DOCUMENT RESUME

ED 413 188 SE 060 765

AUTHOR Jarrett, DeniseTITLE Inquiry Strategies for Science and Mathematics Learning:

It's Just Good Teaching.INSTITUTION Northwest Regional Educational Lab., Portland, OR. School

Improvement Program.SPONS AGENCY Office of Educational Research and Improvement (ED),

Washington, DC.PUB DATE 1997-05-00NOTE 43p.; Photographs may not reproduce well.CONTRACT RJ96006501AVAILABLE FROM Northwest Regional Educational Laboratory, 101 S.W. Main

Street, Suite 500, Portland, OR 97204.PUB TYPE Guides Classroom Teacher (052) Reports Descriptive

(141)

EDRS PRICE MF01/PCO2 Plus Postage.DESCRIPTORS *Cognitive Development; Educational Change; Elementary

Secondary Education; *Inquiry; *Mathematics Instruction;Science Instruction; Teacher Education; *Teaching Methods

IDENTIFIERS Northwest Regional Educational Laboratory

ABSTRACT

Science and mathematics reform standards call for inquiryteaching methods that enable students to contribute their own ideas and topursue their own investigations. Inquiry involves activities and skills thatfocus on the active search for knowledge of understanding to satisfy acuriosity. This publication is intended to furnish K-12 teachers with bothresearch-based rationale and recommendations for effective techniques thatcan be applied in today's complex and changing classrooms. Sections include:"What is Inquiry?"; "Why Use Inquiry?"; "Inquiring into Pendulums inManhattan, Montana"; "Creating an Inquiry-based Classroom"; "Implications forCurriculum"; "Planning an Inquiry Lesson"; "Classroom Discourse andQuestioning"; and "Challenges of Inquiry-based Teaching". Twenty-fiveresources, 8 support organizations, 16 on-line resources, and 13 suppliersare included. Contains 31 references. (DKM)

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PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL

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10 THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

U S DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement

EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

I ument has been reproduced as

Vreceived from the person or organizationoriginating itMinor changes have been made toimprove reproduction quality

Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy

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 JarrettResearch and writingKit PeixottoConceptual support and guidanceDawn DzubayResource research and compilationDenise CrabtreeDesktop publishingLee ShermanEditorial reviewPhotographyDenise 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; Tbny Kneidek: page 24

Inquiry Strategies forScience and MathematicsLearningIt's Just Good

by Denise JarrettScience and Mathematics Education

May 1997

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Northwest Regional Educational Laboratory

Table of ContentsPreface

1

Introduction 2

What is inquiry? 3

Inquiry is on a continuum 3

Inquiry is "just good teaching" 5

Why use inquiry? 5

Improves student attitude and achievement 5

Facilitates student understanding 6

Facilitates mathematical discovery 7

Inquiring into pendulums in Manhattan, Montana 8

Creating an inquiry-based classroom 7

Engage students in designing the learning environment 11

Reflect the nature of inquiry 11

Integrate science laboratories into the regular class day 11

Use inquiry in the mathematics classroom 12

Use management strategies to facilitate inquiry 12

Share control 13

Spark student motivation 13

Take on new roles 14

Implications for curriculum 15

Teaching the "facts" 16

Choosing an inquiry topic 17

Getting at the core content 18

Planning an inquiry lesson 19

Using the Learning Cycle Strategy 19

Planning the use of time 20

Presenting the inquiry topic 21

Classroom discourse and questioning 22

Classroom discourse 22

Questioning 23

Asking probing questions 23

Divergent questions and comments 24

Challenges of inquiry-based teaching 25

Demands on teacher content knowledge 25

Demands on pedagogical skill 26

Conclusior 26

Resources and bibliography 27

5

PrefaceInquiry-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 predictionsabout the relationship between circum-ference and diameter that arise from anexploration of different-sized spheres, orthe high school student's questions thatare provoked by a local environmentalissue, students become actively engagedin the learning process when given theopportunity to hypothesize and investigate.

The Science and Mathematics Educationunit at the Northwest Regional Educa-tional Laboratory offers Inquiry Strategiesfor Science and Mathematics Learning asthe second publication in our It'sJust Good Thaching 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 in theseries will explore standards-based teach-ing and using assessment to informinstruction.

