55

Concept to Application: Development of an IntegratedMathematics/Science Methods Course for Preservice ElementaryTeachers

Carol L. Stuessy Department of Educational Curriculum and InstructionTexas 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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56Methods Course

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 learner’s 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 learner’s 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 individual’s 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 semester’s offering, attention was focused on aparticular aspect of the course. During the first semester’soffering, 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 firstsemester’s 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 don’t really leam ituntil you have to teach it."

The general theme of teachers as problem solvers led to thesecond semester’s 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 science education. Three sections followed,each structured as a classroom transfer problem, that requiredpreservice teachers to integrate their pedagogical and domain-specific knowledge about mathematics and science into thelearning environment of the elementary school classroom.

The first problem was structured to provide opportunitiesfor preservice teachers to listen to children talk as they solvedconservation problems. They used the experience to examinecommonnotionsaboutthe thinkingpatternsanddevelopmentaldifferences in children. Protocols established by Renner andMarek(1988) were used to investigate theconservation abilitiesof children at differing levels of cognitive development Thisproblem was designed to stimulate discussion regardingconstructivist viewpoints regarding learning, misconceptions,and the design of instructional models.

The second problem centered on the development ofmathematics problem-solving activities that were meaningfulin terms of teaching mathematical thinking (MSEB, 1991;NCTM, 1991). Pairs ofpreservice teachers designedproblem-solving activities using mathematics manipulatives forelementary school children at grades one, three, and six. Eachpair piloted the activities with a small group of four or fivechildren at each of three levels. They also assessed theeffectiveness of their teaching and the extent of their students’learning using authentic assessment methods.

The third problem focused on designing a problem-solvinginstructional sequence that integrated scientific andmathematical knowledge, strategies and skills (Alexander,Pate, Kulikowich, Farrell, & Wright, 1989). In this problem,preservice teachers first completed three inquiry problemsrelatedtoflyingobjects.includingparachutes,paperhelicopters,andpaperairplanes. Pairs ofstudents thenplanned,piloted, andevaluated a 2-day problem-solving instructional sequence thatinvolved the direct transfer of what they had learned aboutflying objects to a small group of five or six elementary schoolsixth-grade students.

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58Methods Course

The Third Semester:A Focus on Authentic Assessment Methods

As the planning for the third semester of the course began, itbecame apparent that the outcomes associated with TEED 411indeedwere very different from those ofpasttraditional methodscourses in mathematics and science. There was evidence fromthe second semester that students’ involvement in the teachingtransfer problems facilitated the development of unique, deepunderstandings about the domains of mathematics and scienceknowledge and their appropriateintegration with newly acquiredpedagogical knowledge. Knowledge and skills in solving theteaching problems appeared to develop and improve graduallyover the courseofthe semester but the attempts to documentandassess the changes were basically unsatisfactory. Courseinstructors were faced with the dilemma of many classroomteachers who teach problem solving�how best to design anassessment to reflect the unique outcomes associated with theproblem-solving format.

Recommendations (e.g.. Champagne, Lovitts, & Calinger,1990; Kulm, 1990; Kulm & Malcom, 1991) for the assessmentofhigher level thinking skills in mathematics and science guidedthe design of the assessment for students enrolled in the thirdsemesterofTEED411. Notionsthatassessments for mathematicsand science learning should reflect a focus on broad conceptualunderstanding, problem solving, and habits of thinking wereapplied to the design ofanassessmentforthecourse. Underlyingthe design was an understanding of this type of learning asindividualistic and dependent upon experience and motivation,involving the construction ofconnections with related conceptsand experiences, and developing gradually within the problemscontext. Kulm and Stuessy (1991) recommended thatassessmentofthis type oflearning in mathematics andscience be continuous,sensitive to individual differences, and open-ended enough to becapable of reflecting deep and broad understanding. Theproblems approach ofTEED411 also suggested that alternativeassessment methods were needed to identify, evaluate, andsupport the unique learning outcomes resulting from theintegrated focus of the course.

Performance assessment (Baron, 1990) was adopted as anappropriate method for assessing students’ progress through thecompletion of the three problems, with the use of portfolios(Biddle & Lasley. 1991; Collins, 1991) as vehicles foraccumulating and organizing the products associated with eachof the teaching transfer problems.

