science inservice workshops that work for elementary teachers

5
422 Science Inservice Workshops That Work for Elementary Teachers Thomas 0 ^Brien School of Education and Human Development State University of New York at Binghamton Binghamton, New York 13902-6000 Nowhere is the need for quality inservice education more urgent than for elementary teachers of science. Efforts to enhance the scienceknowledge, teaching skills, and attitudes of elementary teachers should be based on accurate assessment of their characteristics. A recent nationwide survey (Weiss, 1987) found that our nation’s 1.3 million elementary teachers are fairly homogeneous with respect to ethnicity and gender. They are predominantly white (82% of K-3 and 86% of 4-6 grade teachers) and typically female (94% of K-3 and 76% of 4-6 grade teachers). Diversity issues aside, this same survey found that elementary teachers do not feel well-qualified to teach science (23% report this as a problem for the physical sciences), have had little recent science inservice education (50% report 0 hours and 22% report less than 6 hours in the last year), and have years of potential service remaining (80% are less than 50 years old). Add to these three factors, elementary teachers’ weak college science backgrounds, inadequate school budgets, curricula that deemphasize science, and an expanding science- technology knowledge base, and the result is the generally acknowledged low quantity and quality of elementary science education (Tilgner, 1990). The personal, social, and economic consequences of this problem have been cited in numerous reports (e.g., Gardner. 1983; Coleman & Selby, 1983). The National Center for Improving Science Instruction (1989) has outlined an alternative. Its blueprint calls for elementary schools to devote between two and five hours (grades K-3 and4-6,respectively)perweek to science instruction that is: (a) inquiry-based; focusing on the identification and resolution of questions and problems, (b) interdisciplinary and relevant to students’ lives, (c) comprehensible via direct, hands- on explorations of phenomena and social interactions, (d) designed to promote active, minds-on construction of fundamental conceptual themes, process skills, and attitudes, and (e) assessed via formal and informal, diagnostic, formative and summative evaluation techniques (including hands-on performance tasks) (Kulm & Malcom, 1991). Quality elementary science curricula acknowledge, engage, and sharpen childrens’ innate curiosity, conceptualization, and appreciation of the natural and technological worlds and foster informed decision-making about the interactions between the two. Clearly, elementary science curricula that meet thesecriteria are not teacher-proof-the individual teacher is a key instructional variable (Stake & Easley, 1978; DeRose, Lockard, & Paldy, 1979). Therefore, the bridge connecting the real to the ideal world needs to be built on quality staff development and support (Bethel. 1985; Harty & Enochs, 1985; Spector, 1987). The National Science Foundation’s teacher enhancement grants, Title II of the Education for Economic Security Act, teacher centers, professional societies and science-technology industries interested in elementary science are all forces that are striving to bridge the gap (Brinckerhoff, 1989; Yager, 1988). Yet even with adequate funding, designing relevant, well- attended, on-going elementary science inservice programs requires a mixture of creative advertising, pedagogical science, the performing arts, and a dash of luck. The exact ingredients and proportions will vary depending on the specific audience, scheduled time, site, funding level, presenters, and intended purpose. Thefollowing summarizes adultand teacher education research and provides practical tips to help inservice education leaders design their own unique recipes for successful elementary science staff development. Principles of Adult Education The need for lifelong learning has become increasingly compelling in the ever-changing, high-tech business world. Both the numbers of students trained and the money spent on human resource development rival or exceed that of many public education systems. Effective training is guided by the belief that adults: (a) leam best when they understand why they need to know or be able to do something; (b) have a need to be self-directing and may resist being taught unless they are involved in setting objectives; (c) have a greater volume, richer quality and heterogeneity of experiences than children; and (d) are motivated by enhanced self-esteem and job satisfaction as much as by external factors like promotions and higher salaries (Knowles, 1984). Although adults maybe conditioned to more traditional pedagogy, transfer of training to the job site requires attention to helping the learner leam how-to-leam rather than merely transmitting content. Research on Inservice Education Training Components Meta-analyses of inservice education research (Joyce, Showers. & Bennett 1987; Sparks 1983; Wade 1984/1985; Yeany & Padilla. 1986) have found that including each of the following components maximizes training effectiveness: (a) a diagnostic/prescriptive phase to build awareness within the teachers of the need for change, (b) presentation of theory/ School Science and Mathematics

