integrating science and mathematics: perceptions of preservice and practicing elementary teachers

Integrating Science and Mathematics: Perceptions ofPreservice and Practicing Elementary Teachers

Jeffrey R. LehmanScience EducationSlippery Rock University

One hundredandsixty-one undergraduate elementary education majors and sixty elementary teacherscompleted an eight-item questionnaire designed to assess their perceptions toward integrating scienceand mathematics in the elementary grades. The two groups of subjects differed significantly on theirresponses tofive of the eight items. Chi square analyses suggest thatpracticing elementary teachers feltthey hadmore backgroundinmathematics andscience,weremore aware of curriculummaterials in thisarea, did not think that integrationwas currently a commonpractice, andwere more likely to indicatethat there was not sufficient time in the school day to integrate the subjects. Preservice teachers weremore likely to indicate that integrating the disciplines was preferred to teaching them separately. Inaddition to the analyses of data, a list of recommendations are provided for teachers, curriculumdevelopers, andpolicy makers interested inadvancing the concept of integrating science andmathemat-ics in instruction.

During the last few years, individuals (Berlin,1990,1991; House, 1990) and professional organi-zations (AAAS, 1989; NCTM, 1989) have contin-ued their call for the integration of science andmathematics instruction. Several reasons are givento support integration:

1. to increase students* achievement in bothdisciplines;

2. to be motivational and produce morepositive attitudes towards mathematics andscience; and

3. to emphasize relationships between con-cepts resulting in more meaningful learn-ing.

Attempts to integrate mathematics and scienceinstruction have appeared in the literature since thebeginning of the twentieth century (Breslich, 1936;Friend, 1985; Fuller, 1942; Gorman. 1943; Hogan& Schall, 1973; Kolb, 1968; Moore. 1903;Wandersee, 1992; Webb & Ost, 1975). During thissame time period, a diversity of individuals andgroups were developing and disseminating curricu-lum materials and projects which emphasizedmathematics/science interactions. Among thesematerials were the School Mathematics StudyGroup’s books (1965), the Minnesota Mathematicsand Science Project (Minnemast, 1970), the UnifiedScience and Mathematics for Elementary SchoolsProject (USMES, 1973), House’s (1980), Farmerand FarrelTs (1989), and the School Science andMathematics Integrated Lessons (SSMILES)

collections of integrated activities, the LawrenceHall of Science’s Great Explorations in Math andScience Project (GEMS), Fresno Pacific College’sActivities that Integrate Mathematics and Science(AIMS), and the University of Chicago’s TeachingIntegrated Math/Science Project (TIMS). For moredescription of these and other projects, see McBrideand Silverman, 1991. After nearly a century of thisattention and activity, little evidence can be foundfor widespread integration of these disciplinesduring classroom instruction. The importance ofthe teacher in promoting classroom change cannotbe underestimated. One of the two underlyingassumptions of the National Council of Teachers ofMathematics’ Professional Standards for TeachingMathematics (1991) is that "teachers are the keyfigure in changing the ways in which mathematicsis taught and learned in schools" (p. 2). Factors thatappear related to classroom practice are teachers’beliefs and attitudes toward a topic.

While researchers have examined teachers’attitudes toward science (Koballa & Crawley, 1985;Morrisey, 1981), toward mathematics (Ernest,1989; Porter, Floden, Freeman, Schmidt, &Schwille, 1988), and toward the teaching of thesesubject areas (Appleton, 1983; Thompson, 1984),less research has been reported on teachers’ percep-tions toward integrating the two disciplines.Lehman & McDonald (1988) examined the percep-tions ofpreservice and practicing secondary math-ematics and secondary science teachers toward

School Science and Mathematics

Integrating Science and Mathematics

math/science integration. They reported that whilethese current and future teachers generally agreedthat the concept of integration was a desirableteaching method, they were not aware of curriculummaterials focusing on integration, and they did notfeel that there was sufficient time within the schoolday for integration to occur. Lehman andMcDonald inferred from their findings that teach-ers, especially those teaching secondary mathemat-ics, viewed integration as a topic to add to analready overloaded curriculum.

