Inquiry Strategies for Science and MathematicsLearning

It’s Just Good Teaching

Northwest Regional Educational Laboratory

This publication is based on work supported wholly or in part both by agrant and contract number RJ96006501 from the U.S. Department ofEducation. The content of this document does not necessarily reflect theviews of the department or any other agency of the United Statesgovernment. Permission to reproduce this publication in whole or in partis granted with the acknowledgment of the Northwest RegionalEducational Laboratory as the source on all copies.

Comments or queries may be directed to Kit Peixotto, Unit Manager,Science and Mathematics Education, Northwest Regional EducationalLaboratory, 101 S.W. Main Street, Suite 500, Portland, Oregon 97204, (503) 275-9594 or (800) 547-6339 ext. 594.

Appreciation is extended to the many educators who providedinformation and guidance in the development of this publication.Acknowledgments also go to the panel of reviewers and contributors fortheir valuable input: Peggy Cowan, Norie Dimeo-Ediger, John Graves, RexHagans, Berk Moss, Rosalind Philips, Jennifer Stepanek, WalterWoolbaugh, and Shirley Wright. In addition, several individuals madespecial contributions to the development of this product, including:

Denise Jarrett—Research and writingKit Peixotto—Conceptual support and guidanceDawn Dzubay—Resource research and compilationDenise Crabtree—Desktop publishingLee Sherman—Editorial reviewPhotography—Denise Jarrett: front and back covers, pages 3, 6, 7, 9, 12, 16, 17,18, 23, 26; Rick Stier: pages 4, 11, 15, 20, 21, 25; Tony Kneidek: page 24

Inquiry Strategies for Science and MathematicsLearning

It’s Just Good Teaching

by Denise Jarrett

Science and Mathematics Education

May 1997

Northwest Regional Educational Laboratory

Table of ContentsPreface..................................................................................................................1Introduction..........................................................................................................2What is inquiry? ...................................................................................................3

Inquiry is on a continuum..............................................................................3Inquiry is “just good teaching” ......................................................................5

Why use inquiry? .................................................................................................5Improves student attitude and achievement................................................5Facilitates student understanding.................................................................6Facilitates mathematical discovery ...............................................................7

Inquiring into pendulums in Manhattan, Montana..........................................8Creating an inquiry-based classroom................................................................7

Engage students in designing the learning environment.........................11Reflect the nature of inquiry ........................................................................11Integrate science laboratories into the regular class day.........................11Use inquiry in the mathematics classroom ...............................................12Use management strategies to facilitate inquiry.......................................12Share control .................................................................................................13Spark student motivation .............................................................................13Take on new roles..........................................................................................14

Implications for curriculum..............................................................................15Teaching the “facts”......................................................................................16Choosing an inquiry topic ............................................................................17Getting at the core content ..........................................................................18

Planning an inquiry lesson...............................................................................19Using the Learning Cycle Strategy..............................................................19Planning the use of time..............................................................................20Presenting the inquiry topic.........................................................................21

Classroom discourse and questioning............................................................22Classroom discourse ....................................................................................22Questioning ...................................................................................................23Asking probing questions ............................................................................23Divergent questions and comments...........................................................24

Challenges of inquiry-based teaching.............................................................25Demands on teacher content knowledge ..................................................25Demands on pedagogical skill ....................................................................26

Conclusion .........................................................................................................26Resources and bibliography.............................................................................27

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Preface

Inquiry-based teaching is a perfectcomplement to a child’s naturalcuriosity about the world and how it

works. Whether it is the elementary stu-dent’s wonder that is prompted by astory about hibernating animals, themiddle school student’s predictions aboutthe relationship between circumferenceand diameter that arise from an explo-ration of different-sized spheres, or thehigh school student’s questions that areprovoked by a local environmental issue,students become actively engaged in thelearning process when given the oppor-tunity to hypothesize and investigate.

The Science and Mathematics Educationunit at the Northwest Regional Educa-tional Laboratory offers Inquiry Strate-gies for Science and Mathematics Learn-ing as the second publication in our It’sJust Good Teaching series. Intended tofurnish K-12 teachers with bothresearch-based rationale and recommen-dations for effective techniques that canbe applied in today’s complex andchanging classrooms, future topics inthe series will explore standards-basedteaching and using assessment to informinstruction.

All publications follow a similar format.An initial summary of the key themesin the current research and literaturesets the stage for the subsequent discus-sion of research-recommended practices.Included throughout the publicationsare insights from Northwest educatorswho are implementing these strategiesand represent examples of “real-liferesearch in practice.” The listing of printmaterials, organizations, and onlineresources enables teachers to access andexplore additional tools to support theirefforts to provide all students with the

mathematics and science knowledge,skills, and abilities necessary for success.

The Northwest Regional EducationalLaboratory is committed to improve edu-cational results for children, youth, andadults by providing research and devel-opment assistance in delivering equi-table, high-quality educational pro-grams. We are proud to be partners withthe dedicated practitioners who work onbehalf of students throughout theNorthwest. We invite your analysis andfeedback of Inquiry Strategies for Scienceand Mathematics Learning: It’s Just GoodTeaching as a resource to strengthen sci-ence and mathematics education in theregion.

Kit PeixottoUnit ManagerScience and Mathematics EducationMay 1997

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Introduction

In the past 20 years, our understand-ing of how people learn has changeddramatically. Not long ago, educators

and psychologists believed that students’brains were like empty vessels waiting tobe filled with knowledge imparted by ateacher. But advances in cognitiveresearch and developmental psychology,combined with today’s urgency to edu-cate all students in an increasinglydiverse and technological society, havetransformed the way we think aboutteaching mathematics and science(Brown & Campione, 1994; Rosenshine,1995; Roth, 1993; Nowell, 1992; Ornstein,1995).

Today, educators and researchers under-stand that most people learn bestthrough personal experience and by con-necting new information to what theyalready believe or know (NationalResearch Council [NRC], 1996; AmericanAssociation for the Advancement of Sci-ence [AAAS], 1993). Excellent teachingand quality textbooks aren’t enough.Students need to personally constructtheir own knowledge by posing ques-tions, planning investigations, conduct-ing their own experiments, and analyz-ing and communicating their findings.Also, students need to have opportunitiesto progress from concrete to abstractideas, rethink their hypotheses, andretry experiments and problems (NRC,1996; AAAS, 1990, 1993; National Councilof Teachers of Mathematics [NCTM], 1991;Rosenshine, 1995; Flick, 1995). In short,students construct their own knowledgeby actively taking charge of their learn-ing—one of the primary tenets ofinquiry.

Science and mathematics reform stan-dards call for inquiry teaching methodsthat enable students to contribute their

own ideas and to pursue their own inves-tigations (NRC, 1996; NCTM, 1991; AAAS,1990, 1993). However, no single teachingmethod is appropriate in all situations,for all students. Teachers need to knowhow and when to use a variety of strate-gies (Good & Brophy, 1997). Embeddingteaching strategies within an overallinquiry-based pedagogy can be an effec-tive way to boost student performance inacademics, critical thinking, and prob-lem solving.

An inquiry-based classroom is morethan a “gathering of individual learnersbrought together for reasons of econo-my.” Rather, it is a “community ofinquiry” (Schifter, 1996). In this commu-nity, students and teachers share respon-sibility for learning, and collaborate onconstructing new knowledge. Students

have significant input into just aboutevery aspect of their learning—how theirclassroom is set up, how time is struc-tured, which resources are used, whichtopics are explored, how investigationswill proceed, and how findings arereported. No longer are teachers the solepurveyors of knowledge and studentspassive receptacles.

“INQUIRY IS THE [SET] OFBEHAVIORS INVOLVED IN

THE STRUGGLE OF HUMAN BEINGS FORREASONABLE EXPLANATIONS OFPHENOMENA ABOUT WHICH THEY ARECURIOUS.”

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What is inquiry?

Scientific inquiry is more complexthan the traditional notion of it.Rather than a systematic method of

making observations and then organiz-ing them, scientific inquiry is a subtle,flexible, and demanding process, statesthe Benchmarks for Science Literacy(AAAS, 1993).

From a science perspective, inquiry ori-ented instruction engages students inthe investigative nature of science, saysDavid L. Haury in his article, TeachingScience through Inquiry (1993). Haurycites scientist Alfred Novak’s definition:“Inquiry is the [set] of behaviorsinvolved in the struggle of humanbeings for reasonable explanations ofphenomena about which they are curi-ous.” In other words, inquiry involvesactivities and skills that focus on theactive search for knowledge or under-standing to satisfy a curiosity, saysHaury.

Inquiry is also central to mathematics.Today, mathematics education encom-passes more than arithmetic and algo-rithms. It is a diverse discipline thatinvolves data, measurements, and recog-nition of patterns (NRC, 1989). “Theprocess of ‘doing’ mathematics is farmore than just calculation or deduction;it involves observation of patterns, test-ing of conjectures, and estimation ofresults,” states the National ResearchCouncil in Everybody Counts, a report tothe nation on the future of mathematicseducation (1989). “Mathematics revealshidden patterns that help us understandthe world around us.”