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Science Inservice Workshops That Work for ElementaryTeachersThomas 0^Brien School of Education and Human Development

State University of New York at BinghamtonBinghamton, New York 13902-6000

Nowhere is the need for quality inservice education moreurgent than for elementary teachers of science. Efforts toenhance the scienceknowledge, teaching skills, and attitudes ofelementary teachers should be based on accurate assessment oftheir characteristics. A recentnationwide survey (Weiss, 1987)found thatournation’s 1.3 million elementary teachers are fairlyhomogeneous with respect to ethnicity and gender. They arepredominantly white (82% of K-3 and 86% of 4-6 gradeteachers) and typically female (94% of K-3 and 76% of 4-6grade teachers). Diversity issues aside, this same survey foundthat elementary teachers do not feel well-qualified to teachscience (23% report this as aproblem for thephysical sciences),have had little recent science inservice education (50% report0 hours and 22% report less than 6 hours in the last year), andhave years ofpotential service remaining (80% are less than 50years old). Add to these three factors, elementary teachers’weak college science backgrounds, inadequate school budgets,curricula that deemphasize science, and an expanding science-technology knowledge base, and the result is the generallyacknowledged low quantity and quality of elementary scienceeducation (Tilgner, 1990). The personal, social, and economicconsequences of this problem have been cited in numerousreports (e.g., Gardner. 1983; Coleman & Selby, 1983).

The National Center for Improving Science Instruction(1989) has outlined an alternative. Its blueprint calls forelementary schools to devote between two and five hours(gradesK-3 and4-6,respectively)perweek to science instructionthat is: (a) inquiry-based; focusing on the identification andresolution of questions and problems, (b) interdisciplinary andrelevant to students’ lives, (c) comprehensible via direct, hands-on explorations of phenomena and social interactions, (d)designed to promote active, minds-on construction offundamental conceptual themes, process skills, and attitudes,and (e) assessed via formal and informal, diagnostic, formativeand summative evaluation techniques (including hands-onperformance tasks) (Kulm & Malcom, 1991). Qualityelementarysciencecurricula acknowledge, engage,and sharpenchildrens’ innate curiosity, conceptualization, and appreciationof the natural and technological worlds and foster informeddecision-making about the interactions between the two.

Clearly, elementary science curricula that meet thesecriteriaarenotteacher-proof-theindividual teacher is akey instructionalvariable (Stake & Easley, 1978; DeRose, Lockard, & Paldy,1979). Therefore, the bridge connecting the real to the idealworld needs to be builton quality staffdevelopmentand support

(Bethel. 1985; Harty & Enochs, 1985; Spector, 1987). TheNational Science Foundation’s teacher enhancement grants,Title II of the Education for Economic Security Act, teachercenters, professional societies and science-technologyindustries interested in elementary science are all forces that arestriving to bridge the gap (Brinckerhoff, 1989; Yager, 1988).Yet even with adequate funding, designing relevant, well-attended, on-going elementary science inservice programsrequires a mixture ofcreative advertising, pedagogical science,the performing arts, and a dash of luck. The exact ingredientsand proportions will vary depending on the specific audience,scheduled time, site, funding level, presenters, and intendedpurpose. Thefollowing summarizes adultand teachereducationresearch and provides practical tips to help inservice educationleaders design theirown uniquerecipes forsuccessful elementaryscience staff development.

