development and implementation of an integrated mathematics/science preservice elementary methods...

Development and Implementation of an IntegratedMathematics/Science Preservice Elementary Methods Course

Robert A. LonningCurriculum & InstructionUniversity of Connecticut

Thomas C. DeFrancoCurriculum & InstructionUniversity of Connecticut

If integration ofmathematics andscience is to occur, teacher preparationprograms at colleges anduniversities must provide leadership in developing and modeling methods of teaching integratedcontent. This paper describes the development and implementation of an integrated mathematics/science preservice elementary methods course at the University of Connecticut. In planning thecourse several questions were addressed: (a) What does integration of mathematics and sciencemean? (b) What content should be taught in an integrated mathematics/science (IM/S) elementarymethods course? and (c) How should an IM/S elementary methods course be taught? An importantelement of the course involved enlisting an exemplary elementary teacher who was releasedfromher classroom one day per week to co-teach the methods class. Establishing a definition ofintegration proved to be one of the most challenging aspects of course development. The authorsdetermined that most difficulties in integration of disciplines result from attempts to "force" theintegration. As the team struggledwith the philosophical, theoretical and logisticalproblems in thedevelopment of the course, it became apparent why integration has not been more widelyimplemented. It is believed this model can be adapted to allow for integration of all content areas.Plans are currently underway to incorporate social studies into the methods class for Fall of1993.

Calls for integration of mathematics andscience are not new. The earliest reference tointegration in A Bibliography of Integrated Scienceand Mathematics Teaching and Learning Literature(Berlin, 1991), was published in 1905 in SchoolScience and Mathematics. Since that time therehave been numerous articles, curriculum projects,and symposia dedicated to promoting integration(Berlin, 1991). Most recently, a major thrust of thenational initiatives in science and mathematicsreform has been toward increasing the integrationof science, mathematics and other content areas.Such influential documents as Science for AllAmericans (Rutherford & Ahlgren, 1990), Every-body Counts. A Report to the Nation on the Futureof Mathematics Education (National ResearchCouncil, 1989), and Curriculum and EvaluationStandards for School Mathematics (NationalCouncil of Teachers of Mathematics, 1989), allstress the interrelatedness of mathematics andscience and the implications of this relationship forcurriculum and instruction.

In answer to the question "Why integrate?"McBride and Silverman (1991) list four reasons:

1. Science and mathematics are closelyrelated systems of thought and are natu-rally correlated in the physical world.

2. Science can provide students with concreteexamples of abstract mathematical ideasthat can improve learning of mathematicsconcepts.

3. Mathematics can enable students toachieve deeper understanding of scienceconcepts by providing ways to quantifyand explain science relationships.

4. Science activities illustrating mathematicsconcepts can provide relevancy andmotivation for learning mathematics (pp.286-287).

A further, purely practical reason, which is prob-ably even more valid today than when written, waselaborated by Brown and Wall (1976):

A way of treating the dilemmas of amassive amount of material, interrelated-ness of disciplines, articulation of gradelevels, "practical" application of content,concept and process emphases, and the

School Science and Mathematics

Preservice Elementary Methods Course

structure of disciplines is to integratethose facets of traditionally-defineddisciplines where commonalities inter-face. (p.551)

If integration of mathematics and science is tooccur, an important potential source of change isteacher preparation programs at colleges anduniversities. Faculty in schools of education musttake a leadership role in developing and modelingmethods of teaching integrated content. A numberof innovative integration programs are currentlyunderway, for example, Stuessy (1993). It is hopedthe following description of the development andimplementation of the integrated methods course atthe University of Connecticut will provide addi-tional support to this effort.

Background

The School of Education, as a member of theHolmes Group, and in response to the State ofConnecticut Standards for Professional Educationdeveloped an Integrated Bachelor’s/Master’sprogram (IB/M) for teacher preparation. The IB/Mprogram involves three years of upper division andgraduate work leading to a master’s degree ineducation. The first two years of the programrequire an appropriate balance of clinical experi-ences, liberal arts and pedagogical preparation. Thefinal year consists of graduate level coursework andclinical research leading to a thesis. During the fallof the second year the program consists of corecourses, for example, foundations of education,educational psychology, and special education,methods courses in mathematics, science, socialstudies and reading, and a seminar designed tointegrate students’ experiences in core, clinic, andmethods. In this model, a three credit block isallocated to the mathematics, science, and socialstudies methods courses and one credit for generalmethods of teaching. The natural connectionbetween mathematics and science suggested theintegration of these content areas for the initialoffering of the methods course.