Inquiry is on a continuum. Inpractice, inquiry often occurs on a con-tinuum. On one end of the continuumof inquiry might be the use of highly

structured hands-on activities and “cook-book” experiments; in the middle mightbe guided inquiry or the use of sciencekits; and, at the farthest end, studentsmight be generating their own questionsand investigations. A teacher’s goalshould be to strive for the farthest end ofthe continuum where students areinvolved in full inquiry. There are timeswhen she will find it necessary toemploy lower-level inquiry strategies tomeet specific goals. However, a teachershould not assume that a structuredhands-on activity will necessarily haveall of the elements of inquiry.

When choosing from the continuum,teachers will need to consider a numberof variables such as their own teachingskills; student readiness, maturity, andability; and pedagogical goals. Occasion-ally, the teacher will move back andforth on the inquiry continuum to meetcertain goals and circumstances. BerkMoss, science curriculum coordinator forthe Beaverton School District in Oregon,provides an example of how a teacher’sprogression toward full inquiry mightproceed:

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■ Activities focus on textbooks, libraryreports, and worksheets

■ Demonstrations are done for students

■ Students conduct “cookbook experi-ments” (student replications, not discoveries)

■ Students do laboratory activities thatlead to student discoveries

■ Students answer questions generatedby the teacher from open-ended labora-tory activities

■ Students answer questions of their ownfrom open-ended laboratory activities

“Each step represents significantly morerisk taken by the teacher and increas-ingly complex classroom management,”says Moss. “I celebrate each move alongthe continuum.”

“It is quite reasonable to supply some ofthe inquiry steps to students so that theycan focus their learning on other steps,”says Moss. “For example, we might sup-ply the question and ask them to devisethe investigation or give data and askthem to analyze and test a givenhypothesis. The complexity of theseactivities will vary with student age andexperience, but there are entrances forevery child.”

Students can do investigations requiringdata collection that don’t require com-plex laboratory preparation by theteacher, says Moss. “All inquiry experi-ences do not need to involve a mop andapology to the custodian.”

Students engaged in full inquiry aredoing the following, says Moss:

■ Learning in a rich environment

■ Thinking of a question, and shaping itinto something they can investigate

■ Hypothesizing

■ Planning an investigation

■ Collecting data

■ Analyzing that data

■ Forming a conclusion

■ Communicating their findings

Inquiry is “just good teaching.”Research has identified effective teach-ing strategies, many of which are coreelements of inquiry. In the book Effec-tive Teaching: Current Research (Wax-man & Walberg, 1991), Kenneth Tobinand Barry Fraser identify teachingstrategies that are used by exemplarymathematics and science teachers.According to research, exemplary teach-ers ensure that activities are set up toallow students to be physically andmentally involved in the academic sub-jects. Activities are based on the use ofmaterials to investigate questions andsolve problems. Teachers use verbalinteraction to monitor student under-standing of the content, and facilitatepeer interactions by setting up small-group discussions.

At all levels, teachers are effective in arange of verbal strategies which includeasking questions to stimulate thinking;probing student responses for clarifica-tion and elaboration; and providingexplanations to students, say Tobin andFraser. The most successful teachershave deep content knowledge in the sub-ject areas that they teach, and in the rel-evant pedagogical theories and strategies.

They use skillful questioning to focusstudent engagement and to probe formisunderstandings. They provide clearand appropriate explanations. They useconcrete examples and analogies—rele-vant to students’ lives—to illustrateabstract concepts and to facilitate under-standing. They anticipate areas of con-tent that are likely to give students prob-lems, and they conclude lessons by high-lighting the main points (Tobin & Fras-er, 1991).

Why use inquiry?

There is evidence that inquiry-based instruction enhances stu-dent performance and attitudes

about science and mathematics, saysDavid Haury (1993). At the middle schoollevel, students who participate ininquiry-based programs develop betterlaboratory and graphing skills, and learnto interpret data more effectively, hesays. He points to research that indicatesinquiry-based programs foster scientificliteracy and understanding of scientificprocesses; vocabulary knowledge andconceptual understanding; criticalthinking; positive attitudes; higherachievement on tests of proceduralknowledge; and construction of mathe-matical knowledge.

Improves student attitude andachievement. According to EducationWeek (Lawton, 1997), a poll by Bayer Cor-poration of Pittsburgh showed that stu-dents who used hands-on experimentsand team problem solving in scienceclassrooms have a better attitude aboutthe subject than students who learnedscience through lectures and assignedtextbook reading. Three out of five stu-dents, ages 10 to 17, said that they would

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“ALL INQUIRYEXPERIENCES DO

NOT NEED TO INVOLVE A MOP ANDAPOLOGY TO THE CUSTODIAN.”

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be “a lot more psyched” about science ifthey could do more experiments them-selves and use a computer to communi-cate with scientists and other students.Fifty-four percent of the students usingmore inquiry-oriented methods said thatscience is one of their favorite subjects,compared with 45 percent of the stu-dents in traditionally taught classes.Also, nearly 25 percent of the students intraditional classes said that science istheir most difficult subject, while only18 percent of the students using inquirystrategies said so.

The College of Natural Sciences at theUniversity of Iowa (1997) administers aproject called Physics Resources andInstructional Strategies for MotivatingStudents (PRISMS). The project blendssuch inquiry-based strategies asexploratory activities, concept develop-ment, and application activities into alearning cycle. The college compared theacademic achievement of students whoparticipated in the PRISMS project withstudents who did not. The studiesshowed that the PRISMS studentsachieved at a higher level, used higher

level reasoning skills, and had more posi-tive attitudes about physics than thosetaught by more traditional methods(University of Northern Iowa, 1997).

Facilitates student understand-ing. Students develop critical thinkingskills by learning through inquiry activ-ities. They learn to work collaboratively,to articulate their own ideas, and torespect the opinions and expertise ofothers. They learn inquiry skills thatthey can use in other aspects of theirlives and intellectual pursuits.

Building on John Dewey’s premise thatstudents need to be engaged in a questfor learning and new knowledge, andJean Piaget’s statement that, “Experienceis always necessary for intellectual devel-opment; (therefore) the subject must beactive,” researchers in the past twodecades have developed a new under-standing of learning (Brown & Campi-one, 1994; Rosenshine, 1995; Roth, 1993;Nowell, 1992). Constructivist theory statesthat knowledge is constructed throughone’s personal experience by assimilat-ing new information with prior knowl-edge (King & Rosenshine, 1993).

This theory has shifted researchers’ per-spective on knowledge, learning, andteaching, says Raffaella Borasi in herbook, Learning Mathematics ThroughInquiry (1992). Borasi is an associate pro-fessor at the Graduate School of Educa-tion and Human Development at theUniversity of Rochester and has writtenextensively on mathematics and inquiry.Knowledge is viewed not as a stable bodyof established results, she says, but as adynamic process of inquiry, where“uncertainty, conflict, and doubt providethe motivation for the continuous searchfor a more refined understanding of theworld.” In this view, learning is a genera-tive process of meaning making that is

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personally constructed and enhanced bysocial interactions, she says. Teaching isviewed as facilitating students’ ownsearch for understanding by creating arich learning environment that stimu-lates student inquiry.

Learning is also a social process (AAAS,1990; King & Rosenshine, 1993; Magnus-son & Palincsar, 1995). Students need tointeract with their peers and the teacheron inquiry-based investigations. Theyneed ample opportunities to discusstheir own ideas; confer and debate withtheir classmates; then to have time toreflect on the feedback they’ve received,

to make adjustments, and to retry theirexperiment or activity. They need tohave experiences with the kinds ofthought and action that are typical ofscientists, mathematicians, and technol-ogy professionals (AAAS, 1990). In short,students need to understand science,mathematics, and technology as ways ofthinking and doing, as well as bodies ofknowledge (AAAS, 1990).

Facilitates mathematical dis-covery. As the Benchmarks for ScienceLiteracy (AAAS, 1993) points out, the roleof inquiry in the study of mathematicsis just as central as it is in science.

“It is the union of science, mathematics,and technology that forms the scientificendeavor and that makes it so success-ful,” states the Benchmarks. “Althougheach of these human enterprises has acharacter and history of its own, each isdependent on and reinforces the others…It is essential to keep in mind that math-ematical discovery is no more the resultof some rigid set of steps than is discov-ery of science.”

According to standards written by theNational Council of Teachers of Mathe-matics, inquiry is one of the most impor-tant contexts in which students learnmathematical concepts and knowledge:by exploring, conjecturing, reasoninglogically, and evaluating whether some-thing makes sense or not. During dis-course, students develop ideas andknowledge collaboratively, while theteacher initiates and orchestrates discus-sion to foster student learning. This col-laboration “models mathematics as it isconstructed by human beings: within anintellectual community” (NCTM, 1991).

Creating an inquiry-based classroom

Teachers should design and man-age learning environments thatprovide students with the time,

space, resources, and safety needed forlearning. Opportunities for active learn-ing and access to a rich array of tools

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Inquiring intopendulums inManhattan, Montana

AMay blizzard has thrown a

heavy blanket of snow overManhattan, a small farming

community 25 miles west of Bozeman,Montana. This morning, the sun isedging out the storm clouds, and theBridger Range mountains are again inview.

Inside Manhattan Middle School, sev-enth-grade students are settling intotheir chairs in Mr. Walter Woolbaugh’sscience room. A chess game is con-cluded. The motion machine is given atap, and the caged tarantulas aregiven a peek. At the back of the room,behind the laboratory stations, thedoves coo in anticipation.