Finally, much of the research on teacher beliefsand their relationship to practice has centeredaround teachers with three or more years of teach-ing experience (dark & Peterson, 1986). Addi-tional research is needed that compares moreexperienced teachers’ beliefs with those ofpreservice and beginning teachers.

How do elementary teachers perceive the ideaof integrating mathematics with science? Are theirperceptions similar to those of secondary mathemat-ics and science teachers? Are the perceptions ofpreservice elementary teachers similar to those ofpracticing elementary teachers? The purpose of thisstudy was to answer these questions by extendingthe research on teachers’ perceptions of integrationat the secondary level to teachers in elementaryschools.

Method

Lehman and McDonald’s (1988) ten-itemquestionnaire, which was designed to assess theperceptions of secondary school teachers toward theintegration of mathematics and science, was modi-fied to produce an eight-item instrument appropriatefor assessing elementary school teachers’ percep-tions (See Table 1). One hundred, sixty-oneundergraduate elementary education majors (85%female; all juniors or seniors) enrolled in one of sixsections of a methods and materials course inelementary science, at a medium size public univer-sity in western Pennsylvania, completed the ques-tionnaire during the third class session of thesemester. During the last five weeks of the semes-ter, most of these students enrolled in a one semes-ter hour elementary field experience. Sixty elemen-tary teachers in western Pennsylvania, who had oneof these field students assigned to them, voluntarilycompleted and returned the same questionnaire thatthe preservice teachers completed.

Results

For the purpose of analyses, the categoriesstrongly agree and agree were collapsed into thecategory "agree" while strongly disagree anddisagree were collapsed into "disagree." Thisprocedure was followed due to respondents’infrequent use of extreme categories and thesubsequent increased interpretability of three versusfive categories in the chi-square analyses. Thepercentages of responses for the categories agree,neutral, and disagree for all eight items are pre-sented in Table 1.

Preservice TeachersThe item which produced the most agreement

from preservice elementary teachers was Item 1(75.8%). These students felt that for many topics,integrating mathematics and science content waspreferred over teaching the content in separatelessons. This belief may be partially influenced bythe recent emphasis on whole language instructionat the elementary level. In fact, one student wroteon the back of her questionnaire that she thoughtintegrating mathematics with science involvedteaching these two subject areas within othersubject areas, such as language arts and socialstudies. Nearly as many students disagreed with thestatement that hands-on activities are more appro-priate in science lessons than in mathematicslessons (Item 7,69.4%). This perception mayreflect an increased awareness of availablemanipulatives to teach mathematics concepts.Alternatively, the result could also reflect anincreased awareness that hands-on activities inscience can provide, at times, the context withinwhich mathematics can be integrated. A majorityof students (Item 8, 61.6%) answered neutral whenasked to indicate whether or not they thoughtelementary teachers commonly integrated subjectswithin lessons; reflecting these students’ minimalexperiences within elementary classrooms. Sixtypercent of the students (Item 4) believed that therewould be sufficient time to integrate mathematicsand science in lessons, and most did not think thatstudents would become confused with such instruc-tion, again possibly reflecting the preservicestudents’ prior exposure to the advantages ofintegrated instruction through whole languageinstruction. A majority of students (Item 3,51.9%)also indicated that they were not aware of curricu-

Volume 94(2), February 1994


Table 1.

