# Concept to Application: Development of an Integrated Mathematics/Science Methods Course for Preservice Elementary Teachers

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Concept to Application: Development of an IntegratedMathematics/Science Methods Course for Preservice ElementaryTeachersCarol L. Stuessy Department of Educational Curriculum and Instruction

Texas A&M UniversityCollege Station, Texas 77843-4232

Reform activities in curriculum, instruction, andassessmentare under way in mathematics and science education.Frameworks for curricular reform have been constructed by theAmericanAssociation forthe Advancementin Science (AAAS)(1989), the National Science Teachers Association (Aldridge,1991), and the National Council of Teachers of Mathematics(NCTM) (1989). Reformers in mathematics and scienceeducation are attempting to solve the problems of decreasingscores in indicators of mathematics and scientific literacy forthe general population. Declining numbers of individualsentering careers related to mathematics and science are also ofconcern. Of ultimate concern, however, is that of preparingstudents to solve the serious global problems that humans nowface--escalating population growth, destruction of naturalresources, increasingenvironmental pollution, rampantdisease,and threatening nuclear holocaust. The list is long and alarming(AAAS. 1989). There can be no doubt as to the value ofmathematical and scientific literacy in a society ofcitizens whomake decisions with consequences of global magnitude.

Although the need for reform is clear, the avenues formaking reform a reality in the classroom are not so clear. Mostagree, however, that a strong determinant of successful reformin mathematics and science teaching is reform in teacherpreparation. The NCTM (1991) recently published teachingguidelines that conform to their curriculum and evaluationstandards. New initiatives of the National Science Foundation(1992) have prioritized teacher education as needing specialattention in makingreform in science and mathematics teachingareality in theclassroom. With theencouragementofinnovationand reform looming at the national level, the time was right todesign and evaluate an innovative teacher preparation effortthat reflected recommended practice regarding the teaching ofmathematics and science.

It was in this spirit of reform that a 1-semester integratedmathematics and science methods course was developed tointroduce preservice elementary teachers to innovativemathematicsandscience teaching. Thepurpose ofthe followingarticle is 2-fold: (a) to discuss the concept of relevance as itrelates to the development ofa course that prepares elementaryteachers to be effective in teaching mathematics and scienceand (b) to describe briefly the history of the development of thecourse, which models many of the characteristics of the newstandards and recommendations for reforming the teaching of

mathematics and science.

Relevance Through the Integrationof Mathematics and Science

A movement that is gaining momentum in terms ofmakingmathematics and science more relevant is the integration ofmathematics and science teaching and learning. Severalinnovative curriculum projects, such as Voyage of the Mimi,Activities That Integrate Mathematics (AIMS), and TeachingIntegrated Math/Science (TIMS), provide mathematics andscience instruction thatiscontextualizedthrough video scenarios,computersimulations, hands-on laboratories, and/orreal-worldconcrete experience. These integrated curricula are designed tomotivate students by providing problems, projects, or topicsthat connect mathematics and science knowledge and skills.Integrated mathematics and science curricula, through the useofproblems, projects, or topics, provides an optimal setting forstudents to acquire deep understandings about the usefulness ofmathematics and science knowledge, to develop organized,deeply connected knowledge structures about naturalphenomena, and to experience learning that is collaborative andcooperative. The context of a design problem, which isintroduced to students through a videotaped simulation, forexample, provides an excellentway forstudents to worktogetherin understanding the value of mathematics as a tool for solvingthe problem and science as a concrete context for visualizingpatterns symbolized by the mathematics. Innovativemathematics and science learning contexts often advocateindividualized and/or personalized learning and teaching andpromote the use of instructional strategies that encourageparticipatory learning, active inquiry, cooperative learning, andthe development of autonomous learning strategies. As such,these contexts share commonalities with the currently popularinstructional notions ofanchored instruction (Bransford, 1991),situated knowing (Greeno, 1991), grounded knowing (Oliver,1990), situated cognition (Brown, Collins, & Duguid, 1989),and personal relevance (Yager, 1989).