It’s near the end of the school year. Sofar, these seventh-graders have stud-ied geologic processes, and plant andanimal life. Now, they are learningabout mechanical energy. At the frontof the classroom, a long string hangsfrom the ceiling with a bronze weighttied to its end. On the chalkboard iswritten a question: What affects theperiod of a pendulum?

Mr. Woolbaugh steps forward.

“Okay, what kinds of things did we talkabout yesterday?” he asks. The classreviews yesterday’s introductory les-son about potential and kinetic energy,and the vocabulary term, the period ofa pendulum.

Woolbaugh repeats a demonstrationfor determining how many swings a

pendulum makes in one second. AsBrenda readies the stopwatch, Wool-baugh pulls the weight back, andreleases it.

Brenda calls out, “Stop!” and Wool-baugh grabs the weight in mid-swing.

“Okay, we had this problem yesterday,”says Woolbaugh. “What’s the problemwith this method?”

The students conclude that one sec-ond isn’t long enough to measure thefull swing of the pendulum. They sug-gest timing the swings for at least 15seconds in order to capture a fullswing and to collect enough data toaccurately calculate the measurement.Woolbaugh accepts their strategy,then introduces a new problem, set-ting the stage for the next activity.

“Remember, good science starts witha problem,” he says. “Here’s the prob-lem that I want you to address over thenext three days: What affects the peri-od of a pendulum? Is there anythingthat would make the number ofswings per second change? Or is italways the same? That’s what you andyour lab partner are going to solve.”

Before the students break into smallgroups, Woolbaugh leads them in abrainstorming session. He writes theirideas about what might influence theswing of a pendulum on the chalk-board.

“Air pressure,” suggests Tony.

“Okay, if we did this experiment onanother planet, or someplace that hadmore air pressure, that might changeit,” agrees Woolbaugh, “but that’s a

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variable that’s going to be hard for usto control.”

“Length of string,” offers Daniel.

“Okay, that’s a good one. Would a real-ly short string have a short or fast peri-od? Any discussion about the length ofstring before I go on?” He waits a fewseconds before continuing, “Are thereothers?”

“How heavy the weight is,” says Melinda.

“Excellent idea,” says Woolbaugh. “Ilike that one. The weight, yeah! Woulda real heavy weight make a slowerperiod or would it make a faster peri-od? How could we test that?”

“Try different weights,” says Greg.

“Right!” Woolbaugh is clearly pleased,but he presses for more ideas. “Otherhypotheses about the period of thependulum?”

“The diameter of the string mightaffect it,” says Matthew.

“String might matter. Okay, good idea.I don’t have a lot of different stringwidths, so that’s not a variable thateveryone will be able to test, but if youwant to try it, Matt, after you test theother variables, that would be an inter-esting experiment to do.”

Another student says, “Aerodynamicscould make a difference.”

“What do you mean by that?” probesWoolbaugh.

“It could increase the drag on the pen-dulum.”

“Okay, that would be good to test, too.”

“What about friction at the top of thestring, where the string is attached tothe wire on the ceiling?” asks Brenda.

“Good. Friction at the point where thestring meets the wire.”

The students move into small groupsto set up their own experiments onpendulums. Immediately, they startsearching through drawers, shelves,closets, and cabinets for materialswith which to conduct their investiga-tions: string, wire, weights of all sorts.They are familiar with this routine; onlyoccasionally does Woolbaugh preparematerials for them in advance. Withmaterials in hand, they search aroundthe room for interesting places to fas-ten their pendulum: ceiling hooks,faucets, and laboratory stanchions.Everything from bronze weights to apair of scissors serves as the pendu-lum weight.

Members of each group take turnsmanipulating their pendulum, timingits swings, and recording data. After

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25 minutes, they return to their desksto report the data they have collected.As it turns out, the students haveexperimented with only two variables:length of string and the weight.

“Looking at the data, what do youthink?” asks Woolbaugh. “Give mesome hypotheses.”

“I don’t think weight affects it a lot,”says Melinda, wrinkling her brow.

“Why do you say that?” asks Wool-baugh.

“Because the results for each trial areabout the same.”

“Yes, the periods were almost exactlythe same, although we changed theweight in all three trials. Maybe you’reright, maybe the weight doesn’t makethe pendulum swing any faster orslower,” says Woolbaugh. “How aboutlength of string?”

“The shorter the string, the faster theperiod,” says Jennifer.

“It appears that way, doesn’t it?” saysWoolbaugh. “As we get the stringshorter, it appears to go faster. Doesthat mean it’s true? We can’t be sure,because only one test was done oneach variable. Tomorrow, when werepeat our experiments, we’ll need totest each length of string four or fivetimes. This will give us enough datapoints to reach a more accurate aver-age for calculating the period of thependulum.”

Woolbaugh reviews the day’s activity.“Today, we followed the scientificprocess—we brainstormed ideasabout what might affect the period of

a pendulum; we did a few tests ofeach variable, collected and averageddata; and then drew some conclusionsbased on that data,” he says.“Although our findings aren’t conclu-sive, we’ve generated some testablehypotheses. Tomorrow, we’re going toretry our experiments. We want to testeach variable a number of times sothat we have enough data to be confi-dent of the accuracy of our measure-ments.”

Trina raises her hand, and asks, “Whatif you were to hang the weight fromtwo strings attached to the ceiling, likea swing?”

“Good one! Nobody’s ever suggestedthat variable,” says Woolbaugh. “Whydon’t you try that tomorrow?”

Trina smiles and collects her books asthe school bell rings. The next class ofstudents is already pouring in thedoorway as Trina and the others leaveMr. Woolbaugh’s classroom, untiltomorrow.

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and resources are critical to students’ability to do inquiry (NRC, 1996).

Engage students in designingthe learning environment. Askstudents for their ideas and suggestionson such decisions as how to use time andspace in the classroom. This is part ofchallenging students to take responsibil-ity for their learning. Also, as studentspursue their inquiries, they need accessto resources and a voice in determiningwhat is needed. Students often identifyexcellent out-of-school resources. Themore independently students can getwhat they need, the more they can takeresponsibility for their own work (NRC,1996).

Reflect the nature of inquiry. Thelearning environment should reflect theintellectual rigor, attitude, and social val-ues that characterize the way scientistsand mathematicians pursue inquiry(NRC, 1996; Borasi, 1992; Brown & Campi-one, 1994). According to the National Sci-ence Education Standards (NRC, 1996)and literature on inquiry and guideddiscoveries (Borasi, 1992; Brown & Campi-one, 1994), inquiry facilitates students’development of skills and dispositionsthat will serve them throughout theirlives. To create a classroom environmentthat reflects the nature of inquiry, teach-ers will want to:

■ Display and demand respect fordiverse ideas, abilities, and experiences(NRC, 1996).

■ Model and emphasize the skills, atti-tudes, and values of scientific inquiry:wonder, curiosity, and respect towardnature (NRC, 1996).

■ Enable students to have a significantvoice in decisions about the content andcontext of their work, such as setting

goals, planning activities, assessing work,and designing the environment (NRC,1996).

■ Nurture collaboration among students,and give them significant responsibilityfor the learning of everyone in the com-munity (NRC, 1996). Foster communalsharing of knowledge (Brown & Campi-one, 1994).

■ Structure and facilitate discussionsbased on a shared understanding of therules of scientific discourse, such as jus-tifying understandings, basing argu-ments on data, and critically assessingthe explanations of peers (NRC, 1996).

■ Extend the community of learners toinclude people, organizations, and facili-ties away from school (Brown & Campi-one, 1994).

Integrate science laboratoriesinto the regular class day. It isessential to teach students that doing sci-ence is not separate from learning sci-ence, says science teacher Walter Wool-

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baugh of Manhattan Middle School inManhattan, Montana. Woolbaugh con-ducts workshops on inquiry-based teach-ing and is an adjunct professor at Mon-tana State University in Bozeman wherehe teaches classroom management andmethods.

“Science should be lab. Science should bea verb as opposed to a noun,” says Wool-baugh. “Why separate learning sciencefrom doing science? That doesn’t happenin the profession. A paleontologist at theMuseum of the Rockies (in Bozeman)doesn’t say, ‘I think I’ll go back to the lab.’It’s all integrated. So isn’t that the modelwe ought to use when teaching studentsfrom kindergarten on?”

Use inquiry in the mathematicsclassroom. Raffaella Borasi (1992) rec-ommends several strategies for creatingan environment that is conducive to ini-tiating and supporting students’ inquiryin mathematics:

■ Use the complexity of real-life problems.

■ Focus on nontraditional mathematicaltopics where uncertainty and limita-tions are most evident.

■ Use errors as “springboards forinquiry.”

■ Create ambiguity and conflict thatcompels students to ask, “What wouldhappen if things were different?” or“What would happen if we changedsome of the traditional assumptions, def-initions, goals, in mathematics?” Encour-age students to pursue such questions,and to have a sense of the significance ofthe results of their inquiry.

■ Generate reading activities to sustaininquiry and to teach students to usesources of information other than theteacher. This will help them learn tobecome independent learners, problemsolvers, and critical thinkers. Sourcescould include historical and philosophi-cal essays, reports describing specificmathematical applications, and biographies.

■ Provide students with opportunities toreflect on the significance of theirinquiry.

■ Promote exchanges among students.