Preservice and Practicing Elementary Teachers’ Perceptions Toward the Integration of Mathematics andScience

QuestionnaireItem

1. For many topics,integrating mathematicsand science content is apreferable method thanteaching the content inseparate lessons

2. I feel I have sufficientbackground in mathematicsand science to integrateboth in lessons

3. I am aware ofcurriculum materialsdesigned to integratemathematics and science

4. There’s not enough timeduring most lessons tointegrate mathematics andscience content

5. Elementary schoolstudents get confused whenmathematics and scienceare integrated in lessons

6. Classes for giftedstudents would be the mostappropriate place forintegrating mathematicsand science

7. Hands-on activities aremore appropriate inscience lessons than inmathematics lessons

8. During talks with mycolleagues and byobserving elementarylessons, it appears to methat integrating math andscience is common

Teachers

preservice(n=161)

practicing(n=60)

preservice(n=159)

practicing(n=60)

preservice(n=160)

practicing(n=59)

preservice(n=160)

practicing(n=58)

preservice(n=160)

practicing(n=59)

preservice(n=160)

practicing(n=60)

preservice(n=160)

practicing(n=60)

preservice(n=161)

practicing(n=58)

Agree(%)

75.8

50.0

34.0

50.0

21.9

44.1

12.6

41.4

10.6

6.8

25.7

25.0

23.2

15.0

19.5

12.1

Neutral(%)

12.4

23.3

32.1

13.3

26.3

17.0

27.5

13.8

36.3

39.0

26.3

16.7

7.5

11.7

61.6

17.2

Disagree(%)

11.8

26.7

34.0

36.7

51.9

39.0

60.0

44.8

53.2

54.2

48.1

58.3

69.4

73.3

18.9

70.7

ChiSquareValues

13.77*

8.69*

10.67*

22.69*

0.76

2.60

2.35

53.52*

* B. < .05



lum materials designed to integrate mathematicsand science. One of the projects in the students’methods courses in both mathematics and science isto make them aware of such resources. Evaluationof students’ idea files at the end of the semesterrevealed students’ use of integrated curriculummaterials for the construction of lesson plans.Moreover, observations during subsequent fieldexperiences revealed that some students wereindeed using integrated materials in their teaching.The item which produced the most dispersion inresults was the preservice students’ beliefs concern-ing their background in mathematics and science(Item 4). Approximately equal numbers felt theyhad sufficient background, had insufficient back-ground or were unsure of the adequacy of theirbackground at this point in time. Most of thesestudents had taken a combined total of 12 semesterhours of mathematics and science as part of theirelementary certification program. Recently, NCTM(1991) has recommended that teachers of K-4 take aminimum of nine semester hours ofcoursework incontent mathematics and teachers of grades 5-8 takefifteen. A similar argument can be made for theamount of science coursework that these sameteachers should complete, resulting minimally, in acombined total of 18 (K-4 teachers) or 30 (5-8teachers) semester hours of mathematics andscience.

Practicing TeachersSimilar to preservice teachers, the practicing

elementary teachers did not feel that hands-onactivities were more appropriate in science lessonsthan in mathematics lessons (Item 7,73.3%).About the same number of teachers (70.7%) alsoindicated that the integration of mathematics withscience was not common in the elementary grades(Item 8). Fifty percent of the teachers thought theyhad sufficient background in both mathematics andscience to integrate the two (Item 2), and the samenumber believed that for many topics, integratingthem was preferable to teaching the topics inseparate lessons (Item 1). Approximately 50 % ofthe teachers also indicated that integrating topicswould not confuse students during instruction (Item5). About the same number of teachers agreed(44.1%) and disagreed (39.0%) that they wereaware of curriculum materials designed to integratemathematics and science (Item 3). Although suchmaterials have now been available for over 25 yearsand recent efforts associated with the AIMS project

have included the distribution of a newsletter andteacher workshops across the country, only twofifths of the teachers indicated an awareness of suchmaterials. Similarly, practicing elementary teacherswere almost evenly split on whether there wassufficient time during an elementary school day tointegrate the two disciplines.