In the fall, 1991, the Connecticut state educa-tion department was awarded a 5-year grant,entitled Project CONNSTRUCT, from the NationalScience Foundation. Project CONNSTRUCT, astatewide systemic initiative, is designed to improvehow K-12 schools present mathematics, science and

technology to children, and to increase mastery andinterest in these areas.

Project CONNSTRUCT is organized aroundfive components. Component 3 focuses on therestructuring of higher education programs inteacher preparation and professional development.Four specific program areas have been targeted forfunding under this component. One program, theVisiting Fellows Program, was designed to encour-age co-teaching collaborations between educatorsof K-12 schools and institutes of higher education(IHE). The purpose of the Visiting Fellows Pro-gram is to ensure that positive changes in teachingmethods and curriculum be joint ventures andshared commitments of both the K-12 and thehigher education systems.

Through a Visiting Fellows grant awarded tothe authors, an innovative and exemplary elemen-tary (K-2) teacher with 22 years of experience, wasenlisted to co-teach the integrated mathematics/science (IM/S) course. The elementary teacher wasreleased from her classroom one day per week toco-teach the methods class. Funds from the grantwere used to provide for a substitute teacher, paytravel expenses and a stipend for her involment inthe development and teaching of the course. Inaddition, two doctoral students in science educationwith extensive experience in teaching elementaryschool science were invited to the team. As aresult, a five member instructional team wasassembled to plan, teach, and evaluate the IM/Scourse.

Development of the Course

In planning the course several questions wereaddressed: (a) What does integration of mathemat-ics and science mean? (b) What content should betaught in an integrated mathematics/science el-ementary methods course? and (c) How should anIM/S elementary methods course be taught?

What does integration of mathematics and sciencemean?

Since there exists a variety of interpretations ofintegration it was necessary to develop a definitionthat was useful for this course. Initially, attemptswere made to create a new discipline by totallyintegrating mathematics and science. It was hopedthis new discipline could be taught without refer-ence to the terms "mathematics" or "science." This

Volume 94(1), January 1994


ambitious (and somewhat naive) effort proved to beunsuccessful and frustrating. Subsequent effortsinvolved examining different means of relating thetwo disciplines. One approach involved usingscience as the focus. It was hoped that scienceactivities could be found or developed which wouldutilize all necessary mathematics concepts. Afterexamining a variety of science activities, includingthose specifically designed to include integration, itbecame clear that most of these activities utilized alimited number of mathematics concepts, forexample, categorizing and graphing. In fact, itbecame a standard joke, after examining a numberoftradebooks on integrating mathematics andscience, that the mathematics included in mostscience activities could be summarized with thestatement, "We could always make a graph!"Attempts to use mathematics as the focus wereequally unsatisfactory. In this model, mathematicsconcepts formed the central themes and appropriatescience activities would be selected to fit them.Complete reliance on this model would require astrong science background with ready access to awide variety of appropriate science activities.Eventually it was realized the difficulties stemmedfrom attempts to force the integration of mathemat-ics and science. It became clear that not everymathematics concept lends itself to a scienceapplication and not every science activity involvesappropriate mathematics concepts.

It was realized that the integration of instruc-tion of mathematics and science could be viewed asa continuum (see Figure 1). The idea of a con-tinuum, described by Brown and Wall (1976),provides an accurate representation of the evolutionof the authors’ thinking as they came to grips withhow to integrate mathematics and science instruc-tion. In this model the primary consideration isnot "How can mathematics and science concepts beintegrated?" but rather, "What is the best way toteach them?" There are certain mathematics andscience concepts that are best taught independentlywhile others lend themselves to natural integration,that is, relevant science activities utilizing mean-ingful mathematics skills (see Appendix A).

What content should be taught in an IM/S elemen-tary methods course?