Performance assessment. Learning activities within eachof the three problems were labeled as tasks (seeFigure 1). Taskswere chosen to fostercritical inquiryandproblem solving withinthe context of teaching elementary school science. The taskswere embedded within a standard inquiry format (Lunetta &Novick, 1982), which was designed to carry the science studentthrough an inquiry sequence of Planning and Designing,Performance, Analysis and Interpretation, and Application.

This sequence was used for each of the three teaching transferproblems, with the exception that the Application phase ofthestandard inquiry format was replaced with Critical Reflection.The learning tasks associated with each phase providedexperiences for preservice teachers to construct and usepedagogical content knowledge, a type of knowledgecharacterizedbyShulman (1986)as unique to teachersinvolvingthe integration or synthesis of their pedagogical knowledgeand subject matter knowledge.

Figure 1 also lists the products suggested for each of thetasks. Theproducts were scored analytic-holistically (Randall,Lesser, & O’Doffer, 1987). Scoring rubrics for each productwere developed collaboratively by the two professors and theteaching assistant assigned to assist in the course. Initially, theinstructional team carefully examined the products, whichwere contained as a set within a student portfolio. Descriptivestatements were written by the team for each product to reflectthe quality of the product. Each statement reflected consensusregarding the quality of 4, 3,2, and 1 products. In each case,a 0 indicated that the product was absent. In some of thesimplerproducts (e.g., a lesson sequence), therubrics consistedonly of4 and 1 or 0 statements. Products were then scored ona scale from 0 to 4. Figure 2 provides examples of scoringrubrics and their associated scores that were developed forthree of the products in the first problem. Table 1 provides adistribution of students’ raw scores on the twelve productsassociated with the first teaching transfer task that wereaccumulated in Portfolio One.

Portfolios. Portfolios held the records and productsassociated with each of the problems. Although products foreach ofthe tasks were suggested by the instructors, the studentdetermined the sequence andpresentation oftheproducts in thefinal preparation of the portfolio. Some products in theportfolio required students to show evidence of analysis,synthesis, and reflection of the teaching transfer experience.The portfolio therefore provided a veliicle for students toreflect on their journey through the solution of the teachingproblem. The portfolio also focused the attention of thelearners, as well as the instructors, on standardizedproducts forthe course that were specifically identified and thereforetrackable throughout the three problems of the course. Areasof difficulty were identified by instructors as tasks werecompleted within the instructional sequences of the problemsand led to the structuring of specific learning and instructionalstrategies to correct difficulties in task performance. After thecompletion ofthe first portfolio, for example (see Table 1), theinstructors designed an assignment to allow students moreexperience with tasks 7 and 9. High numbers of scores below3 on those particular tasks indicated to the instructors thatspecial classroom experiences wereneededto improve students’understanding of the tasks.

Grading. A system was developed to determine letter

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Methods Course

Figure 1. Tasks and products included in the portfolios/or each transfer problem.

TasksPlanning and Designing

Products

Plan and CalendarAbstracts & Reflection Questions

Laboratory CheckpointsLesson Sequence

Records (e.g., videotapes, observer scripts)Evidence of Student Learning

Written Descriptions, Graphs, Visual RepresentationsConclusion Statements

Written Synthesis

1. For each problem develop an overall plan.2. Acquire essential content-specific and

pedagogical knowledge related to the problem.3. Develop skills essential for the in-school problem.4. Design the in-school sequence.Performance5. Teach the in-school lesson sequence.6. Collect data from students in the school environment.Analysis and Interpretation7. Analyze your teaching records and student data.8. Make conclusions regarding: (a) your teaching

and (b) students’ learning.9. Relate pertinent literature (see 2 above)

to the in-school problem.Critical Reflection10. Reflect on your own learning experiences,

identify your own conceptual changes andnew learning.

Journal Entries. Journal Synthesis

11. Evaluate the overall effectiveness of Evaluative Statementthe teaching experience.

Overall Quality of Portfolio12. Develop a portfolio that is appropriate,

organized, and complete.

Figure 2. Sample protocols developed to reflect the quality of products for the tasks in Problem One.