Principles of Adult Education

The need for lifelong learning has become increasinglycompelling in the ever-changing, high-tech business world.Both the numbers of students trained and the money spent onhuman resource development rival or exceed that of manypublic education systems. Effective training is guided by thebelief that adults: (a) leam best when they understand why theyneed to know or be able to do something; (b) have a need to beself-directing and may resist being taught unless they areinvolved in setting objectives; (c) have a greater volume, richerquality and heterogeneity of experiences than children; and (d)are motivated by enhanced self-esteem and job satisfaction asmuch as by external factors like promotions and higher salaries(Knowles, 1984). Although adults maybe conditioned to moretraditional pedagogy, transfer oftraining to thejob site requiresattention to helping the learner leam how-to-leam rather thanmerely transmitting content.

Research onInservice Education Training Components

Meta-analyses of inservice education research (Joyce,Showers. & Bennett 1987; Sparks 1983; Wade 1984/1985;Yeany & Padilla. 1986) have found that including each of thefollowing components maximizes training effectiveness: (a) adiagnostic/prescriptive phase to build awareness within theteachers of the need for change, (b) presentation of theory/

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Science Inservice Workshops423

concepts to give teachers the background on what it is that theyare to leam and why (i.e., its outcome in terms of improvedteaching/learning relative to the costofthe change), (c) modelingor demonstrations by skilled trainers of the techniques andbehaviors trainees are toacquire, and (d) practiceunder simulatedconditions with feedbacksuch as microteaching androleplaying.Programs designed around these four elements are much moreeffective than the "spray and pray, hit and run" lecture variety.In addition to these training components, Joyce and Showers(1983) arguethatfollow-up and coaching in theactual workplacewith teachers helping teachers via peer feedback,companionship, and modeling is essential.

The Concerns-Based Adoption Model (CBAM)and Teacher Change

In theearly 1970s, theResearch and DevelopmentCenter forTeacher Education at the University of Texas-Austin beganstudying the role of teacher concerns (i.e., the composite of thefeelings, preoccupations, thoughts, and considerations) in theadoption and use of various innovations. CBAM’s underlyingphilosophy andassociated research instrumentsprovidea usefulframework and diagnostic tools for inservice design andevaluation (Hord, Rutherford, Huling-Austin, & Hall, 1987).CBAMresearch supports the following beliefs (Hall, 1979):1. Change within schools is a process that takes time and

intervention strategies, not just an administrative decision orevent.

2. The primary focus of intervention aimed at classroomchange should be the individual teacher.

3. Change is a highly personal experience where teacherperceptions and feelings are at least as important as theinnovation’s trappings and technology.

4. Teachers move through developmental Stages ofConcernand Levels of Use with respect to the innovation.

5. A good operational description of the innovation is a keyto success with intervention efforts.

6. Inservice programs using a client-centered, diagnostic,prescriptive model geared to teachers’ Stages of Concern andLevels of Use profiles best facilitate change.

7. The change facilitator must work in an adaptive fashionassessing the change effort as it evolves.

Although not specifically developed for studying scienceeducation innovations, CBAMinstrumentshaveproven valuablein curriculum implementation and staff development efforts.James and Francq (1988) and James and Hord (1988) provideoverviews of the use of CBAM in this particular context.

Practical Implicationsfor K-6 Science Teacher Workshops

Elementary teachers are typicallyoverburdenedwith multiplecourse preparations, management tasks, extracurricularresponsibilities, and the challenges of increasingly diverse

studentpopulations (including especially,moreat-risk students).Some may have experienced science inservice workshopswhose quality did not merit their time. A few may haveunprofessional attitudes about the importance of science andinservice education. These factors along with the low prioritygiven to science in most elementary schools make it difficult toinitiate science inserviceprograms. Although it is not practicalto give a single, universal recipe for success. the aboveresearchsuggests designers/presenters of K-6 science inserviceprograms should consider the following guidelines.