In deciding on appropriate content for thecourse the following factors were considered:

Skills, concepts, processes, and attitudescommon to science and mathematics. The twodisciplines of mathematics and science share asignificant amount of content, including concepts,processes and attitudes, which provides a basis fordeveloping an integrated curriculum (see Figure 2).The six learning areas, (1) sorting and classifying,(2) measuring, (3) using spatial and time relation-ships, (4) interpreting data, (5) communicating, and(6) formulating and interpreting models, are ex-amples of the interrelationship of mathematics andscience processes (Brown and Wall, 1976).

Differences between mathematics and science.Although mathematics and science curricula havemuch in common in terms of concepts, processes,and attitudes, strategies for integrating mathematicsand science instruction are influenced by someinherent differences:

1. The NCTM Standards recommend bothcurriculum and instructional strategies forelementary mathematics. Most beginningelementary school teachers are at leastfamiliar with basic mathematics skills,(e.g., addition, subtraction, fractions, etc.).

2. Science curriculum is generally determinedat the school district level. Since mostelementary teachers have a limited back-ground in science content, they are depen-dent on packaged curriculum materials,(e.g., textbooks, commercial science kits,etc. and the like for both content andinstructional strategies).

Pedagogical issues. It was decided the courseshould address both content and pedagogical issuesall modeled within a hands-on/minds-on frame-work. In addition, concepts dealing with generalmethods (e.g., designing lesson plans), the integra-tion of technology into the curriculum, national

Figure 1. Continuum a/integration of mathematics and science concepts.

INDEPENDENTMATHEMATICS

1These concepts are best

taught in a purelymathematical context.

MATHEMATICSFOCUS

What mathematics conceptsare being taught? Are therescience activities that support

these concepts?

BALANCEDMATHEMATICSAND SCIENCE

Activities which provide anatural integration of

mathematics and scienceconcepts.

SCIEFOC

What sciencare being ta

appropriate rconcepts be i

-NCE INDEPE:US SCIE

ce conceptsught? Canmathematicsncorporated?

These conerequire omathen

NDENTNCE

epts do notr involvenatics.



mathematics and science reform standards, alterna-tive forms of assessment, and cooperative learningwere also to be integrated in the course.

Students* beliefs about mathematics andscience. The background of the students was also afactor in designing the curriculum. It was assumedstudents perceived the elementary mathematicscurriculum as a well defined body of mathematics,areas of which they either have forgotten, dislikedor expressed concern about teaching. The goal ofthe course in this area was to change their attitudesabout mathematics and to provide instruction about"how" to teach this material. Similarly, manystudents perceived the content of science as a bodyof unrelated facts, most of which were unfamiliar tothem. Since these students believed their ownscience content background was weak, they fearedteaching the subject. Again, major course goals forscience were to change their attitudes about schoolscience, strengthen their content background andhelp them develop strategies for teaching science.

Sources of authority. Identifying sources ofauthority for science and mathematics curricula andexamining their recommendations provided guide-lines which helped to narrow the choices for whatshould be taught.

Figure 2. Integrated mathematics and scienceprocesses

Mathematics.The National Council of Teachers of Math-

ematics (NCTM) has developed a list of standardsfor curriculum, evaluation, and instruction whichoutline both what is to be taught and how it shouldbe taught. These standards have become widelyaccepted and are being implemented across thecountry. The content of the methods course re-flected the traditional K-8 mathematics contentareas as interpreted by the Standards.

Science.In contrast to mathematics, national science

education standards are still being developed. Thisis due, in part, to the enormous amount of sciencecontent available as well as the lack of agreementon what concepts are most important. Efforts arecurrently underway by the Standards Task Force ofthe NSTA and the National Research Council todelineate a comprehensive set of standards forcurriculum, teaching and assessment. In themeantime, textbook publishers, school districtcurriculum guidelines, commercial science kits,science trade books, and science museums all haverecommended science curricula which have beenadopted by individual school districts. Althoughthere is much variation in recommended sciencecontent, there is much greater agreement on scienceprocesses , for example, observing, classifying,measuring, predicting, which cut across all sciencecontent areas. Since there is also general agreementon a de-emphasis on memorization of science factsin the elementary grades, most science programsstress process skills.

