relatedto elementary school mathematics. The desire to learn about currentresearch will be directly related to the extent that the teacher perceivesthis research to be of value to him.This latter statement suggests once again that we as researchers

are at least partially responsible for the current situation. Maybe wehave the same problems some teachers share, namely that we expectour "pupils to learn as we teach." Thus we fail to show teachersthe relevance of research or in discussing it in everyday practicalterms. Remember that research gives credence to theory and theoryties the "loose ends" of practice together. Could it be that our

2. The authors personally feel that alternative #6, namely having selected elementary teachers keep informedon current research in a particular field, such as mathematics education, has great potential. In fact, many schoolsare recruiting elementary teachers with such expertise and interest in hopes of developing a better balanced faculty.Much to our dismay, this feeling was not shared by the elementary teachers interviewed.

3. These informative bulletins are a product of the’ ’Interpretive Study of Research and Development in ElementarySchool Mathematics" sponsored by the Research Utilization Branch, Bureau of Research, United States Officeof Education.

436 School Science and Mathematics

’ "practice" minded teachers cannot tie the business of teaching togetherinto some kind of meaningful theoretical structure and therefore cannotget enthused about the task of refining "theory" through research?Or are we as researchers not articulate enough to relate our researchfindings to some established theoretical threads?

NUCLEAR BINDING ENERGY

Indiana University physicists have placed another piece in a vast "jig-sawpuzzle" of modern science.The puzzle concerns the nature of the immense forces within the nucleus

of the atom�the forces which account for the great energies released innuclear reactions. Over the years, the puzzle is slowly being solved ^s physiciststhe world over fill in the gaps in basic knowledge.The new contribution concerns the effects of the spin of protons, which

are major components of nuclei and are generally regarded as one of themost fundamental particles in nature. It has been known for many yearsthat protons spin, just as the earth spins about its axis.Long unanswered in the field of high energy physics has been the central

question of how proton spin affects the interaction of protons with otherelementary nuclear particles. The answer to this question is of fundamentalimportance to the formulation of a complete theory of particle interactionsand is required for a full understanding of many phenomena in nuclear andsubnuclear physics.Homer A. Neal, I.U. physicist, conceived an experiment which involved

using an intense beam of protons to bombard a target composed of "polarized"protons, that is, protons all spinning in the same direction. Neal and hiscolleagues worked at Argonne National Laboratory, near Chicago, utilizinga high energy proton beam produced by the Zero Gradient Synchrotron.This machine produces a beam of 10 billion protons per second, each protonhaving an energy of up to 12 billion electron volts. At such high energies,protons are moving nearly as fast as light.

This beam was directed onto a proton target which had been polarizedby a technique called "dynamic nuclear orientation."The experiment has provided striking verification of a theory proposed

in 1971. Interpreted in terms of theory, the results of the experiment implythat the proton can be thought of as a sphere with a radius of only onetenth of a millionth of a millionth of an inch.

Further, the implication is that "flipping," or reversing, of the protonspin occurs usually when two colliding protons pass through one anotherwith their centers separated by a distance equal to this radius.