Maximizing Attendanceat Voluntary Inservice Programs

1. Begin by presenting at a well-established conference(i.e., superintendents’ day, state or regional science teacherconferences) to build contacts and a receptive audience forfuture workshops. Don’t overlook popular, non-scienceconferences such as those on whole language, mathematics,and other areas that encourage integration across disciplines.

2. Seek out co-sponsors such as teacher centers, universityscienceand scienceeducation departments, local scienceteacherassociations, science museums, professional scienceorganizations, science-technology industries, etc. Involvelocal elementary teachers in theneeds assessmentand planningprocess to ensure relevance, ownership, and follow-up.

3. Advertise a minimum of six weeks in advance. Sendnotices to individual teachers or at least to individual schoolsand teacher centers. Encourage principals to participate bothfor the training they’ll obtain and the message it sends to theirteachers. Make the announcement visually appealing and theregistration form simple to complete and easily duplicated.

4. Provideincentives foradvanceregistration and attendance(i.e., free calculators, science education magazines, and doorprizes for early registrants; resource materials, district fundsfor supplies, inservice credits, and/or monetary incentives forall attendees). When possible, negotiating one-halfto full-dayrelease time sends a clear signal that elementary science andprofessional development arevalued. After-school or Saturdayprograms can net good participation if the groundwork hasbeen laid. Optimally, a mix ofpersonal time and release timeis needed to establish an on-going support network forelementary science.

5. If the time schedule permits, offer a variety of types ofsessions geared to a range of grade levels instead of a one sizefits all type program. "Make-and-take, leam-it-today, teach-it-tomorrow" sessions that directly address the issue ofclassroompracticality ("Butwhatcan I do with iton Monday?")are especially popular. Sessions that require expensive (andtherefore unreplicable formany teachers),commercial materialsshould bekept to a minimum relative to those that use low-costhousehold supplies, improvised equipment, and toys. Catchy,clever session titles and descriptions also help.

6. Set registration limits on the size of each session that

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reflect the degree of active participation the presenters requestand that encourage pre-registration.

7. Include at least some presenters who are known andrespected by teachers in your area. Try to confirm the qualityof any unknowns before putting them on the program.

8. Advertise thatpresenters will providehandouts describingtheir session’s activities. This assures teachers that they won’thave to scramble to copy ideas but instead will be able toactively participateknowing theyhavetheinformationnecessaryfor classroom implementation.

9. Try to get a co-sponsor to provide food and refreshments.If necessary, however, a small registration fee can sometimesbe an incentive for participation if the program is clearlyadvertised as a great buy.

10. Drafta letterto send tobuildingprincipalsacknowledgingthe participation of (heir teachers and encouraging them toprovide post-workshop support.

Design and Deliveryof Individual Workshop Sessions

Workshops should provideparticipants with theopportunityto work with and shop for ideas, materials, and resources. Theyshould reflect what is known about science and learning. Thatis: (a) science is a process for interacting with, understanding,and appreciating the natural world, notjust a collection of factsand (b) learning is an active process ofconceptual construction(and reconstruction) that is facilitated by hands-on/minds-onactivities and social interaction.not the passive absorption ofprepackaged knowledge (Osborne & Freyberg, 1985).Increasing teachers’ pedagogical contentknowledge (Shulman,1987) requires integrating science content with teachingmethodologies and theory (Cochran, 1991). For maximumeffectiveness, workshops should be designed and delivered ina manner that:

1. Recognizes and acknowledges teachers as fellow adultprofessionals with individual need, and attempts to meet themwhere they are. Elementary teachers’ prior knowledge andattitudes about science and science teaching often result in lowself-confidenceand limited involvement with science teaching.Yet. ifthey are encouraged to askquestions and feel comfortablewith not knowing all the answers, their basic student-centered,motivational teaching strategies lead them to embrace hands-on/minds-on science. Icebreaking activities that encouragelow-risk sharing ofconcerns are effective, especially when timeconstraints prevent formal pre-workshop assessment. Typicalstrategies include a quick poll of participants’ experience withand attitudes about teaching science; brief, small groupdiscussions highlighting barriers to science teaching; or the useof puzzles, analogies, cartoons, anecdotes or discrepant eventdemonstrations to motivate reflection about personal anxieties.