Use management strategies tofacilitate inquiry. There appears to bea critical link between classroom man-agement, teaching, and learning (Tobin& Fraser, 1991; Flick, 1995). Research oninquiry and teaching methods indicatethat effective teachers use “significantmanagerial skill while promoting theactive participation of students” duringinquiry activities (Flick, 1995).

While an inquiry-based classroom allowsstudents significant freedom to create,chart their own learning, debate, and

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engage in activities (NRC, 1996), theirexplorations should be within a struc-ture. The teacher provides this structurewith management strategies that helpher to create a safe, well-organized, andeffective environment where all stu-dents can learn. She orchestrates discus-sions so that student participation andthinking are at a high level. She alsoensures that students understand thecore content in every lesson.

Student-teacher interaction is anotherimportant element of effective class-room management (Wang & Walberg,1991). In a classroom with effective man-agement strategies in place, the teacherconsiders one of her primary curricu-lum goals to be developing students’autonomy and independence (Tobin &Fraser, 1991). She maintains control-at-a-distance over the entire class, and active-ly monitors student behavior by movingaround the room and speaking withindividual students. Students work bothindependently and cooperatively ingroups.

Rules are firmly in place but rarely need-ed, the authors say. When a studentexhibits off-task behavior, the teacherquickly and quietly speaks to that stu-dent without disturbing others. She mon-itors student engagement and under-standing, and establishes routines thatenable her to cope with a relatively large

number of students with diverse learn-ing needs. She emphasizes students’ activeparticipation in their own learning, andchooses activities that ensure activethinking. Students are encouraged to tryto work out difficulties on their own, con-sulting other resources such as textbooksand peers (Tobin & Fraser, 1991).

Woolbaugh remembers his early effortsat using inquiry in the classroom beforehe had management strategies in place.“It caused me problems the first year,because classroom management is sucha key issue in inquiry,” he recalls. “Wemake such a push in mathematics andscience to do inquiry, when in reality it’sprobably something that teachers aregoing to be able to do consistently onlyin their third, fourth, or fifth year,because they need to get managementskills down first. That first-year teachermay do an awful lot of pencil, paper, andopen-the-book kinds of things, just for amanagement survival strategy.”

Share control. Full inquiry is whenstudents are actively engaged in aninvestigation, manipulating concreteobjects, conferring with peers, pursuingtheir own line of inquiry, and creatingtheir own solutions to a problem (NRC,1996). It takes a skillful teacher to guidestudents’ learning, to keep students on-task, to know when to let classroom dis-cussions go off in a new direction, tomake sure the lesson progresses coher-ently toward learning goals. It also takesa courageous teacher to encourage stu-dents to offer their own ideas, to makecomments, to debate the validity ofexplanations and solutions, and to takepart in the decisionmaking (Borasi, 1992).

Spark student motivation. Stu-dents’ individual characteristics can becritical in determining their learningoutcomes, say Margaret Wang and Her-

“SCIENCE SHOULD BE LAB.SCIENCE SHOULD BE A VERB AS OPPOSEDTO A NOUN.”

bert Walberg in their article, Teachingand Educational Effectiveness: ResearchSynthesis and Consensus from the Field(1991). Regulating and taking responsi-bility for one’s own learning is the mostimportant characteristic for highachievement, they say. Other importantcharacteristics are perseverance onlearning tasks and motivation for con-tinual learning.

Science and mathematics teacher Ros-alind Philips of New Century HighSchool in Tumwater, Washington, speaksnationally about inquiry, and scienceand mathematics standards. One of herstrategies for boosting student motiva-tion is to provide them with a variety oftasks, activities, and objectives duringthe course of a 90-minute class period.

“I try to interact with students, and I tryto set up class so that we do about fourdifferent things over the course of theperiod,” says Philips. “I lecture, we watcha video, and we have two activities thatthe students do. I try to keep class mov-ing. There are days when I talk morethan I probably should, and there aretimes when we go by without doingenough labs because of where we are inthe curriculum.”

Take on new roles. In classroomswhere one of the teacher’s primary goals

is to help students become good problemsolvers and critical thinkers, teachersand students assume new roles. The listsbelow depict those things that teachersand students will do in an inquiry-basedclassroom (NRC, 1996; NCTM, 1991; AAAS,1990, 1993; Borasi, 1992; Flick, 1995):

What teachers do:

■ Create a rich learning environment

■ Identify important concepts studentswill investigate

■ Plan the inquiry

■ Present the inquiry

■ Solicit student input to narrow thefocus of the inquiry

■ Initiate and orchestrate discussion

■ Ask prompting and probing questions;pursue students’ divergent commentsand questions, when appropriate

■ Guide students’ learning in order toget at the core of the content

■ Provide opportunities for all studentsto demonstrate their learning by pre-senting a product or making a publicpresentation

What students do:

■ Contribute to the planning of aninquiry investigation

■ Observe and explore

■ Experiment and solve problems

■ Work both as a team member andalone

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IN A COMMUNITY OFLEARNERS, TEACHERS AND

STUDENTS WORK SIDE BY SIDE,COLLABORATIVELY CONSTRUCTINGKNOWLEDGE.

■ Reason logically, pose questions

■ Confer and debate with peers and theteacher

■ Discuss their own ideas, as well as devel-op ideas and knowledge collaboratively

■ Make logical arguments and constructexplanations

■ Test their own hypotheses

■ Communicate findings

■ Reflect on feedback from peers andthe teacher

■ Consider alternative explanations

■ Retry experiments, problems, and projects

Implications forcurriculum

An inquiry-based teachingapproach is time intensive. Sig-nificant implications are raised

regarding how much of the curricula ateacher can “cover.” Education reform lit-erature recommends that teachers focuson essential topics (AAAS, 1990; NCTM,1989), but most teachers are accountableto state-mandated curriculum goals.States are responding to this dilemma byreexamining the curriculum and goalsthey require teachers to follow. Moststates in the Northwest are aligningtheir standards with national standardswhich call for teachers to ensure thatstudents are actively and mentallyengaged in mathematics and sciencecontent that has enduring value. Accord-ing to Science for All Americans (AAAS,1990), concepts should be chosen on thebasis of whether they can serve as a“lasting foundation on which to buildmore knowledge over a lifetime.”

It is unrealistic, says Borasi (1992), toexpect students to “solve complex real-lifeproblems, read about the history ofmathematics, or study extracurriculartopics where uncertainty and contradic-tion are especially evident, in addition tocovering all the topics already includedin the overcrowded state-mandated cur-ricula for precollege school mathematics.”

The open-ended character of inquiryrequires a lot of flexibility in choosingcurriculum content, she says. Teacherswill frequently need to diverge from theoriginal lesson plan to follow up on stu-dents’ questions, to allow a debate todevelop, or to follow a new lead. “Indeed,the best discussions and explorations aremost often those that have not been pre-

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planned, or even conceived as possible,by the teacher,” she says.

For students to develop into criticalthinkers, they need to experience thefreedom—and responsibility—of direct-ing and focusing their own inquiries, shesays. The teacher must skillfully bal-ance the overarching objectives of the

course while providing students withgenuine involvement in decisionmak-ing. This will affect the “extent, purpose,emphasis, and sequence” of the contentcovered, says Borasi.

Teaching the “facts.” While allow-ing students optimum input into deci-sionmaking, the teacher must ensurethat curriculum goals are met in mean-ingful ways. This sometimes means thatthe teacher will prepare his students forthe inquiry activity by first teachingthem some basic facts and vocabulary.Without these facts, students can be leftwith the impossible task of reinventingknowledge, or they may construct seri-ously flawed understandings.

“There’s a misconception that in order todo an inquiry approach, you never teachkids facts, you never stand up at theboard and lecture; you do all of this dis-covery learning,” says Philips. “My feel-ing is that there is a basic body of math-ematics that all kids should have memo-rized, because it helps a student to focuson what the problem is asking, and noton the routine grunt work.

“I think they should know these thingsbecause it means that when they’re try-ing to identify patterns and solve a prob-lem, those basic facts fall readily intoplace,” she says. “If you can’t recognizethe common patterns of mathematicsand science, then you can’t have aninquiry approach in the class. You can’tinquire about something unless youhave a basis to found it on.”

Philips offers an amusing, though trou-bling, anecdote illustrating how one canconstruct knowledge incorrectly. Yearsago, a friend living on the East Coastwanted to meet Philips halfway betweenBoston and Seattle for a holiday. Thefriend suggested Hawaii.

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“Now I’m thinking about the fact thatHawaii’s in the middle of the PacificOcean, and I say, ‘Where do you thinkHawaii is?’ And she says, ‘It’s off the coastof Texas. Remember that map we had atschool? Hawaii is off the coast of Texas!’She never understood that that was agraphic inset. So there’s an example ofsomebody who’s constructed their ownknowledge, used absolutely good reason-ing, and used an appropriate tool, butshe constructed a misperception thatwas left uncorrected. So, what we have todo with inquiry, if we’re going to facili-tate students’ construction of knowledge,is to offer students a little bit of help.”