Consideration of these factors led to thedevelopment of the following guidelines for select-ing curriculum:

1. The course content would emphasizescience processes over facts. Until nationalstandards are finalized, the enormous scopeof available science content makes select-ing what science to teach a completelysubjective decision. It is also not possibleto completely upgrade the content back-ground of preservice elementary educationstudents in a one semester methods class.

2. Trade books and published materials wereused as the major source of science activi-ties and content. Instruction on locatingand using available materials providedscaffolding for students with weak sciencebackgrounds.

3. NCTM curriculum standards providedguidance for incorporating recommendedmathematics concepts.

How should an IMIS elementary methods course betaught?

The multiple levels of objectives characteristicof methods of teaching courses posed severalproblems for the instructional design. Methodsstudents were faced with learning both what to



teach and how to teach it. Methods instructors werefaced with determining what mathematics andscience content to teach and how to teach it, whatinstructional strategies the methods students shoulduse to teach the content in an integrated fashion,and how to teach these instructional strategies to themethods students. One result of the multi-leveledobjectives, typical of methods courses, was thechanging of roles of the instructors and students.While modeling integrated instruction, methodsinstructors became elementary teachers and themethods students became elementary students.While teaching mathematics and science content orinstructional methods, instructors and studentsreturned to their typical roles. Methods studentsbecame elementary teachers and their peers elemen-tary students when they taught mini-lessons theyhad developed.

The instructional team believed that goodteaching should be modeled and not lectured; thatis, participating in integrated activities and observ-ing models that facilitate integrated learning aremuch more powerful and meaningful ways to learnabout teaching than passively listening to lecturesabout effective teaching. Therefore, hands-on,activity-centered, guided discovery methods formedthe basis of all instruction whether the objectiveswere teaching science and mathematics content,methods of instruction, or integrated elementarylessons.

In keeping with the course philosophy outlinedabove and to reflect recommendations of thenational initiatives for science and mathematicseducation, a theme-based, problem solving modelwas adopted for developing the integrated lessons.The thematic approach is described below:

Selection of Themes. Themes, for example,animals, the pond, patterns, natural resources,recycling, and so forth, provide an organizationalframework that ties together activities from all areasof the curriculum. Exploration of a theme involvesengaging students in solving problems and can takea few days, weeks, months, or an entire school year.

Identification of Questions or Problems.Posing relevant questions or problems motivatesstudents to become actively involved in elaboratingthe theme. A problem solving approach allows forintegration at two levels. First, when students areinvolved in solving problems or answering ques-tions, they will discover that resources from avariety of content areas are useful. Mathematics,science, social studies, language arts, and fine arts

all come into play as students search for answersand solutions. Second, due to the relationshipbetween mathematics and science, students willoften be engaged in science activities that usemathematics and mathematics activities that involvescience.

The choice of a particular problem or questioncan be driven by specific mathematics or scienceconcepts that are included in the curriculum orcome from content areas outside the mathematics orscience domain.

Selection of Activities. Once a question orproblem has been identified, activities can beselected based on the following criteria:

1. What mathematics concepts can be relatedto the theme or problem? (Are there anyscience materials that can be incorporatedinto the mathematics instruction?)Resources: NCTM Standards, mathematicsmethods textbooks, use of manipulatives.

2. What science concepts do I wish to teachthat can be related to the theme or prob-lem? (Many science activities use math-ematics concepts.)Resources: Science trade books, sciencetextbooks, commercial science kits.

3. What activities related to the theme orproblem utilize both mathematics andscience concepts? (Note: Integratedmathematics/science activities may involveanswering questions or solving problemsthat utilize mathematics usually taught andunderstood at one grade level and scienceat a different grade level.)Resources: Integrated mathematics/sciencetrade books, commercial science kits,technology based learning tools.

This delivery system is a more powerful way toteach and a more meaningful way to learn since thequestion or problem creates a need to use math-ematics/science to answer the question or resolvethe problem.

Implementation

During the summer, 1992, the instructionalteam met for the equivalent of five full days todesign the course. As a result themes were selected,problems and activities were identified and col-lected, and a syllabus was written.