All publications follow a similar format.An initial summary of the key themes inthe current research and literature setsthe stage for the subsequent discussionof research-recommended practices.Included throughout the publications areinsights from Northwest educators whoare implementing these strategies andrepresent examples of "real-life researchin practice." The listing of print materi-als, organizations, and online resourcesenables teachers to access and exploreadditional tools to support their efforts toprovide all students with the mathemat-

1

ics and science knowledge, skills, andabilities 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 programs.We are proud to be partners with thededicated practitioners who work onbehalf of students throughout the North-west. We invite your analysis and feed-back of Inquiry Strategies for Science andMathematics Learning: It's Just GoodThaching as a resource to strengthen sci-ence and mathematics education in theregion.

Kit PeixottoUnit ManagerScience and Mathematics EducationMay 1997

6

IntroductionIn 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).

'Ibday, 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. Stu-dents need to personally construct theirown knowledge by posing questions,planning investigations, conducting theirown experiments, and analyzing andcommunicating their findings. Also, stu-dents need to have opportunities toprogress from concrete to abstract ideas,rethink their hypotheses, and retryexperiments and problems (NRC, 1996;AAAS, 1990, 1993; National Council ofTbachers of Mathematics [NCTM], 1991;Rosenshine, 1995; Flick, 1995). In short,students construct their own knowledgeby actively taking charge of their learn-ingone of the primary tenets ofinquiry.

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

2

own ideas and to pursue their owninvestigations (NRC, 1996; NCTM, 1991;AAAS, 1990, 1993). However, no singleteaching method is appropriate in all sit-uations, for all students. Teachers needto know how and when to use a varietyof strategies (Good & Brophy, 1997).Embedding teaching strategies within anoverall inquiry-based pedagogy can bean effective way to boost student perfor-mance in academics, critical thinking,and problem solving.

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

ii NQUIRY IS THE [SET] OFBEHAVIORS INVOLVED IN

THE STR GLE OF HUMAN BEINGS FORREASONABLE EXPLANATIONS OFPHENOMENA ABOUT WHICH THEY ARECURIOUS."

have significant input into just aboutevery aspect of their learninghow 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.

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, 'leachingScience 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.Tbday, 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.

3

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, notdiscoveries)

Students do laboratory activities thatlead to student discoveries

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

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

Each step represents significantly morerisk taken by the teacher and increasing-ly 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 given hypoth-esis. The complexity of these activitieswill vary with student age and experi-ence, but there are entrances for everychild."

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:

1 Learning in a rich environment

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

E Hypothesizing

E Planning an investigation

Collecting data

U Analyzing that data

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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 EffectiveTeaching: Current Research (Waxman &Walberg, 1991), Kenneth Tbbin and BarryFraser identify teaching strategies thatare used by exemplary mathematics andscience teachers. According to research,exemplary teachers ensure that activitiesare set up to allow students to be physi-cally and mentally involved in the acad-emic subjects. Activities are based on theuse of materials to investigate questionsand solve problems. Thachers use verbalinteraction to monitor student under-standing of the content, and facilitatepeer interactions by setting up small-group discussions.

LL INQUIRYEXPERIENCES DO

LVE A MOP AND

APOLOGY TO THE CUSTODIAN."

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 Tbbin andFraser. The most successful teachershave deep content knowledge in thesubject areas that they teach, and in therelevant pedagogical theories and strate-

gies. They use skillful questioning tofocus student engagement and to probefor misunderstandings. They provideclear and appropriate explanations. Theyuse concrete examples and analogiesrelevant to students' livesto 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 (Tbbin & Fraser,1991).