2. Reflects your enthusiasm and seeks to sell the philosophyofactive, participatory,cooperativelearning (Johnson.Johnson,Johnson-Holuber, & Roy, 1984) by way of example. The first

five minutes ofthe workshop are crucial in terms ofestablishingpatterns of social interaction and group expectations. Laughterand activity are contagious, the antithesis of apathy anduninvolvement, and effective means of enrolling participants.

3. Addresses informational and personal concerns beforeproviding detailed management and consequence information.If the group is highly diverse in terms prior experience withscience, splityourpresentation toprovideformoreindividualizedoptions.

4. Highlights both the similarities and differences betweenteaching science and other content areas. Demonstrate thebenefits of integrating science into their existing curriculum(Farmer & Farrell, 1989; Haves-Jacobs, 1989) without anoversell that sets up their pastpractice as being wrong. Respectthe teachers as caring professionals who want to provide aquality learning environment for their students. Aidingdevelopmental growth rather than deficit correction is the goal(McLaughlin & Berman, 1977).

5. Models effective teaching strategies and materialsmanagement techniques (O’Brien, 1991). Practice what youpreach in termsofenergy, interactive teaching, and organization.Constructivist-oriented instructional models (such as theBiological Sciences Curriculum Study’s engagement,exploration, explanation, elaboration, and evaluation or theSCIS learning cycle) can be especially effective insimultaneouslypromotingknowledgeaboutscienceandscienceteaching (Bybee&Landes, 1990; Lawson, Abraham, &Renner.1989; Loucks-Horsley et al.. 1990). Provide multipleopportunities for hands-on/minds-on activities that relate to thebroader conceptual themes of science and convey that teachingand learning science is fundamental. Remember all threesensory elements of the Chinese proverb, "I hear and I forget,I see and I remember, I do and I understand."

6. Seeks to build a sense of community and sharedresponsibility for learning and teaching by encouragingquestioning, risk-taking, experimentation, and collaborativeproblem solving. Day-long, focused programs are especiallyeffective in that they allow sufficient time for individual orteam microteaching, group feedback sessions, and post-workshop peer planning.

7. Provides information on how to access other free or lowcost resources and professional organizations such as theNational Science Teachers Association and the School Scienceand Mathematics Association.

8. Counters feelings ofpassiveconsumerismbyencouragingteachers to share ideas, activities, and resources (children’stradebooks, sourcebooks, etc.) in scheduled swap shops and/orinformally during breaks and mealtimes.

9. Begins to build a local support network for elementaryscience. Where possible, encourage teachers to develop peercoaching as a means of post-workshop professionaldevelopment. Minimally, provide participants with a roster ofnames and professional addresses and phone numbers.

10. Includes a workshop evaluation that addresses the

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evolution of teacher concerns, issues of relevance andeffectiveness, andexplores ideas forfollow-up. Identify teachersinterested in becoming involved in future programs.

Increasing Net Work(shop) Efficiency

Science inservice workshops informed by research can andshould work to serve the needs of elementary teachers-needsthat go well beyond one-shot, motivational events that entertainand provide grab bags of unrelated tricks. Enhancing thequantity and quality ofK-6 science education is a multi-facetedproblem thatrequires on-going, collaborativepartnershipsamongteachers, parents, schools, teacher centers, universities, science-technology industries, and other community groups (Atkin &Atkin, 1989; Eitinge & Glass, 1988). Local, regional, andnational support networks are needed to change school culturesthat implicitly, by lack of attention, deemphasize the place ofscience and related staff development in the elementary school.The National Center for Improving Science Education, theTriangle Coalition (affiliated with NSTA), and professionalscience organizations provide practical tips for multiplying thenetwork of those concerned with conveying the message thatscience is elementary and fundamental for all children (andtheir teachers).