Preservice Versus Practicing TeachersPreservice and practicing elementary teachers

differed significantly on their responses to five ofthe eight questionnaire items (1,2, 3,4, 8). Thedata suggest that preservice teachers were morelikely to indicate that integrating disciplines waspreferred to teaching content in separate lessons(Itemi; x2 [2, N=221] =13.77, p=.0011).Further, it appeared that practicing teachers felt thatthey had more background in mathematics andscience (Item 2: %2 [2, N = 219] = 8.69, p =.0130), and they were more aware of curriculummaterials that integrated these two disciplines (Item3: x2 [2, N =221]= 10.67. p=.0048). Finally, inthis sample practicing teachers were also morelikely to indicate that there was not enough time tointegrate mathematics and science content (Item 4:^2 [2, N= 218] = 122.69. p = <0001), and that theintegration of mathematics and science in elemen-tary school lessons was uncommon (Item 8: %2 [2,N=219]= 53.52./?=<0001).

Discussion

Although a larger percentage of practicingteachers than preservice believed they had sufficientcontent background to integrate mathematics andscience, less than 50% of all of those surveyed feltthey had sufficient background. These resultsshould be considered by university faculty who areexamining the amount and type of undergraduatemathematics and science courses that future el-ementary teachers will be required to take in theircertification programs. If desirable goals forelementary teachers are to have them teach: (a)mathematics; (b) science; (c) how mathematics isapplied in science; (d) how scientific inquiry oftenleads to developments in mathematics; and (e) howthe two disciplines interface, then appropriatepolicy must emanate from current curriculum andteacher preparation reform movements. Discus-sions related to reform should not only address theissues of mathematics and science requirements forelementary education majors, but also ensure that



these teaching majors are provided with opportuni-ties to experience the integration of the disciplinesin their own instruction. However, content prepara-tion, while necessary, does not appear to be asufficient condition to assure integration withinlessons. Lehman and McDonald (1988) found thatwhile secondary mathematics and science teachersgenerally felt they had sufficient background inboth disciplines, they were unaware of curriculummaterials available to them. Likewise, they foundthat secondary mathematics teachers did not believethere was enough time to teach integrated lessons.Consequently, integration at the secondary level didnot seem to be common. Similar results, withrespect to curriculum materials and time, wereobtained in the present study. While practicingteachers were more aware of integrated curriculummaterials than the preservice teachers, less than50% of the practicing teachers were aware of suchmaterials. It appears that additional disseminationefforts, beyond newsletters and journal advertise-ments, are needed to supplement current efforts.For example, a building or district leader in math-ematics or science, may decide to not only distrib-ute materials/updates to colleagues at the elemen-tary level, but also decide to model demonstrationlessons as a means of continued professionaldevelopment of staff.

Practicing teachers’ perception of inadequatetime to integrate lessons may reveal the realities ofwhat has been identified as overstuffed and under-nourished curricula (AAAS, 1989). Integratingmathematics with science is seen as another add-ontopic. Moreover, elementary teachers who haveeither local or state syllabi often express that theydo not know how or where integrated lessons matchthe stated curricula.

Andersen (1990) noted that reform projects,like NSTA’s Initiatives, are calling for the develop-ment of curricula that integrate science with othersubject areas and which provide for a more unified,in-depth treatment of topics. Similar recommenda-tions have been made by NCTM (1989) in theirCurriculum and Evaluation Standards, where theyemphasize the need for teachers to relate mathemat-ics to other curriculum areas in order to helpchildren make connections between the abstractmathematical concepts and their real-world applica-tions. These suggestions are also consistent withProject 2061: Science for All Americans (AAAS,1989) which challenges educators to direct more oftheir attention to the connections among science,

mathematics, and technology and to considerteaching less in order to teach more. Integrationmust not be viewed as an addition to mathematicsand science curricula but instead as an integral partin the delivery of more meaningful instruction.Such an integrated approach is significantly differ-ent from what most teachers have experienced intheir own education. Hence, both preservice andinservice offerings must be developed whichdemonstrate the integrated, in-depth treatmentsuggested above.

Conclusions and Recommendations

The elementary teachers surveyed here andtheir secondary counterparts surveyed previously byLehman and McDonald (1988) perceive integrationas a viable alternative to always teaching mathemat-ics and science content in separate lessons. Theseperceptions, however, generally do not carry overinto instructional practice. The challenge to math-ematics and science educators is to develop modelsto overcome constraints that limit integration.These constraints appear to include teachers’knowledge of available curriculum materials, theperception that integration is another topic to add tocurrent curricula, elementary teachers’ lack ofbackground knowledge in mathematics and science,the difference in perceptions between preserviceand practicing elementary teachers, and elementaryteachers’ understanding and experience withintegrated mathematics and science. Based on theabove discussion, the following recommendationsappear warranted.