An integrated curriculum designed to explicitly reveal theusefulness ofthe two domainsprovidesa synergistically uniquelearning environment. The two disciplines make distinctcontributions in terms ofknowing and interpreting (Bransford,1991). Integrated curricula provide a natural learning

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environment (Greeno, 1991) for developing modes of thoughtwhich are both versatile and powerful (Mathematical SciencesEducation Board [MSEB], 1991), including modeling,abstraction, optimization, logical analysis, inference, and theuse of symbols. Meaningful mathematical and scientificknowledge are constructed in context. New knowledge isconstructed from interactions ofthe learner with various aspectsofthe learning environment,andlearning within thatenvironmentbrings the learners own cognitive strengths and weaknessesinto play, as well as those of other learners engaged in thelearning activities. Learning science within the integratedcontext provides learners with the understanding that scientificknowledge is needed to develop effective solutions to problemsand to develop deep understandings about the biophysicalenvironment. Learners also experience the sensibility of thescientific habits ofmind involved when one considers evidence,makes logical arguments,and thinks criticallyandindependently(AAAS, 1989). Teaching less does indeed become more whenone considers how science and mathematics are taught withinthe integrated context.

Many of the preferred learning outcomes associated with thenew mathematics and science curricula emphasize theprocessesof problem finding and problem solving, among other higher-level thinking skills and abilities (Kulm & Stuessy, 1991). Theintegrated problem, project, or topic provides a natural settingfor students to use and develop the higher-level skills associatedwith enriching their sets ofconcepts and relations and offindinguseful concepts in the constructive processes of reasoning(Greeno, 1991). The framework of the problem provides aterrain for students to explore, to make new connections, and todeepen theirconceptual understandings. Traditional assessmentmeasures, such as those associated with lower-level mastery offactual information, are inappropriate forevaluating the learningthat occurs as a result of the contextualized problem, project, ortopic. Learning occurs as aresultofindividual and collaborativeinteractions with materials, resources, the teacher, and thecognitive strengths and weaknesses of other learners.

Methods recommended for assessing the learning associatedwith integrated curricula parallel those suggested in the reformfor mathematics and science education. Recommended areauthentic, non-intrusive, individualized, performance-basedmethods that document and assess the learners synergisticabilities to use domain-specific knowledge, procedures, andskills in doing tasks that require higher-level thinking. Just asthe role of assessment is central in reforming mathematics andscience learning, it is also central in reforming mathematics andscience teaching. If learning to teach science and mathematicsis to be relevant in the lives ofpreservice teachers, they must useand develop their own unique interests, skills, and knowledge.Assessment shouldbeauthentic to each individuals preparation.

Course Description

TEED 411 was developed as an integrated mathematics/

science methods course for preservice elementary teachersenrolled in a 5-year elementary teacher certification program.The course was developed either to stand alone for studentsdeclaring neither mathematics nor science as their specialtyarea or to be the first in a sequence succeeded by individualcourses in the methods ofmathematics and/or science teachingfor students declaring either or both as an area of specialty.Class meetings were scheduled for five hours per week forintegrated lecture/laboratories. The course was structuredaround eight days ofelementary classroom teaching that werescheduled during regular class meeting times. Classroomteaching was essential in providing a personally relevant,situated, grounded context for the learning activities of thecourse. Characteristics ofTEED411 as it was offered includeda strong field component, team teaching, a focus on curriculumand instructional practices that lead to relevant and usefulunderstandings about mathematics and science, a teaching andlearning context of collaborative problem solving, andperformance-based assessment.