Choosing an inquiry topic. Whatknowledge of enduring value should thestudent be guided to discover? This is thequestion posed by Ann Brown andJoseph Campione in their article, GuidedDiscovery in a Community of Learners(1994). Most teachers are accountable forthe course requirements of their schools.Rather than allowing students to discov-er curriculum content on their own,“charting their own course of studies,”the teacher sets bounds on the curricu-lum to be covered. While the teacherchooses the main themes, students arestrongly encouraged to nominate specif-ic topics within those themes (Brown &Campione, 1994).

For example, the teacher might select atheme on endangered species, say theauthors. He solicits questions from stu-dents who discuss what they alreadyknow, and what they want to find outabout endangered species. Then, theirquestions are written on Post-itsTM anddisplayed on a bulletin board. After con-sulting books the teacher has selected,students generate more questions. Final-ly, the questions are grouped into sub-themes from which topics are identified.This process fosters teamwork and helps

students to feel ownership in what theyselect for study (Brown & Campione,1994).

Teachers will want to ensure that theinquiry activities they plan require stu-dents to use high-level reasoning skills.According to research, inquiry activitiesthat require high-level thinking havethe following features (Flick, 1995):

■ The path of action is not fully speci-fied in advance, nor is it apparent from asingle vantage point

■ There are multiple solutions, eachwith costs and benefits

■ Uncertainty exists; everything thatbears on the task at hand is not known

■ Higher-order thinking skills arerequired; students direct most of theirown steps in the thinking process

■ Considerable mental work is involvedin elaboration and judgment

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Getting at the core content.Whether or not teachers are workingunder mandated goals, objectives, andcontent, they will want to examine theextent to which a curriculum includesinquiry. Engaging students in inquiryhelps them to make a critical linkbetween understanding science as aprocess, and understanding scientific

concepts (NRC, 1996). Inquiry requiresstudents to do more than observe, infer,and experiment. It requires them tocombine scientific processes with con-tent knowledge—they must use scientificreasoning and critical thinking to devel-op their understanding of science (NRC,1996).

“I could do magic tricks all year long,and students would come out of heresaying, ‘This is the greatest science classwe’ve ever had,’” says Woolbaugh, who isa professional magician as well as a sci-ence teacher. “But when you look at thenuts and bolts of the activities, there’s noscience content in it. The students hadfun, and they used some processing(thinking) skills, but they didn’t get atthe science content. So we, as teachers,need to look at that scope and sequence,the ‘big picture,’ and the standards tomake sure that we’re covering what weneed to be covering. I need to look at thatcore content, and then make adjust-ments—that’s a never-ending job.”

John Graves, who received a PresidentialAward for Excellence in Science andMathematics Teaching in 1996, teachesscience and English at Monforton Mid-dle School in Bozeman, Montana. Gravesprovides an example of when an inquiryactivity misses the core of the content.

“Based on the Learning Cycle Strategy(see “Planning an Inquiry Lesson”), eachone of the phases—exploration, conceptintroduction, application—is just asimportant as the other phase. The explo-ration is certainly key, but the conceptdevelopment has to have equal weight,”says Graves. “For example, we’re doingCartesian divers right now (a commonexperiment to demonstrate the effects ofair pressure.) Here’s how you can blowthat inquiry lesson: Let the kids buildtheir own divers—that’s the exploration

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phase—but never ask students, ‘How doesthis happen in real life?’ ‘Can you find asituation where the change of pressurein something causes it to move?’ So theexploration is great, but if that’s all youdid, you’d really be wasting your time,and I think the kids’ time.”

Doing an inquiry activity that doesn’tget to the core of the content alsoincreases the possibility that studentswill construct flawed understandings,says Graves.

“To allow an inaccuracy to continuemight mean that that student gets to bea senior in high school taking physics,and they are still holding a misconcep-tion that they developed in secondgrade,” he says. “If teachers don’t takethem beyond the exploration phase, theydo a real injustice to students’ learningprocess.”

Planning an inquirylessonUsing the Learning Cycle Strat-egy. The Learning Cycle is a modelthat can be used to facilitate inquiry.Developed in the 1960s as part of the Sci-ence Curriculum Improvement Study(sponsored by the National ScienceFoundation), the strategy uses questions,activities, experiences, and examples tohelp students develop a concept, deepentheir understanding of the concept, andapply the concept to new situations(Beisenherz & Dantonio, 1996).

In their book, Using the Learning Cycleto Teach Physical Science (Beisenherz &Dantonio, 1996), the authors identifythree phases to the Learning Cycle:

exploration, concept introduction, andapplication. During these phases, stu-dents learn to use and understand suchscience processes as observing; compar-ing and contrasting; ordering; categoriz-ing; relating; inferring; communicating;and applying.

At the beginning of the cycle, studentsactively explore materials, phenomena,problems, and ideas to make observationsand collect data. An initial, less structuredexploration allows students to exploreobjects and systems at their own paceand with little guidance. Students oftenbecome highly motivated when they arepermitted to do hands-on explorationsbefore the concept is introduced. Thenanother, more structured explorationallows students to reexamine the sameobjects and systems more scientifically.During this time, students generate ques-tions, and form and test their ownhypotheses (Beisenherz & Dantonio, 1996).

In the next phase, the teacher uses scien-tific vocabulary to introduce the con-cept related to students’ observations.Together, the teacher and students orga-nize the observations and experiences,and the resulting patterns often match

KNOWLEDGE IS VIEWEDNOT AS A STABLE BODYOF ESTABLISHED

RESULTS, BUT AS A DYNAMIC PROCESS OFINQUIRY, WHERE “UNCERTAINTY,CONFLICT, AND DOUBT PROVIDE THEMOTIVATION FOR THE CONTINUOUSSEARCH FOR A MORE REFINEDUNDERSTANDING OF THE WORLD.”

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the targeted concept of the lesson. Dur-ing discussion, the teacher and studentscompare how the newly introduced con-cept affects students’ preconceptions.The teacher can further explain the con-cept by using the textbook, audiovisualaids, and other materials (Beisenherz &Dantonio, 1996).

Depth of understanding is facilitatedwhen the concept is reinforced orexpanded during the application phase,often through the use of hands-on activ-ities. (Activities in this phase will oftendo double duty, serving as the initialactivity in the exploration phase of anew, closely related concept that will bedeveloped in a separate learning cycle.)The hands-on activities in the explo-ration and application phases can serve

to motivate students as they encounterproblems that arouse their curiosity(Beisenherz & Dantonio, 1996).

The problem can be introduced by using“discrepant events”—encounters that stu-dents find perplexing. Before being pre-sented with a discrepant event, studentsshould have a familiarity with the con-cepts, skills, and techniques that allowthem to, first, be able to recognize a dis-crepant event, and, second, be able tosuggest hypotheses and procedures forcollecting data. Beisenherz and Dantonioprovide an example: “The observationthat water expands when it freezes is dis-crepant to students only if they havebeen led to infer from previous activitiesthat liquids expand when heated andcontract when cooled.” Using discrepantevents to introduce a new topic is partic-ularly effective at piquing students’curiosity, say the authors.

Planning the use of time. Teach-ers face many time constraints, but theyshould use available time so that stu-dents can experience concepts, not once,but periodically, in different contextsand at increasing levels of sophistication(AAAS, 1990). Structure time so that stu-dents can engage in extended investiga-tions. Students need time to discuss anddebate with one another, to try out ideas,to make mistakes, to retry experiments,and to reflect. Students also need time towork together in small groups, sharetheir ideas in whole-class discussions,and work together and alone on a vari-ety of tasks, including reading, experi-menting, reflecting, writing, and dis-cussing (NRC, 1996).

The National Science Education Stan-dards (1996) recommend that teachersplan curriculum goals that are flexibleso that they can respond to students’needs and interests: “Teaching for under-

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standing requires responsiveness to stu-dents, so activities and strategies are con-tinuously adapted and refined to addresstopics arising from student inquiriesand experiences. An inquiry might beextended or an activity added if itsparks the interest of students or if aconcept isn’t being understood.”

Students need time for exploring andtaking wrong turns; testing ideas anddoing things over again; time for build-ing things and collecting things; time forconstructing physical and mathematicalmodels for testing ideas; time for askingand arguing; and time to revise their pre-vious notions of things (AAAS, 1990).

“It’s very rare, in most of my classes, thatI make an opening statement, presentthe lesson, the students go though thelesson, and then I bring it to closure, inone period,” says Woolbaugh. “Some ofmy activities might go four days. Someare ongoing in that I pull ideas fromwhat we did two months ago into a cur-rent lesson—that’s when I do some realteaching.”

Presenting the inquiry topic.John Graves uses the Learning CycleStrategy as a way to introduce aninquiry topic to his students.

“You need to introduce it somehow, youdon’t just put the materials out on thetable and turn students loose,” saysGraves. “The Learning Cycle is a greatmodel for inquiry, especially if you startit with an ‘interesting question’ so thekids have a reason to move into theexploration. You base your interestingquestion on a ‘discrepant event’—some-thing that is counter-intuitive. A dis-crepant event is a situation that doesn’tgo the way you think it should, and itengages you in wondering why. Based onthe discrepant event, the teacher asks aninteresting question.

It is best when students are prompted bythe discrepant event to produce theirown interesting questions, says Graves.

The K-W-L (what you know, what youwant to know, and what you’ve learned)charts are another useful tool for gettingstudents into inquiry, says Graves. The K-W-L charts are traditionally used atthe elementary grades, but are equallyeffective in middle and high school.