Planning and DesigningTask 1: For each problem, develop an overall group plan.Product: Plan and CalendarScores:

4 = Dates and times are explicit, and plan is specific3 = Dates and times are present, but what was done is not specific2 = Calendar is present, no evidence of planning0 = Neither calendar nor plan is included

Analysis and InterpretationTask 7: Analyze your teaching records and student data.Product: Graph of Student DataScores:

4 = Graph of data is representative and shows relationships within the data3 = Graph is appropriate, but there are few relationships shown2 = Graph is not appropriate but it is present1 = Evidence that there are some attempts made to quantitatively analyze and/or synthesize the data0 = No graph and no analysis/synthesis

Critical ReflectionTask 11: Evaluate the overall effectiveness of the teaching experience.Product: Evaluative StatementScores:

4 = A formal evaluative synthesis of the teaching experience was made3 = There is some evidence of periodic or summative evaluative activity0 = There is no evidence of evaluative activity

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Methods Course60

Table 1

Raw Scores and Distributions of Tasks and Products Associatedwith Problem One

Student

12

34567891011121314

Tasks

1234

44443444

444444443444244424444444444444443444444444443444

Tai

5

44

424434344444

sks

6

24

023424430442

Ta

7

32

424314133432

isk

8

00

320414300340

s

9

43

242422230024

Tas

10

42

342433240342

sks

11

43

433434303334

Task I

12

22

444443342244

^aw Score Distributions

43210

8120153301

82101813006320110 1 1 0 04332092100542107300243104740019210071301

Letter Grade

AB

AABACABBCBAB

grades based on the total number of 4s, 3s, 2s, and Is a studentreceived during the semesteron the three portfolios and the finalexamination. Table 1, which presents a summary of thedistributions of scores for Problem One, gives an example ofhow the grading system was devised. The requirement for an Aportfolio on Problem One was that students receive at least eight4 scores; B portfolios must receive at least eight 4 and 3 scores;and C portfolios must receive at least eight 4, 3, and 2 scores.The grade distribution oftheclass on Problem Onewas thereforesix As, six Bs, and two Cs. The required number of scores waschanged to 10 for Portfolios Two and Three, and the requirednumber was 8 for the final examination. The final examinationconsisted of 12 items and required students to use data from theproducts of the three problems to answer self-evaluative,reflective questions about their teaching and learning during thesemester. Students’ answers to the examination questions alsowere scored analytically-holistically by the teaching team. Theoverall awardingoflettergrades for the semesterwasdeterminedby total number of 4s, 3s, 2s, and Is on the three portfolios andthe final examination. An A required at least thirty-six 4s, a Brepresented at least thirty-six 4s and 3s, and so on.

Course Evaluation

Three sources of data were used in the third semester ofimplementation as indicators of the relevance of TEED 411 inpreparing preservice teachers to teach mathematics and science,as follows: (a) paper-and-pencil, multiple-choice measures ofstudents’ self-efficiacy in teaching mathematics and science; (b)student performance data, as measured by the three portfoliogradesand the final examination; and (c) students’ exitresponsesfrom informal interviews and departmental course evaluations.

Students’ self-efficacy in the teaching of science wasmeasured using the Science Teaching Efficacy BeliefsInstrument(STEBI)(Riggs&Enochs, 1990). TheMathematicsTeachingEfficacy Beliefs Instrument(MTEBI) wasdevelopedfrom the science measure simply by replacing the wordsscience and experiment appearing in the items on the STEBIwith mathematics and manipulatives. Pre-test reliabilities,calculatedas Cronbach’s alpha, for the scienceandmathematicsinstruments were 0.72 and 0.12, respectively. Posttestreliabilities on the STEBI and MTEBI were 0.94 and 0.92,respectively. The very low reliability on the mathematics pro-measure may have indicated that students were unfamiliar atthe beginning ofthe course with the term manipulative that wasused in the MTEBI to replace the more familiar experiment inthe STEBI. A high posttest reliability for the MTEBImay haveindicated that students were much more familiar with the termat the end of the semester. Correlated Mests indicatedsignificant differences in the means for pre- and posttests onthe science measure (M = 82.92 and M = 90.64) and on themathematics measure (M=81.42andM=94.71),r(13)=2.72,p < 0.008 and f(13) = 3.22, p < 0.0035, respectively.

Student performance data on the three teaching transfertasks(see Table 2) indicate that 11 of 14 students scored more3s and4s on Portfolio Three than they scored on Portfolio One.Two students (Nos. 2 and 13) had the same number of 3s and4s on both portfolios and one student (No. 6) received lowerscores on Portfolio Three. Overall, the students in the classdemonstrated higher performance on all tasks associated withthe teaching transferproblems. Additionally, the high numbersofAs andBson the final exam indicated that studentswereableto answer questions requiring students to use higher-levelthinking skills of analysis and synthesis.