Why use inquiry?Tbhere is evidence that inquiry-

ased instruction enhances stu-dent performance and attitudes

about science and mathematics, saysDavid Haury (1993). At the middleschool level, 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 BayerCorporation of Pittsburgh showed thatstudents who used hands-on experi-ments and team problem solving in sci-ence classrooms have a better attitudeabout the subject than students wholearned science through lectures andassigned textbook reading. Three out offive students, ages 10 to 17, said that

they would be "a lot more psyched"about science if they could do moreexperiments themselves and use a com-puter to communicate with scientistsand other students. Fifty-four percent ofthe students using more inquiry-orient-ed methods said that science is one oftheir favorite subjects, compared with 45percent of the students in traditionallytaught classes. Also, nearly 25 percent ofthe students in traditional classes saidthat science is their most difficult sub-ject, while only 18 percent of the stu-dents using inquiry strategies 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 comparedthe academic achievement of studentswho participated in the PRISMS projectwith students who did not. The studiesshowed that the PRISMS studentsachieved at a higher level, used higher

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level reasoning skills, and had more pos-itive 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 activi-ties. 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, "Experi-ence is always necessary for intellectualdevelopment; (therefore) the subjectmust be active," researchers in the pasttwo decades have developed a newunderstanding of learning (Brown &Campione, 1994; Rosenshine, 1995; Roth,1993; Nowell, 1992). Constructivist theo-ry states that knowledge is constructedthrough one's personal experience byassimilating new information with priorknowledge (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 associateprofessor at the Graduate School of Edu-cation and Human Development at theUniversity of Rochester and has writtenextensively on mathematics and inquiry.Knowledge is viewed not as a stablebody of established results, she says, butas a dynamic 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

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 of sci-entists, mathematicians, and technologyprofessionals (AAAS, 1990). In short, stu-dents need to understand science, math-ematics, 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, therole of inquiry in the study of mathemat-ics is 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 oth-ers... It is essential to keep in mind thatmathematical discovery is no more theresult of some rigid set of steps than isdiscovery 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 managelearning environments that pro-vide students with the time, space,

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

Inquiring intopendukmis inManhattan, Montana

AMay blizzard has thrown aheavy 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 lessonabout potential and kinetic energy,and the vocabulary term, the period ofa pendulum.

Woolbaugh repeats a demonstrationfor determining how many swings a

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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

13

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," saysMelinda.

"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.

t. I 9

"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 you

want 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 scientificprocesswe brainstormed ideasabout what might affect the period of

10

,

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.

15

resources are critical to students' abilityto do inquiry (NRC, 1996).

Engage students in designingthe learning environment. Askstudents for their ideas and suggestionson such decisions as how to use timeand space in the classroom. This is partof challenging students to take responsi-bility 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.The learning environment should reflectthe intellectual rigor, attitude, and socialvalues that characterize the way scien-tists and mathematicians pursue inquiry(NRC, 1996; Borasi, 1992; Brown & Cam-pione, 1994). According to the NationalScience Education Standards (NRC, 1996)and literature on inquiry and guided dis-coveries (Borasi, 1992; Brown & Campi-one, 1994), inquiry facilitates students'development of skills and dispositionsthat will serve them throughout theirlives. Tb create a classroom environmentthat reflects the nature of inquiry, teach-ers will want to:

II 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).

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

goals, planning activities, assessingwork, 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).

11

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-

16

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 hap-pen in the profession. A paleontologistat the Museum of the Rockies (in Boze-man) doesn't say, 'I think I'll go back tothe lab' It's all integrated. So isn't thatthe model we ought to use when teach-ing students from 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:

B3 Use the complexity of real-lifeproblems.

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Focus on nontraditional mathematicaltopics where uncertainty and limitationsare most evident.

Use errors as "springboards forinquiry."

Create ambiguity and conflict thatcompel 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 significanceof the 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, andbiographies.

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 manage-ment, teaching, and learning (TbbinFraser, 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 effectivemanagement strategies in place, theteacher considers one of her primarycurriculum goals to be developing stu-dents' autonomy and independence(Tbbin & Fraser, 1991). She maintainscontrol-at-a-distance over the entireclass, and actively monitors studentbehavior by moving around the roomand speaking with individual students.Students work both independently andcooperatively in groups.

CIENCE SHOULD BE LAB.

SCIE CE SHO LD BE A VERB AS OPPOSEDTO A

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 studentwithout disturbing others. She monitorsstudent engagement and understanding,and establishes routines that enable her tocope with a relatively large number of stu-

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dents with diverse learning needs. Sheemphasizes students' active participationin their own learning, and chooses activi-ties that ensure active thinking. Studentsare encouraged to try to work out difficul-ties on their own, consulting otherresources such as textbooks and peers('Ibbin & 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,and open-the-book kinds of things, justfor a management survival strategy."