“Maybe you’re starting something onsnow,” he says, “so you ask students whatdo they already know about it, and whatdo they want to know about it. Out ofthat discussion, questions are raised. Stu-dents are now engaged in the activity,and that leads them into inquiry.”

Teachers’ knowledge of the content areabecomes critical in these strategies. Typi-cally, the elementary teacher has beentrained as a generalist because she mustteach all subjects to her students. Butwhen a teacher is doing full inquiry atany grade level, she often will find her-

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self dipping deeper into her knowledgereserves. In Graves’ example, the teacherwill need to know the science behindsnow—at least enough to know where tohelp her students look for answers.Teachers can reinforce their contentknowledge by seeking out mentors; talk-ing to professionals in the fields of sci-ence and mathematics; using other orga-nizations and the Internet as resources;reading widely; and taking advantage ofas many professional developmentopportunities as they can.

However, knowing it all is not onlyimpossible, it’s unnecessary. An impor-tant aspect of inquiry teaching is beingable to say to students, “I don’t know, let’sfind out.” In a community of learners,teachers and students work side by side,collaboratively constructing knowledge.

Classroom discourseand questioning

Akey to meaning making, say theauthors of Learning from Exem-plary Teachers (Tobin & Fraser,

1991), is to enable students to interactverbally with their teacher and peers. Ininquiry, questioning is one of the basictools for instruction (Good & Brophy,1997). To use their higher-order cognitiveskills, students need opportunities todescribe and clarify; elaborate and justi-fy; speculate and analyze; and reconsiderand form a consensus (Tobin & Fraser,1991).

Valuable classroom discussions can takevarious forms. Sometimes discourse takesplace during guided discussions inwhich the teacher facilitates learning byasking questions such as “Do you think

so?” and “Tell me why” (van Zee, et al.,1996). At other times, student-generatedinquiry discussions often “erupt into acacophony in which students vociferous-ly share their thinking. These may bemoments during which students makegreat progress in developing their under-standing” (van Zee, et al., 1996). Lastly,classroom discourse during inquiryoften takes place during small-groupinteractions in which students engage inindependent yet collaborative thinking(van Zee, et al., 1996).

Classroom discourse. Exemplaryteachers use a nonthreatening andencouraging debating style to involvestudents in whole-class discussions(Tobin & Fraser, 1991). They avoid a ten-dency to call on the same three to fivestudents. When questioning a student,teachers sometimes use “safety nets,”such as giving students hints andprompting a correct answer, but only tohelp a struggling student who would beotherwise embarrassed in front of herpeers. Teachers use positive feedbackduring activities and social interactions.Occasionally, teachers motivate studentsby offering rewards, such as giving extrapoints for quick and accurate work.Teachers’ practices are sensitive to theneeds and feelings of students andencourage participation in learningtasks (Tobin & Fraser, 1991).

PURSUING STUDENTS’DIVERGENT QUESTIONS AND COMMENTSIS ONE OF THE CENTRAL ELEMENTS OFINQUIRY TEACHING.

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Questioning. In their book, Methodsfor Teaching: A Skills Approach (Jacob-sen, et al., 1993), the authors discuss thecritical role of questioning in effectiveteaching. In inquiry, skillful questioningis essential. It allows the teacher to fosterhigh-level discussions, either with thewhole class, in small groups, or withindividual students.

To spark high-level thinking, theauthors say, teachers should ask ques-tions that require intellectual processingon the part of the student, rather thanasking questions that require a studentonly to recall something from memory.Below are some questioning strategiesthat elicit high-level thinking from stu-dents (Jacobsen, et al., 1993):

■ Require students to manipulate priorinformation by asking questions such as,“Why do you suppose?” or “What can youconclude from the evidence?”

■ Ask students to state an idea or defini-tion in their own words.

■ Ask questions that require the solutionto a mathematical problem.

■ Involve students in observing anddescribing an event or object by askingquestions such as, “What do you noticehere?” “Tell me about this,” and “What doyou see?”

■ Ask students to compare two or moreobjects, statements, illustrations, ordemonstrations, and to identify similari-ties or differences between them. Whileidentifying similarities, students willbegin to establish patterns that can leadto understanding of a concept or generalization.

The authors also recommend that teach-ers wait three seconds or longer after

asking a student a question beforeprompting or calling on another student.When teachers increase their wait timeduring questioning, the quality and fre-quency of student responses improves.

Asking probing questions. Stu-dents need opportunities to processinformation by justifying or explainingtheir responses—dealing with the “why,”“how,” and the “based upon what” aspectsof a concept. Probing promotes reflectiveand critical thinking. Because it requiresteachers to think quickly in themoment, it can also be one of the mostdifficult questioning techniques (Jacob-sen, et al., 1993).

For a student who is having troubleanswering a question, probing can beeffective (Ornstein, 1995). When a stu-dent’s response to a question is accuratebut incomplete, a teacher needs to askprobing questions to get the student tothink deeper about an hypothesis orproblem. Asking for clarification,rephrasing the question, asking relatedquestions, and restating the student’s

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ideas are all aspects of probing (Orn-stein, 1995).

Divergent questions and com-ments. Pursuing students’ divergentquestions and comments is one of thecentral elements of inquiry teaching. Itnot only engages students in classroomdiscussions, it allows them to thinkindependently, creatively, and morecritically. It teaches them to take own-ership of their own learning—whilealso feeling a shared responsibility forthe learning of the entire class—and torespect others’ opinions and ways ofthinking.

A teacher can ask divergent questionsto elicit many different answers. Forexample, there could be many appro-priate answers to questions like, “Howare the beans alike?” or “Give me anexample of a first-class lever” (Jacob-sen, et al., 1993). Divergent questionsallow a number of students to respondto the same question, encouraging stu-dent participation. Redirecting ques-tions will also help to increase thenumber of students participating in a

discussion, but teachers need to make astrong effort to call on all studentsequally. When students are called onwith the same frequency and in thesame manner, student achievementincreases, while behavior problems andabsenteeism decreases (Jacobsen, et al.,1993). Redirecting questions—especiallydescription and comparison questions—to numerous students during a discus-sion fosters positive teacher/studentinteraction.

Knowing when to follow up on a stu-dent’s divergent question or commenttakes skill and experience. Teachersmust decide whether to set aside a stu-dent’s question, to answer directly, or totry to follow up on a student’s ideasthrough an extended discussion (vanZee, et al, 1996). The authors of Teachersas Researchers: Case Studies of Studentand Teacher Questioning DuringInquiry-based Instruction (van Zee, etal., 1996), a paper presented at the meet-ing of the American Association forthe Advancement of Science in Seattle,Washington, identify a number ofdilemmas teachers face regarding stu-dents’ questions:

■ Gauging the interest of the rest ofthe class in the question

■ Assessing the risk of confusing oth-ers while examining the issue raised

■ Assessing the risk of exceeding one’sown knowledge and being able to pro-ceed appropriately even if one doesn’tknow the answer

■ Pondering the best way to addressissues on the spot or perhaps at a latertime

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■ Considering the time available to theend of the lesson and the end of theterm

How a teacher handles divergent ques-tions depends on the circumstances, saysGraves. “A lot of times, if the kids areable to generate questions that are wor-thy of the exploration, you go withthem,” he says. “The other aspect of thisis the instructor’s skill in taking a stu-dent’s question and refocusing it so thatit becomes the question needed (to get tothe core of the content). A skilledteacher can elicit these kinds of ques-tions. You can go back into the teacher’slesson plan and find the exact questionthat the teacher wanted—it’s fun whenthat happens.”

Responding effectively to divergentquestions can be difficult, especially fora new teacher, says Graves. “It takes timeto develop good questioning skills,” hesays, “Even for a seasoned teacher, youcan’t expect to do it with every lesson. Idon’t think that’s realistic.”

Challenges ofinquiry-basedteachingDemands on teacher contentknowledge. Inquiry can make signif-icant demands on teachers’ contentknowledge (Magnusson & Palincsar,1995). By including students in decision-making, and encouraging them to askquestions, debate, and negotiate, ateacher must rely even more heavily onhis expertise in the subject, knowledgeof resources, and ability to think quick-ly. With sufficient content knowledge, a

teacher can prepare multiple learningexperiences for his students, providingthem with ample opportunity to developdeeper understandings of concepts(Tobin & Fraser, 1991).

“In some situations you don’t just doinquiry on one thing, only one time,”says Graves. “For example, doing the airpressure experiment with Cartesiandivers, you need more than two little popbottles and the medicine dropper. Youneed to have another air pressuredemonstration that the kids can do, andanother one, and another one—as manyof those as you can get.”

Teachers will want to pursue everyopportunity to deepen their knowledgeof the subjects they teach. In addition toattending workshops and conferencesrelated to their fields of expertise, teach-ers can pursue advanced studies or fel-

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lowship opportunities at a local universi-ty or college; attend summer institutes;seek opportunities to work with scien-tists and mathematicians in authenticresearch; and read widely. Teachers canalso develop out-of-school contacts withprofessionals who can offer expert adviceand resources. Not only will a teacherdevelop expertise in his subject areas by

undertaking some of these endeavors, hewill model valuable lifelong learningpractices to his students.

Demands on pedagogical skill.Teacher skill is crucial to inquiry. It iseven more critical if the teacher lackssufficient classroom equipment andmaterials (Flick, 1995). Even with suffi-cient support, a teacher will face manydilemmas when engaged in inquiry.