1. Preservice elementary teacher educationmajors should be meeting the mathematics contentrecommendations contained within NCTM’s (1991)Professional Standards for Teaching Mathematics.Similarly, as the parallel science standards nowbeing developed under the direction of the NationalResearch Council become known, these sameteachers should also be meeting science contentrecommendations.

2. In addition to content in mathematics andscience, preservice teachers should receive instruc-tion in the integration of mathematics and science,including familiarity with existing curriculumresources. For a description of a recently developedintegrated methods course at Texas A&M Univer-sity see Stuessy (1993).

3. Preservice teachers should have theopportunity to teach integrated mathematics and


Integrating Science and Mathematics 63

science lessons during supervised field experiences.When possible, these students should be placedwith an elementary teacher who integrates math-ematics and science and who can serve as a rolemodel for the preservice teacher. Additionally,university-elementary school partnerships canprovide a long-term, supportive environment for theprofessional development of both preservice andinservice elementary teachers.

4. Alternative models for both the preserviceand inservice training in mathematics/scienceintegration must be explored. One such modelcurrently under development involves a university-elementary school partnership. In the program,practicing elementary teachers will be released fromtheir teaching duties periodically throughout asemester to attend/participate in a methods courseto be taught at the school site. Each teacher will bepaired with three or four different undergraduateelementary education majors who will also beenrolled in the course. Each of theseteams will cooperatively develop integrated math-ematics/science lessons that the undergraduatestudents will then field test in the practicingteacher’s classroom during a supervised fieldexperience. It is anticipated that such a model willprovide the preservice teachers with a supportiveenvironment to implement the theoretical consider-ations discussed in the methods course. Simulta-neously, the practicing elementary teachers willreceive additional training in both mathematics andscience content and in the integration of the two.

5. Hord and Ruling-Austin (1986-87) foundthat it takes at least three years for teachers to makesignificant changes in their teaching practices.Hence, administrators and university-school part-ners must realize that in many schools the success-ful integration of mathematics and science willrequire long term and continuous support.

6. Concurrent with efforts to integratemathematics and science, mathematics and scienceeducators have also been examining ways tosuccessfully implement technology into instruction.It appears feasible to promote dialogue that ad-dresses the integration of mathematics and scienceusing technology as a tool.

7. For the purpose of this study, data werenot collected with respect to the grade levels thatthe practicing teachers taught. Recently however,K-3 teachers were reported to be using technologysignificantly less in mathematics and scienceinstruction than teachers in grades 4-6 (Lehman,

1993). Hence, additional research on practicingteachers’ perceptions toward integrated mathemat-ics and science and their subsequent classroompractice should examine similarities and differencesbetween teachers at various grade levels.

8. Additional dissemination efforts of avail-able curriculum resources and model lessons areneeded. One possibility is the development of a setof videotapes (local or national) where exemplaryelementary teachers or preservice field studentsteach demonstration lessons and also provideinformation concerning curriculum materials. Suchmaterials should be supported by professionalorganizations and be readily available for wide-spread distribution.

9. Staff working with elementary teachersmust clearly communicate to them how integratedmathematics and science is to be viewed within thecurriculum. For instance, how does such instruc-tion "match" current mathematics and sciencecurricula, supplement it, or replace it? This ques-tion is possibly the most fundamental one whichmust be answered to help teachers reconcile forthemselves what the nature and extent of integrationat the elementary school level should be.

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Note: Jeffrey R. Lehman’s address is ScienceEducation, 117 McKay Education, Slippery RockUniversity, Slippery Rock, PA 16057.


integrating science and mathematics: perceptions of preservice and practicing elementary teachers

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