Share control. Full inquiry is whenstudents are actively engaged in an inves-tigation, manipulating concrete objects,conferring with peers, pursuing their ownline of inquiry, and creating their ownsolutions to a problem (NRC, 1996). Ittakes a skillful teacher to guide students'learning, to keep students on-task, toknow when to let classroom discussionsgo off in a new direction, to make surethe lesson progresses coherently towardlearning goals. It also takes a courageousteacher to encourage students to offertheir own ideas, to make comments, todebate the validity of explanations andsolutions, and to take part in the decision-making (Borasi, 1992).

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

bert Walberg in their article, Ttachingand 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 Ttimwater, 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.

N A COMMUNITY OFLEARNERS, TEACHERS AND

S ENTS WORK SIDE BY SIDE,

COLLABORATIVELY CONSTRUCTING

KNOWLEDGE.

"I try to interact with students, and 1 tryto set up class so that we do about fourdifferent things over the course of theperiod," says Philips. "I lecture, wewatch a video, and we have two activi-ties that the students do. I try to keepclass moving. There are days when Italk more than I probably should, andthere are times when we go by withoutdoing enough labs because of where weare in the curriculum."

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

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is to help students become good problemsolvers and critical thinkers, teachersand students assume new roles. The listsbelow depict those things that teachers andstudents will do in an inquiry-based class-room (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

Reason logically, pose questions

El Confer and debate with peers and theteacher

Discuss their own ideas, as well asdevelop ideas and knowledge collabora-tively

Make logical arguments and constructexplanations

Illbst their own hypotheses

Communicate findings

111 Reflect on feedback from peers andthe teacher

N Consider alternative explanations

Retry experiments, problems, andprojects

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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 explo-rations are most often those that have

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not been preplanned, or even conceivedas possible, by the teacher," she says.

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

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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 thecoast of 'Texas. Remember that map wehad at school? Hawaii is off the coast ofTexas!' She never understood that thatwas a graphic inset. So there's an exam-ple of somebody who's constructed theirown knowledge, used absolutely goodreasoning, and used an appropriate tool,but she 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 isthe question 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 PostitsTM 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):

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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

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concepts (NRC, 1996). Inquiry requiresstudents to do more than observe, infer,and experiment. It requires them tocombine scientific processes with con-tent knowledgethey must use scientif-ic reasoning and critical thinking todevelop 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'sno science content in it. The studentshad fun, 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 atthat core content, and then make adjust-mentsthat's a never-ending job."

John Graves, who received a Presiden-tial Award for Excellence in Science andMathematics Thaching in 1996, teachesscience and English at Monforton MiddleSchool 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 phasesexploration, conceptintroduction, applicationis 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 buoyancy.)Here's how you can blow that inquirylesson: Let the kids build their owndiversthat's the exploration phasebut

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never ask students, 'How does this hap-pen in real life ?' Can you find a situa-tion where the change of pressure insomething 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.

"lb 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 theScience 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 Cycle toMach Physical Science (Beisenherz &Dantonio, 1996), the authors identifythree phases to the Learning Cycle:

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NOWLEDGE IS VIEWED NOT

AS A STABLE BODY

OF ESTABLISHED RESULTS, BUT

AS C PROCESS OF INQUIRY, WHEREUNCERTAINTY, CONFLICT, AND DOUI31

PROVIDE THE MOTIVATION FOR THECONTINUOUS SEARCH FOR A MORE REFINEDUNDERSTANDING OF THE WORLD."

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 pace andwith little guidance. Students often becomehighly motivated when they are permittedto do hands-on explorations before the con-cept is introduced. Then another, morestructured exploration allows students toreexamine the same objects and systemsmore scientifically. During this time, stu-dents generate questions, and form andtest their own hypotheses (Beisenherz &Dantonio, 1996).

In the next phase, the teacher uses sci-entific vocabulary to introduce the con-cept related to students' observations.lbgether, the teacher and students orga-nize the observations and experiences,and the resulting patterns often match

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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 (BeisenherzDantonio, 1996).