The rationale for integrating mathematics and sciencebecame much stronger over the three semesters that the coursewasdeveloped. Initially, the need to integratemathematics andscience was purely practical. In response to newly mandatedstate guidelines restricting the number of education coursesthat a student could apply towards an undergraduate degree, a5-year teacher certification program began in the Fall of 1990.Those designing the new certification program to comply withtheserestrictions understoodin ageneral sense thatmathematicsand science were in some ways similar and that it might bepossible to teach many ofthe major pedagogical features oftheisolated mathematics and science methods courses in anintegrated fashion. The designers reasoned that the previoussix hours of mathematics methods and science methods couldbe compressed into a 3-hour integrated methods course forfifth-year certification students. Additionally, they stipulatedthat students who declared mathematics or science as theircertification specialty would be required to take an additionalmethods course within their specialty. For undergraduatestudents who did not declare a specialty in mathematics orscience, however, the 1 -semester, compressed course replacedthe 2-course requirement of the old program.

History of Course Development

The course was developed overa period ofthree semesters.With each semesters offering, attention was focused on aparticular aspect of the course. During the first semestersoffering, instructors focusedon the identificationandintegrationofmathematicsand sciencecontentandpedagogicalknowledgethat was common to both disciplines. The focus during thesecond semester was on the adoption of a field experience-based problems approach to the teaching ofthecourse. Duringthe third semester, nontraditional assessment methods wereincorporated toevaluateperformanceofthepreservice teachers

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in the class. The focus on nontraditional assessment during thesemester led to many ofthe final changes in the structure ofthecourse,whichreflects thepracticesandphilosophies associatedwiththenewthinkingaboutmathematicsandsciencecurriculum,instruction, and assessment.

The First Semester:A Focus on Content and Pedagogical Knowledge

The first semester course was designed and piloted by twoprofessors in mathematics education and science education.Contentknowledgeparticular to one or the other discipline wastaught separately by the mathematics or science educationprofessor; pedagogical knowledge appropriate for teachingboth elementary mathematics and science was taught by bothprofessors. Both professors attended all lecture/laboratorysessions, and when one professor had major responsibility forthe concepts thatwere being demonstrated, the other interactedwith students as a participant in the class. A result of the firstsemesters offering was the realization that there indeed weremany similarities in thepedagogicalknowledgeofmathematicsand science which stimulated discussions that focused on thesignificant differencesbetween the two disciplines,particularlyin the deep understanding ofthe disciplines ofmathematics andscience as particular, organized domain-specific bodies ofknowledge(Steen, 1991). Ofparticularinterestto the instructorswas the synergistic relationship that existed between theknowledge domains of mathematics and science in problem-solving situations, with mathematics often providing thelanguage for scientific phenomena, and science providing anatural context for the learning of particular mathematicsconcepts. Pedagogical knowledge appropriate for teachingmathematics and science was stressed, including anunderstanding of the developmental and other cognitivedifferences in children, an adoption of current constructivistnotions regarding misconceptions, the use of instructionalmodels that emphasize discovery and the use of hands-onmaterials, and employment of authentic assessment methods.Similarities shared by both mathematics and science reformwere also stressed: (a) teaching less as more, (b) emphasizingthe big ideas ofthe discipline, (c) stressing problem solving andother higher-level thinking activities, (d) making connectionsto the real world, and (e) integrating technology into theeducational milieu.

The Second Semester:A Focus on Transfer Problems

Another discovery of the first semester led to the adoptionofthe problems structure for the second semester ofthe course.Several times during the first semester, preservice studentswere given open-ended assignments that required them totranslate their university learning into lessons for elementaryschool children. The instructors discovered that the preservice

students showed much more interest, discussion, andinvolvementin learninghow to usenewmathematics or scienceinstructional methods and materials when their learning wastieddirectly tofieldexperienceswithelementaryschoolchildren.A recurring question was; "Will we be using this when we goout to the schools?" The real-world context of the classroomstimulated students active engagement in learning the newpedagogical knowledge that came from the laboratory of themethods class. Translating pedagogical and domain-specificknowledgeinto appropriateinstruction in theelementary schoolclassroom was a problem to be solved. Students experiencedfirst hand the old teachers adage that, "You dont really leam ituntil you have to teach it."

The general theme of teachers as problem solvers led to thesecond semesters design ofthe course. Thescopeandsequenceof the course changed from isolated topics in pedagogy to fourgeneral sections. A first section introduced students to therecommendations of the major reforms documents inmathematics and s...

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