How can the teacher facilitate discoveryand provide guidance? When does theteacher intervene, and when does hestand back and allow students to make“mistakes”? How can a teacher determinewhen a problem centers on an impor-tant principle or a trivial one? Whatdoes a teacher do when he doesn’t knowthe answer? Many of these dilemmascan be met with questioning and man-agement strategies.

Conclusion

Today’s view of teaching suggeststhat students and teachers mustshare responsibility for learning.

No longer are teachers thought to be soledispensers of knowledge. Rather, theymust balance the need to ensure that stu-dents have ample opportunity to learncore concepts, with students’ need toexplore—alone and with one another—and to construct their own understand-ings. Inquiry is central to mathematicsand science learning (NRC, 1996). It is animportant tool teachers can use in help-ing students boost their performance inacademics, critical thinking, and problemsolving (Haury, 1993; Flick, 1995). On thefollowing pages, teachers will find fur-ther resources to help them implementstrategies from the inquiry continuum.

Resources & Bibliography

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Resources for furtherreading

Aldridge, B. (Ed.). (1995). A high schoolframework for national science educa-tion standards. Washington, DC:National Science Teachers Association.

American Association for the Advance-ment of Science. (1993). Benchmarksfor science literacy: Project 2061. NewYork, NY: Oxford University Press.

American Association for the Advance-ment of Science. (1997). Resources forscience literacy: Professional develop-ment. Project 2061. Washington, DC:Author.

Boujaoude, S. (1995). Demonstrating thenature of science. The Science Teacher,62(4), 46-49.

Borasi, R. (1992). Learning mathematicsthrough inquiry. Portsmouth, NH:Heinemann.

Boujaoude, S. (1995). Demonstrating thenature of science. The Science Teacher,62(4), 46-49.

Cohen, E. (1991, April). Classroom man-agement and complex instruction. Apaper presented at the annual meet-ing of the American EducationalResearch Association, Chicago, IL.(ERIC ED333547)

Colburn, A., & Clough, M. (1997). Imple-menting the learning cycle. The Sci-ence Teacher, 64(5), 30-33.

Driver, R. (1989). Students’ conceptionsand the learning of science: Introduc-tion. International Journal of ScienceEducation, 11(5), 481-490.

Grosslight, L.,. Unger, E., & Smith, D.(1991). Understanding models andtheir use in science: Conceptions ofmiddle and high school students andexperts. [Special Issue] Journal ofResearch in Science Teaching, 28(9),799-822.

Kyle, W.C., Jr. (1980). The distinctionbetween inquiry and scientificinquiry and why high school stu-dents should be cognizant of the dis-tinction. Journal of Research in Sci-ence Teaching, 17(2), 123-130.

McGilly, K. (Ed.). (1994). Classroomlessons: Integrating cognitive theoryand classroom practice. Cambridge,MA: The MIT Press.

National Academy of Sciences. (1996).Resources for teaching elementaryschool science. Washington, DC:Author.

National Academy of Sciences. (1996). Sci-ence for all children: A guide toimproving elementary science educa-tion in your school district. Washing-ton, DC: Author.

National Council of Teachers of Mathe-matics. (1989). Curriculum and evalu-ation standards for school mathemat-ics. Reston, VA: Author.

National Council of Teachers of Mathe-matics. (1991). Professional standardsfor teaching mathematics. Reston, VA:Author.

National Research Council. (1996).National science education standards.Washington, DC: National Academy ofSciences.

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National Research Council. (1989). Every-body counts. Washington, DC: NationalAcademy of Sciences.

National Science Resource Center. (1996).Science for all children: A guide toimproving elementary science educa-tion in your school district. Washing-ton, DC: National Academy Press.

Roth, K.J. (1989). Science education: It’snot enough to ‘do’ or ‘relate.’ TheAmerican Educator, 13(4), 16-22; 46-48.

Roth, W. (1991). Open-ended inquiry: Howto beat the cookbook blahs. The Sci-ence Teacher, 58(4), 40-47.

Saul, W., & Reardon, J. (Eds.). (1996).Beyond the science kit: Inquiry inaction. Portsmouth, NH: Heinemann.

Schauble, L., Klopfer, L., & Raghavan, K.(1991). Students’ transition from anengineering model to a science modelof experimentation. [Special issue]Journal of Research in Science Teach-ing, 28(9), 859-882.

Unruh, R., Countryman, L., & Cooney, T.(1992). The PRISMS approach: A spec-trum of enlightening physics activi-ties. The Science Teacher, 59(5), 36-41.

Willis, S. (1995, Summer). Reinventing sci-ence education. Reformers promotehands-on, inquiry-based learning.Association for Supervision and Cur-riculum Development, CurriculumUpdate, pp. 1-8.

Organizations

American Association for theAdvancement of Science (AAAS)1200 New York Avenue, N.W.Washington, DC 20005(202) 326-6400http://www.aaas.org/

The American Association for theAdvancement of Science is a nonprofitprofessional society dedicated to theadvancement of scientific and techno-logical excellence across all disciplines,and to the public’s understanding of sci-ence and technology. AAAS provides avariety of publications and resources,including Inquiry in the Library, a 1997publication edited by Maria Sosa andJerry Bell promoting student inquiry inthe library and in the classroom.

National Council for Teachers ofMathematics (NCTM)1906 Association DriveReston, VA 20191-1593(703) 620-9840Fax: (703) 476-2970http://www.nctm.org/

The National Council of Teachers ofMathematics is a nonprofit professionalassociation dedicated to the improve-ment of mathematics education for allstudents in the United States and Cana-da. All NCTM members receive councilpublications including regular issues ofthe News Bulletin, Student Math Notesand one or more of their four journals.NCTM also publishes books, videotapes,software, and research reports.

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National Science Foundation (NSF)4201 Wilson BoulevardArlington, VA 22230(703) 306-1234E-mail: info@nsf.govhttp://www.nsf.gov/

The National Science Foundation is anindependent U.S. government agencyresponsible for promoting science andengineering by funding research andeducation projects. Information aboutNSF programs, activities, funding oppor-tunities, current publications, meetingsand conferences are available in a num-ber of publications, including the NSFBulletin, available online athttp://www.nsf.gov/od/lpa/news/publicat/bulletin/bulletin.htm, andFrontiers newsletter, available online athttp://www.nsf.gov/od/lpa/news/publicat/frontier/start.htm. Inquiriesabout subscribing to the print version ofthis newsletter should be sent to blom-bard@nsf.gov

National Science TeachersAssociation (NSTA)1840 Wilson BoulevardArlington, VA 22201-3000(703) 243-7100 Fax: (703) 243-7177http://www.nsta.org/

The National Science Teachers Associa-tion is the largest organization in theworld committed to promoting excel-lence and innovation in science teachingand learning for all. The Associationpublishes five journals, a newspaper,many books, and a new children’s maga-zine, and conducts national and regionalconventions.

Northwest Regional EducationalLaboratory (NWREL)Science and Mathematics Education101 S.W. Main Street, Suite 500Portland, OR 97204-3297(503) 275-9500Kit Peixotto, Unit Director, (503) 275-9594E-mail: peixottk@nwrel.orghttp://www.nwrel.org/psc/same/

The Northwest Regional EducationalLaboratory provides leadership, exper-tise, and services to educators and othersin the states of Alaska, Idaho, Montana,Oregon, and Washington. The Scienceand Mathematics Education (SAME)unit provides services in support of effec-tive curriculum, instruction, and assess-ment, and maintains a lending libraryof books, videos, and other materials ona variety of topics, including inquiry-based teaching, equity issues, educationreform, standards and assessment, andeffective instructional practices.

Science and MathematicsConsortium for Northwest Schools (SMCNWS)Columbia Education Center171 N.E. 102ndPortland, OR 97220-4169(503) 760-2346Ralph Nelsen, DirectorE-mail: ralph@col-ed.orghttp://www.col-ed.org/smcnws

The SMCNWS is one of 10 regional Eisen-hower consortia that disseminatespromising educational programs, prac-tices, and materials and provides techni-cal assistance and training in support ofstate and local initiatives for quality sci-ence and mathematics content, curricu-lum improvement, and teacher enhance-ment.

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Southwest Educational DevelopmentLaboratory (SEDL)211 East Seventh StreetAustin, TX 78701-3281(512) 476-6861http://www.sedl.org

The Southwest Educational Develop-ment Laboratory produces the publica-tion Classroom Compass, which presentsexamples of instructional activities thatillustrate each issue’s theme. See the Fall1995 issue: Volume 2, No. 1, Science asInquiry, also available online athttp://www.sedl.org/scimath/com-pass/v02n01/welcome.html.

Technical Educational ResearchCenter (TERC)2067 Massachusetts AvenueCambridge, MA 02140(617) 547-0430http://www.terc.edu

Produces the semi-annual publication,Hands On! For subscription contact:Communications@terc.edu

See Volume 18, No. 1, Coping with Inquiry,available online athttp://www.terc.edu/handson/spring_95/copinquiry.html. The author, TimBarclay, addresses succeeding and failingat inquiry, an inquiring attitude, andvarious teaching strategies.