Depth of understanding is facilitatedwhen the concept is reinforced orexpanded during the application phase,often through the use of hands-on activi-ties. (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

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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 isdiscrepant 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. Mach-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 outideas, to make mistakes, to retry experi-ments, and to reflect. Students also needtime to work together in small groups,share their ideas in whole-class discus-sions, and work together and alone on avariety of tasks, including reading,experimenting, reflecting, writing, anddiscussing (NRC, 1996).

The National Science Education Standards(1996) recommend that teachers plancurriculum goals that are flexibleso that they can respond to students'needs and interests: "Thaching for under-

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standing requires responsiveness to stu-dents, so activities and strategies arecontinuously adapted and refined toaddress topics arising from studentinquiries and experiences. An inquirymight be extended or an activity addedif it sparks 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 buildingthings and collecting things; time for con-structing 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,that I make an opening statement, pre-sent the lesson, the students go thoughthe lesson, and then I bring it to closure,in one period," says Woolbaugh. "Someof my activities might go four days.Some are ongoing in that I pull ideasfrom what we did two months ago into acurrent lessonthat's when I do somereal teaching."

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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. Basedon the discrepant event, the teacher asksan interesting 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. TheK-W-L charts are traditionally used at theelementary grades, but are equally effec-tive in middle and high school.

"Maybe you're starting something onsnow," he says, "so you ask studentswhat do they already know about it, andwhat do they want to know about it. Outof that discussion, questions are raised.Students are now engaged in the activi-ty, 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 behindsnowat 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 'Thachers (Tbbin & 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). lb use their higher-order cogni-tive skills, students need opportunitiesto describe and clarify; elaborate andjustify; speculate and analyze; andreconsider and form a consensus (Tbbin& Fraser, 1991).

Valuable classroom discussions can takevarious forms. Sometimes discoursetakes place during guided discussions inwhich the teacher facilitates learning byasking questions such as "Do you think

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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 inquiry oftentakes place during small-group interac-tions in which students engage in inde-pendent yet collaborative thinking (vanZee, et al., 1996).

URSUING STUDENTS'

RGENT QUESTIONS AND COMMENTSOF THE CENTRAL ELEMENTS OF

INQUIRY TEACHING.

Classroom discourse. Exemplaryteachers use a nonthreatening andencouraging debating style to involvestudents in whole-class discussions(Tbbin & 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. 'leachers use positive feedbackduring activities and social interactions.Occasionally, teachers motivate studentsby offering rewards, such as giving extrapoints for quick and accurate work.'leachers' practices are sensitive to theneeds and feelings of students andencourage participation in learning tasks(Tbbin & Fraser, 1991).

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Questioning. In their book, Methodsfor Raching: A Skills Approach (Jacobsen,et al., 1993), the authors discuss the crit-ical role of questioning in effectiveteaching. In inquiry, skillful questioningis essential. It allows the teacher to fos-ter high-level discussions, either withthe whole class, in small groups, or withindividual students.

'Ib spark high-level thinking, the authorssay, teachers should ask questions thatrequire intellectual processing on thepart of the student, rather than askingquestions that require a student only torecall something from memory. Beloware some questioning strategies that elic-it high-level thinking from students(Jacobsen, et al., 1993):

Require students to manipulate priorinformation by asking questions such as,"Why do you suppose?" or "What canyou conclude from the evidence?"

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

Ask questions that require the solu-tion to a mathematical problem.

E Involve students in observing anddescribing an event or object by askingquestions such as, "What do you noticehere?" "Thll 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 orgeneralization.

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.

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Asking probing questions. Stu-dents need opportunities to processinformation by justifying or explainingtheir responsesdealing with the "why,""how," and the "based upon what"aspects of a concept. Probing promotesreflective and critical thinking. Becauseit requires teachers to think quickly inthe moment, it can also be one of themost difficult questioning techniques(Jacobsen, 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 learningwhilealso feeling a shared responsibility forthe learning of the entire classand 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

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discussion, but teachers need to makea strong effort to call on all studentsequally. When students are called onwith the same frequency and in thesame manner, student achievementincreases, while behavior problemsand absenteeism decreases (Jacobsen,et al., 1993). Redirecting questionsespecially description and comparisonquestionsto numerous students dur-ing a discussion fosters positiveteacher/student interaction.