The methods course met on consecutiveMonday mornings from 8:00 a.m. - 12:00 noonduring the fall semester, 1992. The integratedmathematics/science portion of the course wasteam-taught during the first 9 weeks of the 14 weeksemester with the remaining time devoted to socialstudies. There were 43 students registered for thecourse and it was scheduled to meet in three class-rooms; a large mathematics/science laboratoryroom, containing 10 tables seating approximately50 students and equipped with mathematicsmanipulatives and science kits, and two smallerconference rooms.

Schedule of Class ActivitiesTypical class sessions began with a large group

presentation which served as an introduction to theday’s activities. During this time students wereintroduced to the topics that would be taught,provided with background information necessary tounderstand the material, and informed of theschedule of the day’s activities. Students were thendivided into three groups and rotated among threehour-long activities which were conducted in one ofthe three classrooms. These activities were coordi-nated by one or two instructors. The day endedwith the whole group meeting to reflect on theday’s activities, to assign work, and to discussbriefly upcoming activities.

On days in which special topics were discussed(e.g., developing lesson plans, students creatingand presenting integrated lessons, etc.) the day’sschedule was modified. These activities rangedfrom whole group instruction to students working insmall groups lasting the entire morning period.

For example, some class time was devotedexclusively to the teaching of mathematics/sciencecontent and methods followed by discussions ofways to implement these ideas in the classroom. Atother times a question or a problem was the moti-vating factor driving the teaching/learning of themathematics/science content and methods.

Five Member InstructionalTeamThe five member instructional team provided a

unique opportunity for university faculty, doctoralstudents and an experienced elementary teacher tocollaborate and learn from each other throughoutthe course. The doctoral students and the K-2teacher complemented the university faculty byproviding students with the "day-to-day practicalclassroom knowledge" necessary to become

effective elementary teachers. (On informalevaluations at the end of the course, studentsremarked to the university faculty that" It was nicebeing taught by real teachers.")

This working relationship proved to be excitingand academically enriching for all participants. Forexample, through informal debriefing and planningsessions each week and observations during thecourse, university faculty were able to draw uponthe teaching experience and expertise of the teach-ers and gain valuable insight into the realistic worldof elementary classroom teaching. The doctoralstudents gained valuable experience in designingand teaching a preservice elementary methodscourse, while the classroom teacher enjoyed work-ing and teaching at the university level.

In addition, this collaboration proved to beextremely beneficial to the students. From aninstructional perspective, students were able toexperience two or three different activities taughtby various combinations of instructors each week.In retrospect, the instructional model set up to teachthis class proved to be an effective way for studentsto learn and faculty to teach.

Student Reactions

An author developed survey provided anec-dotal evidence that students’ attitudes towardsteaching integrated science and mathematicsimproved during the course. In addition to thepositive changes in attitudes expressed in thesurvey, students were extremely enthusiastic aboutthe course in final written course evaluations.

Conclusion

The development of an integrated mathematics/science elementary preservice methods course wasextremely challenging and extremely rewarding.The instructional team was committed to the goal ofdeveloping a course that would help future elemen-tary teachers make science and mathematicsinstruction more meaningful to their students. Asthe team struggled with the philosophical, theoreti-cal and logistical problems in the development ofthe course, it became apparent why integration hasnot been more widely implemented. It is believedthe model we have developed can be adapted toallow for the ultimate integration of all contentareas. Plans are currently underway to incorporate



social studies into the methods class for fall of1993.

The five member instructional team proved tobe a rewarding and effective model in teaching thiscourse. As one of the strengths of this course,future courses will include a similar structure.

One aspect of the program that will be im-proved is in the area of assessment. The modeldeveloped at Texas A & M University (Stuessy,1993), will be useful in this process. It is alsoanticipated that new and improved science andmathematics activities will be developed andintegrated with social studies as the course contin-ues to evolve.

References

Berlin, D. F. (1991). A bibliography of integratedscience and mathematics teaching and learningliterature. School Science and MathematicsAssociation Topics for Teacher Series Number6. Bowling Green, OH: School Science andMathematics Association.

Brown. W. R.. & Wall. C. E. (1976). A look at theintegration of science and mathematics in theelementary school - 1976. School Science andMathematics, 76 (7), 551-562.