References

American Association for theAdvancement ofScience. (1989).Science for all Americans: Project 2061. Washington, DC:Author.

Atkin, J.M..& Atkin, A. (1989). Improving science educationthrough local alliances. Santa Cruz, CA: NetworkPublications.

Bethel.L.J. (1985). Science teacherpreparation and professionaldevelopment. In D. Holdzkom & P. Lutz (Eds.), Researchwithinreach: Science education (pp.143-157). Washington,DC: National Science Teachers Association.

Brinckerhoff.R.F. (1989). Resource centers serve the needs ofschool science teachers. School Science and Mathematics,89,12-18.

Bybee, R. W., & Landes, N. M. (1990). Science for life andliving: An elementary school science program fromBiological SciencesCurriculum Study. TheAmericanBiologyTeacher, 52(2). 92-98.

Cochran,K.F. (1991). Pedagogical contentknowledge: Teachers’transformations ofsubject matter. Reprinted inNARSTNews,33(3), 7-10.

Coleman,W. T. Jr., & Selby, C C. (1983). Educating Americansfor the 21st century. Washington, DC: National ScienceFoundation.

DeRose. J. V., Lockard. J. D.. & Paldy, L. G. (1979). Theteacher is thekey:AreportofthreeNSFstudies. The ScienceTeacher, 46(4), 31-37.

Eitinge, E.M..& Glass, L.W. (1988). Meeting modem science

education goals through partnerships. School Science andMathematics, 88, 16-23.

Farmer, W.A.,&Farrell,M.A. (1989). Activitiesfor teachingK-6 math/science concepts, Bowling Green, OH: SchoolScience and Mathematics Association.

Gardner, D.P. (1983). A nation at risk: The imperative foreducational reform. Washington, DC: US Department ofEducation

Hall.G.E. (1979). Theconcerns-basedapproach for facilitatingchange. Educational Horizons, 57.202-208.

Harty, H., & Enochs, L. (1985). Towards reshaping theinservice education of science teachers. School Scienceand Mathematics, 85,125-135.

Haves-Jacobs, H. (Ed.). (1989). Interdisciplinary curriculum:Design and implementation. Alexandria, VA: Associationfor Supervision & Curriculum Development.

Hord. S.M.. Rutherford. W. L., Huling-Austin. L., & Hall. G.T. (1987). Taking cfiarge of cfiange. Alexandria, VA:Association forSupervision and Curriculum Development.

James, R. K., & Francq, E. (1988). Assessing theimplementation ofa science program. School Science andMathematics, 88,149-159.

James,R.K..& Hord, S.M. (1988). Implementingelementaryschool scienceprograms. School Science and Mathematics,88, 315-334.

Johnson,D.W.,Johnson,R.T.,Johnson-Holuber,E..andRoy,P. (1984). Circles oflearning.’cooperation in the classroom.Alexandria, VA: Association for Supervision andCurriculum Development.

Joyce, B., & Showers. B. (1983). Power in staff developmentthroughresearchon training. Alexandria, VA: Associationfor Supervision and Curriculum Development.

Joyce. B..& Showers, B..&Bennett,B. (1987). Synthesis ofresearch on staff development: A framework for futurestudy and a state-of-the-art analysis. EducationalLeadership, 45(3), 77-87.

Knowles.M. S. (1984) The adult learner: A neglected species.(3rd ed.). Houston. TX: Gulf Publishing Co.

Kulm,G..&Malcom,S.M.(Eds.). (1991). Science assessmentin the service of reform. Washington, DC: AmericanAssociation for the Advancement of Science.