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, orto try to follow up on a student's ideasthrough an extended discussion (vanZee, et al, 1996). The authors of 'Mach-ers as Researchers: Case Studies of Stu-dent and teacher Questioning DuringInquiry-based Instruction (van Zee, etal., 1996), a paper presented at themeeting of the American Associationfor the Advancement of Science inSeattle, Washington, identify a numberof dilemmas teachers face regardingstudents' 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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U 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,says Graves. "A lot of times, if the kidsare able to generate questions that areworthy 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 getto the 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 wantedit's fun whenthat happens."

Responding effectively to divergentquestions can be difficult, especially fora new teacher, says Graves. "It takestime to develop good questioning skills,"he says, "Even for a seasoned teacher,you can't expect to do it with every les-son. I don't think that's realistic."

ChaHeng s einquiry- basedteachingDemands on teacher contentknowledge. Inquiry can make signifi-cant 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 quickly.With sufficient content knowledge, a

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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 (buoyancy) experiment withCartesian divers, you need more thantwo little pop bottles and the medicinedropper. You need to have another airpressure demonstration that the kids cando, and another one, and another oneas many of those as you can get."

Tbachers 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. leachers canalso develop out-of-school contacts withprofessionals who can offer expertadvice and resources. Not only will ateacher develop expertise in his subjectareas by undertaking some of theseendeavors, he will model valuable life-long learning practices to his students.

Demands on pedagogical skill.'leacher 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 deter-mine when a problem centers on animportant principle or a trivial one?What does a teacher do when he doesn'tknow the answer? Many of these dilem-mas can be met with questioning andmanagement strategies.

ConclusionToday'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 toexplorealone and with one anotherand to construct their own understand-

Ns

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ings. Inquiry is central to mathematicsand science learning (NRC, 1996). It is animportant tool teachers can use in helpingstudents boost their performance in acad-emics, critical thinking, and problem solv-ing (Haury, 1993; Flick, 1995). On thefollowing pages, teachers will find fur-ther resources to help them implementstrategies from the inquiry continuum.

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Resources &Bibliography

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t esources fcr furtherreadingAldridge, B. (Ed.). (1995). A high school

framework for national science educationstandards. Washington, DC: NationalScience 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.

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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, WC., Jr. (1980). The distinctionbetween inquiry and scientific inquiryand why high school students shouldbe cognizant of the distinction. Journalof Research in Science Teaching, 17(2),123-130.

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

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

National Academy of Sciences. (1996).Science for all children: A guide toimproving elementary science educationin your school district. Washington, DC:Author.

National Council of Teachers of Mathe-matics. (1989). Curriculum and evalua-tion standards for school mathematics.Reston, VA: Author.

National Council of leachers 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 guideto improving elementary science educa-tion in your school district. Washington,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:How to beat the cookbook blahs. TheScience 'Thacher, 58(4), 40-47.

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

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

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

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

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BEST COPY AVAILABLE

OrganizationsAmerican 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 lbachers 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 Notes andone or more of their four journals.NCTM also publishes books, videotapes,software, and research reports.

National Science Foundation (NSF)4201 Wilson BoulevardArlington, VA 22230(703) 306-1234E-mail: infognsf.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, and Fron-tiers 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 leachersAssociation (NSTA)1840 Wilson BoulevardArlington, VA 22201-3000(703) 243-7100Fax: (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.

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Northwest Regional EducationalLaboratory (NWREL)Science and Mathematics Education101 S.W. Main Street, Suite 500Portland, OR 97204-3297(503) 275-9500Kit Peixotto, Unit Manager, (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) unitprovides services in support of effec-tive curriculum, instruction, and assess-ment, and maintains a lending library ofbooks, videos, and other materials on avariety of topics, including inquiry-basedteaching, 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 regionalEisenhower 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/compass/v02n01 /welcome.html.

lbchnical 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 withInquiry, available online athttp://www.terc.edu/handson/spring_95/copinquiry.html. The author,Tim Barclay, addresses succeeding andfailing at inquiry, an inquiring attitude,and various teaching strategies.

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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 lbachers' 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 Discus-sion Groups for Educators (and Students)are provided.

Eisenhower National Clearinghousefor Mathematics and ScienceEducationhttp://www.enc.org/

This is a nationally recognized informa-tion source for K-12 mathematics andscience 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.

iwonder Inquiry-Based Learningand leaching: Mathematics andScience 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,and interactive 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, Massa-chusetts.