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Methods Course61

Table 2

Distributions ani

Student

1234567891011121314

d direction of change in scon

N

Portfolio One

43210

812015330182101813006320110 1 1 0 04332092100542107300243104740019210081201

esfor students on Portfolio.umbers of Scores in Each C

Portfolio Two

43210

91110722019300011 1 0 0 010 1 1 0 06130211100012 0 0 0 012000

12 0 0 0 012 0 0 0 0541116500193000

? One, Two, and 7

category

Portfolio

4321

7320531112 0 0 010 1 1 08300522082008400910011 1 0 012 0 0 011 1 0 010 1 1 011 1 0 0

’hree

Three

0

02001320200000

Change*

+=+++-++++++==+

"Direction ofchange is a measure ofthe difference in total numbers of categories4 and 3 on Portfolios One andThree as indicated:positive change (+), no change (=), negative change (-)

Interviews conducted by the instructors at the end of thesemester with each of the students indicated high levels ofsatisfaction with the course in terms ofpreparing them to teachmathematics and science in the elementary school. Manystudents agreed that the course was very demanding in time.Responses on the departmental evaluation forms were similarregarding expressions ofinterest in the contentofthe course andconcerns about time demands.

These sources of evaluative data indicated that TEED 411was a very successful teacher preparation course. Scores on thescience and mathematics teaching efficacy beliefs instrumentsshowed significant positive gains in students’ beliefs aboutthemselves as successful teachers of mathematics and science.Comparison offinal and initial portfolio scores indicated higherlevels in performanceon tasks specifically related to the teachingofmathematics and science in the elementary school classroom.Student satisfaction with the course was also high, as indicatedby exit interviews and departmental evaluation forms. Uponthe basis of these data, TEED 411 was judged to be highlyrelevant in preparing preservice elementary teachers to teachmathematics and science.

Conclusion

The place ofan integrated mathematics and science methodsclass within the sequence of a preservice teachers’ training hascontinued to be a point of discussion by those, involved indeveloping the course, as well as by interested bystanders who

teach the traditional elementary science and mathematicsmethods courses. Some think that such a course should beoffered as the first in a sequence that also includes individualmethods classes in both mathematics and in science. Othersprefer the placement of the course as last in the sequence. Stillanother viewpoint is that the integrated mathematics and sciencemethods course is more appropriate for graduate learners and/orexperienced teachers who arereturning foradvancedmethodsof teaching mathematics and science. Most discussants agree,however, that an integrated methods course should enhance andnotreplace traditional methods courses that have the purpose ofproviding a pedagogical focus to the separate and uniqueconcepts, processes, and attitudes associated with the teachingand learning of the knowledge domains of mathematics andscience.

Content goals of integrating the teaching and learning ofmathematics and science in TEED 411 were for preserviceteachers to: (a) experience successful mathematics and scienceteaching in the real world context of the elementary schoolclassroom and (b) view the role of the teacher of mathematicsand science as a problem solver who designs instruction thatencourages learners to identify, access, leam andapply scientificand mathematicalknowledgewithin contexts thatrequire higher-level thinking skills. A contextual goal was that TEED 411provide a learning environment for preservice teachers todevelop the concept of integrated mathematics and scienceteaching and to apply it in the elementary school classroom.The problems format and emphasis on similarities, differences,

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62Methods Course

and complementary aspects of mathematics and scientificknowledgeprovidedachallenging,relevantlearningenvironmentfor learning how to teach mathematics and science. Theperformance/portfolio methods used to evaluate the preserviceteachers’ learning reflected the nature of the teachers’ ultimatetasks in the classroom-to plan, perform, analyze, and reflect ontheir own teaching. As such, the assessment was authentic tolearners/teachers who shared an understanding of the methodsclass as a learning environment where teaching is viewed as aninquiry process. In Cochran-Smith’s (1991) words, the design ofthe course was to provide opportunities for students to "createcritical dissonance... to help students broaden their visions anddevelop the analytical skills needed to interrogate and reinventtheir own perspectives" (p. 282). Instructors involved inteaching TEED 411 would agree that the course resulted in thissort of learning, with experiences and outcomes that are uniqueto the integrated aspects of mathematics and science teachingand learning.

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