Online ResourcesAccess Excellence: Classrooms of the21st Centuryhttp://www.gene.com/ae/21st/

This teaching and learning forumexplores current issues in curriculum,instruction, and assessment, and con-nects science teachers with innovatorswho are developing creative ways to usetechnology as a tool in science class-rooms.

Busy Teachers’ WebSitehttp://www.ceismc.gatech.edu/BusyT/TOC.html

This site is designed to provide K-12teachers with direct source materials,lesson plans, and classroom activitieswith a minimum of site-to-site linking.Mathematics, science, and other topicsare covered. Links to Internet DiscussionGroups for Educators (and Students) areprovided.

Eisenhower National Clearinghousefor Mathematics and Science Educationhttp://www.enc.org/

This is a nationally recognized informa-tion source for K-12 mathematics and sci-ence teachers sponsored by the U.S.Department of Education, Office of Edu-cational Research and Improvement.Resources include curriculum resources,a monthly list of outstanding Internetsites, thousands of classroom-readylessons and activities, and links to othersites.

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iwonder — Inquiry-Based Learningand Teaching: Mathematics and Science through Museum Collectionshttp://iwonder.bsu.edu/

This site is devoted to inquiry-basedteaching strategies and provides teach-ing tools, including lesson plans, work-shops, classroom ideas and strategies, andinteractive student links.

Make It Happen! Integrating Inquiryand Technology into the MiddleSchool Curriculumhttp://www.edc.org/FSC/MIH/

In the Make It Happen! approach, inter-disciplinary teams of teachers designand implement inquiry-based I-SearchUnits and integrate technology intothese units in meaningful ways. Make ItHappen! is the result of 10 years ofresearch, evaluation, and technical assis-tance at the Education DevelopmentCenter, Inc. (EDC) in Newton, Massachu-setts.

Materials World Modules: An NSFInquiry-Based Science & TechnologyEducational Programhttp://mrcemis.ms.nwu.edu/mwm/

The Materials World Modules (MWM) isa National Science Foundation fundedproject producing a series of interdisci-plinary educational modules centeredon aspects of materials science. Themodules are intended for use in highschool science and mathematics class-rooms. Some modules are also suitablefor use in middle school settings.

Mathematics Learning Forumshttp://www.edc.org/CCT/mlf/MLF.html

The Bank Street College of Educationhosts a series of online seminars focusedon the “how to” of mathematics instruc-tion for elementary and secondaryteachers, providing ongoing support toteachers as they implement reform intheir own classrooms. Participantsactively exchange ideas, share concerns,and construct new understandings asthey converse with colleagues. For a reg-istration form and more informationphone (212) 807-4207; e-mail cct@edc.orgor visit the Web site.

Perspectives of Hands-On ScienceTeachinghttp://www.ncrel.org/sdrs/areas/issues/content/cntareas/science/eric/eric-toc.htm

This book is posted on the North CentralRegional Educational Laboratory’s Path-ways to School Improvement Internetserver. It was published by ERIC Clear-inghouse for Science, Mathematics, andEnvironmental Education, and writtenby David L. Haury and Peter Rillero in1994. This book/site presents answers tofrequently asked questions about hands-on approaches to science teaching andlearning. A number of resources, curric-ula, programs, strategies, and techniquesare cited.

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Project-Based Science: RealInvestigation, Real Sciencehttp://www.imich.edu/~pbsgroup/

The goal of the PBS group is to improvethe way science classes are taught byinvolving students in finding solutionsto authentic questions through extendedinquiry, collaboration, and use of tech-nology.

Science Educationhttp://www.tiac.net/users/lsetter/index.htm#pageindx

This page is the culmination of a doctor-al project completed by Linda S. Setter-lund at the University of Massachusetts,Lowell College of Education. It provides acollection of links on inquiry, construc-tivism, problem solving and creativity,and other mathematics and science sites.

Science Learning Network http://www.sln.org/info/

The Science Learning Network (SLN) isan online community of educators, stu-dents, schools, science museums, andother institutions demonstrating a newmodel for inquiry science education.SLN is an NSF project that incorporatesinquiry-based teaching approaches, tele-computing, collaboration among geo-graphically dispersed teachers and class-rooms, and Internet resources.

The Supportive Inquiry-BasedLearning Environment (SIBLE)http://www.ls.sesp.nwu.edu/sible/

The Supportive Inquiry-Based LearningEnvironment project is developing soft-ware to support project-based scienceand learning in classrooms. The softwareis intended to be used by both teachersand students for developing science pro-jects, supporting project tasks, andassessing projects.

The Why Files? Science Behind the Newshttp://whyfiles.news.wisc.edu/

A project of the National Institute forScience Education, this site is an elec-tronic exploration of the science behindthe news. Designed for teachers and stu-dents, the goal is to aid inquiry andbroaden the conversation among science,engineering, mathematics, technology,and the rest of society.

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Student Sites

Interesting Places for Kidshttp://www.crc.ricoh.com/people/steve/kids.html

This is an ongoing collection of linksthat might be interesting to children. Sci-ence and mathematics, museums, art, lit-erature, and many other topics are listed.

Kid’s Search Toolshttp://www.rcls.org/ksearch.htm

Six search engines, including: Berit’s BestSites for Children, which includes over590 sites; Pathfinder’s SiteSeeker searcheskid-safe Web sites; Magellen ReviewedWeb Sites targets sites appropriate foryoung audiences; Librarians’ Index tothe Internet (Select Kids), and more.

Yahooligans! The Web Guide for Kidshttp://www.yahooligans.com/

A special version of Yahoo designedspecifically for eight- to 14 year-olds pro-vides searching and browsing capa-bilities.

SuppliersThe suppliers listed below offer a varietyof materials and resources useful forinquiry-based teaching. While presenceon this list does not imply endorsementby NWREL, the entries are representa-tive of those available.

Activities Integrating Mathematicsand Science (AIMS) Education FoundationPO Box 8120Fresno, CA 93747-8120(888) 733-2467Fax: (209) 255-6396http://www.AIMSedu.org/E-mail: aimsed@fresno.edu

American Association of Physics TeachersOne Physics EllipseCollege Park, MD 20740-3845(301) 209-3300

American Chemical SocietyEducation Division1155 Sixteenth Street, N.W.Washington, DC 20036(800) 209-0423

Carolina Biological Supply Company2700 York RoadBurlington, NC 27215-3398(800) 334-5551Fax: (800) 222-7112

Creative Publications5040 West 111th StreetOak Lawn, IL 60453(800) 624-0822

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Cuisenaire Company of America, Inc.PO Box 5026 White Plains, NY 10601-5026Customer Service: (800) 237-3142Fax: (800) 551-RODSE-mail: INFO@CUISENAIRE.COM

Dale Seymour PublicationsPO Box 10888Palo Alto, CA 94303-0879(800) 872-1100Fax: (415) 324-3424

Delta Education, Inc.PO Box 3000Nashua, NH 03061-3000(800) 442-5444Fax: (800) 282-9560

Great Explorations in Math and Science (GEMS)University of CaliforniaBerkeley, CA 94720(510) 642-7771

Heinemann361 Hanover StreetPortsmouth, NH 03801-3912(800) 541-2086Fax: (800) 847-0938

Minnesota Educational ComputingCompany (MECC)Brookdale Corporate Center6160 Summit DriveMinneapolis, MN 55430-4003(800) 685-6322

National Aeronautics and SpaceAdministration (NASA)Education DivisionMail Code FEWashington, DC 20546-0001

Request Publication: How to AccessNASA’s Education Materials and Services

NW Region’s Teacher Resource Center (415) 604-3574

Pitsco, Inc.1002 E. AdamsPO Box 1708Pittsburg, KS 66762-1708(800) 835-0686Fax: (800) 533-8104http://www.pitsco.com

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Borasi, R. (1992). Learning mathematicsthough inquiry. Portsmouth, NH:Heinemann.

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Johnson, D., & Johnson, R. (1991). Class-room instruction and cooperativelearning. In H. Waxman, & H. Walberg(Eds.), Effective teaching: Currentresearch (pp. 277-293). Berkeley, CA:McCutchan Publishing Corporation.

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Lawton, M. (1997, April 23). Hands-on sci-ence gets a thumbs up from students.Education Week, p. 12.

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National Council of Teachers of Mathe-matics. (1989). Curriculum and evalu-ation standards for school mathemat-ics. Reston, VA: Author.

National Council of Teachers of Mathe-matics. (1991). Professional standardsfor teaching mathematics. Reston, VA:Author.

National Research Council. (1989). Every-body counts. Washington, DC: NationalAcademy of Sciences.

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National Research Council. (1996).National science education standards.Washington, DC: National Academy ofSciences.

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Seifert, E., & Simmons, D. (1997). Learningcentered schools using a problem-based approach. National Associationof Secondary School Principals Bul-letin, 81(587), 90-97.

Simpson, D. (1996, February). Engagingstudents in collaborative conversa-tions about science. Paper presented atthe meeting of the American Associa-tion for the Advancement of Science,Seattle, WA.

Tobin, K., & Fraser, B. (1991). Learningfrom exemplary teachers. In H. Wax-man, & H. Walberg (Eds.), Effectiveteaching: Current research (pp. 217-236). Berkeley, CA: McCutchan Pub-lishing Corporation.

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Northwest Regional Educational Laboratory101 S.W. Main Street, Suite 500Portland, Oregon 97204(503) 275-9500