Lawson, A. E.. Abraham, M. R.. & Renner, J. W. (1989). Atheory of instruction: Using the learning cycle to teachscience concepts and thinking skills. Cincinnati, OH:National Association for Research in Science Teaching.

Loucks-Horsley, S., Kapitan, R., Carlson, M.D., Kuerbis, P. J.,dark, R. C.. Melle. G. M., Saschse, T. P.. & Walton, E.(1990). Elementary school sciencefor the ’90s. Alexandria,VA: Association for Supervision and CurriculumDevelopment.

McLaughlin, M.. & Berman. P. (1977). Retooling staffdevelopment in a period of retrenchment. EducationalLeadership, 55(3). 191-194.

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Getting started in science:Ablueprint/or elementary schoolscience education. Andover, MA: National Center forImproving Science Education, The NETWORK, Inc.

O’Brien, T. (1991). The science and art of sciencedemonstrations. Journal of Chemical Education, 68,933-936.

Osbome. R., & Freyberg, P. (1985). Learning in science: Theimplications of children* s science. London: Heinemann.

Shulman, L. S. (1987). Knowledge and teaching: Foundationsof thenewreform. Harvard Educational Review, 57(1), 1-22.

Sparks, G. M. (1983). Synthesis of research on staffdevelopment foreffective teaching. EducationalLeadersliip.41 (3), 65-72.

Spcctor, B.S. (1987). Overview: Meeting the needs of scienceteachers for continuing education. In B.S. Spector (Ed.). Aguide toinservice teachereducation:Researchintopractice(pp. 13-56). Columbus, OH: Association for the Educationof Teachers in Science.

Stake,R.E..&Easley,J.A. (1978). Case studies in scienceeducation, Vol. II: Design, overview and general findings.Urbana: Center for Instructional Research and CurriculumEvaluation and Committee on Culture and Cognition,University of Illinois at Urbana-Champaign.

Tilgner, P. J. (1990). Avoiding science in the elementaryschool. Science Education, 74,421-431.

Yager, R. E. (1988). Funding science education ideas,activities, and projects. School Science and Mathematics,88, 500-508.

Yeany, R. H., & Padilla. M. J. (1986). Teaching scienceteachers to utilize better teaching strategies: A researchsynthesis. Journal ofResearch in Science Teaching, 23,85-95.

Wade, R. K. (1984/1985). Whatmakes adifference in inserviceteachereducation? Ameta-analysisofresearch. EducationalLeadership, 42(4), 48-54.

Weiss. I. R. (1987). Report of the 1985-86 national survey ofscience and mathematics education. Research TrianglePark. NC: Research Triangle Institute.

Problem Solving withNumber Patterns

David R. Duncan andBonnie H. Litwiller

University of Northern Iowa

Monograph #1 in the SSMA Classroom ActivitiesSeries

A practical compendium of activities for use by teachersto interest students in the middle, junior, and senior highschools to develop higher-order thinking skills. Presented on8 1/2 by 11 inch pages suited for duplication in the schools.

The study ofpatterns consists of three parts: (1)discovering the pattern; (2) formulating aconjecture; and (3) verifying that the pattern istrue.... The ability to make a generalization,tliat is, to find a pattern, is very important inmathematics in general andproblem solving inparticular. Finding a pattern is a key strategyin the problem solving process.

Activity titles include:

Differences of SumsProducts of Sequences

Fraction SquaresRectangles on Triangular Arrays

Paths on GridsNested TrianglesSums and Skips

Answer keys for all the activities are included, as well asseveral tables andpapermasters forduplication in the schools.

Paperbound, approximately 160 pages-ISBN 0-912047-06-2

Price $9.50 (postage included on prepaid orders)SSMA members receive a 20% discount

Order from: Executive Office, School Science andMathematics Association, 126Life ScienceBuilding,BowlingGreen State University. Bowling Green, OH 43403-0256,telephone (419) 372-7393.

School Science and Mathematics