McBride, J. W., & Silverman, F. L. (1991). Inte-grating elementary/middle school science andmathematics. School Science and Mathematics,91 (7), 285-292.

National Council of Teachers of Mathematics(1989). Curriculum and evaluation standardsfor school mathematics, Reston, VA: Author.

National Research Council (1989). Everybodycounts. A report to the nation on the future ofmathematics education. Washington, DC:National Academy Press.

Rutherford, F. J., & Ahlgren, A. (1990). Science forAll Americans. New York: Oxford Press.

Stuessy, C. L. (1993). Concept to application:development of an integrated mathematics/science methods course for preserviceelemetary teachers. School Science andMathematics, 93 (2), 55-62.

Appendix A

Sample Integrated Lesson: BalancedMathematics and Science

In order to illustrate the authors’ conception ofintegration of mathematics and science instruction,a "balanced mathematics and science" lesson willbe described. In keeping with the model of instruc-tional design outlined, selected activities should bebased on a problem solving, thematic approach.Food is a theme which provides many opportunitiesfor varying degrees of integration of mathematicsand science instruction at a variety of grade levels.

A middle school lesson on specific gravity willbe used to illustrate what the authors consider abalanced integrated lesson, that is, a lesson in whichboth mathematics and science concepts and skillsare necessary for understanding the concept. Insuch a balanced lesson, neither the mathematics norscience concepts are artificially included in order toachieve integration.

Question: Will an orange sink or float in water?What happens when the orange is peeled?

Intended Learning Outcomes:1. Students will understand why objects float.2. Students will develop increased under-

standing of the following concepts:a) Volumeb) Specific gravityc) Water displacementd) Mass

3. Students will develop or improve thefollowing skills:a) Measuring volume by water displace-

ment.b) Measuring the mass of an object with a

balance.c) Measuring the mass of a volume of

water.d) Calculating specific gravity by compar-

ing the mass of an object with an equalvolume of water.

Materials Needed:� oranges, one per group of three or fourstudents (fresh oranges with thick skin workbest)

� objects which float or sink, e.g. corks,chunks of paraffin, lumps of clay, stones, etc.



� triple beam balances� 500 ml beakers� large jars or containers to catch overflowwater from beakers

� graduated cylinders� water� calculator

What mil the children do?1. Working in groups of three or four, stu-

dents begin by predicting whether or nottheir orange will float. After testing theirprediction (it should float), studentsmeasure the volume of their orange bymeasuring the amount of water that isdisplaced when the orange is submerged ina 500 ml beaker.Students should offer hypotheses to explainwhat happened to their orange.

2. Students will find the mass of the orangeand the mass of the displaced water andthen compare the mass of the orange to themass of an equal volume of water (thedisplaced water) that is, specific gravity.

3. Using other materials provided, for ex-ample, lumps of clay, paraffin, corks,students will repeat the procedure in steps1 and 2 and record the data in a table.

4. From the data accumulated in the investi-gation, students will form a generalizationabout the relationship between specificgravity and ability to float.

5. The students will then make a predictionabout what will happen when the orange is

peeled. Students then calculate the specificgravity of the peeled orange and comparetheir findings with the data collectedearlier.

6. Students will develop explanations for theirfindings based on their understanding ofthe concept of specific gravity.

Integration:This activity includes the science and math-

ematics concepts of mass, volume, water displace-ment, and specific gravity and requires skills inusing a balance, a graduated cylinder and thetechniques involved in measuring volume by waterdisplacement. Each of these concepts and skillswere required to answer the questions posed at thebeginning of the activity. Such an activity whichinvolves "real" science, that is, science as done byactual scientists and real mathematics is consideredbalanced in terms of integration.

Notes: Dr. Thomas C. DeFranco teachesmathematics education at the University of Con-necticut, Department of Curriculum and Instruction,School of Education, Box U-33, 249 GlenbrookRd., Storrs, CT 06269.

Dr. Robert A. Lonning’s address is Departmentof Curriculum and Instruction, School of Education,Box U-33, University of Connecticut, 249Glenbrook Rd., Storrs, CT 06269.

Internet: [email protected]


development and implementation of an integrated mathematics/science preservice elementary methods...

Documents