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 centered onaspects of materials science. The mod-ules are intended for use in high schoolscience and mathematics classrooms.Some modules are also suitable for usein middle school settings.

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Mathematics Learning Forumshttp://www.edc.org/CCT/m1f/MLF.html

The Bank Street College of Educationhosts a series of online seminars focusedon the "how to" of mathematics instruc-tion for elementary and secondary teach-ers, providing ongoing support to teach-ers as they implement reform in theirown classrooms. Participants activelyexchange ideas, share concerns, and con-struct new understandings as they con-verse with colleagues. For a registrationform and more information phone (212)807-4207; e-mail cctgedc.org or visitthe 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 solutions toauthentic questions through extendedinquiry, collaboration, and use of tech-nology.

Science Educationhttp://www.tiac.net/users/Isetter/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 providesa collection of links on inquiry, construc-tivism, problem solving and creativity,and other mathematics and science sites.

Science Learning Networkhttp://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.

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BEST COPY AVAILABLE

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 sci-ence, engineering, mathematics, tech-nology, and the rest of society.

33 38

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

This is an ongoing collection of links thatmight be interesting to children. Scienceand mathematics, museums, art, litera-ture, and many other topics are listed.

Kid's Search lbolshttp://www.rcls.org/ksearch.htm

Six search engines, including: Berit's BestSites for Children, which includes over590 sites; Pathfinder's Site Seeker search-es kid-safe Web sites; Magellen ReviewedWeb Sites targets sites appropriate foryoung audiences; Librarians' Index to theInternet (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.

34

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) EducationFoundationPO Box 8120Fresno, CA 93747-8120(888) 733-2467Fax: (209) 255-6396http: / /www.AlMSedu.org/E-mail: aimsed@fresno.edu

American Association ofPhysics 'leachersOne 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 SupplyCompany2700 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 ofAmerica, Inc.PO Box 5026White 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 andScience (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

BES1 COPY AVAILABLE

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

Request Publication: How to AccessNASA's Education Materials and ServicesNW 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

4035

BibliographyAmerican Association for the Advance-

ment of Science. (1990). Science for allAmericans: Project 2061. New York, NY:Oxford University Press.

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

Beisenherz, P., & Dantonio, M. (1996).Using the learning cycle to teach physicalscience: A hands-on approach for themiddle grades. Portsmouth, NH: Heine-mann.

Borasi, R. (1992). Learning mathematicsthough inquiry. Portsmouth, NH: Heine-mann.

Brown, A., & Campione, J. (1994). Guideddiscovery in a community of learners.In K. McGilly (Ed.), Classroom lessons:Integrating cognitive theory and class-room practice (pp. 229-270). Cambridge,MA: The MIT Press.

Flick, L. (1995, April). Complex instructionin complex classrooms: A synthesis ofresearch on inquiry teaching methodsand explicit teaching strategies. Paperpresented at the meeting of theNational Association for Research inScience Tbaching, San Francisco, CA.

Good, T, & Brophy, J. (1997). Looking inclassrooms (7th ed.). New York, NY:Longman.

Haury, D. (1993). teaching science throughinquiry. Columbus, OH: ERIC Clearing-house for Science, Mathematics, andEnvironmental Education. (ED359048).

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Hiebert, J., Carpenter, T., Fennema, E.,Fuson, K., Human, P., Murray, H.,Olivier, A., & Wearne, D. (1996). Prob-lem solving as a basis for reform incurriculum and instruction: The caseof mathematics. Educational Researchei;25(4), 12-21.

Jacobsen, D., Eggen, P., & Kauchak, D.(1993). Methods for teaching: A skillsapproach (4th ed.). Columbus OH:Merrill.

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.

King, A., & Rosenshine, B. (1993). Effectsof guided cooperative questioning onchildren's knowledge construction.Journal of Experimental Education, 61(2),127-148.

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

Magnusson, S., & Palincsar, A. (1995). Thelearning environment as a site of sci-ence education reform. Theory IntoPractice, 34(1), 43-50.

National Council of 'leachers of Mathe-matics. (1989). Curriculum and evalua-tion standards for school mathematics.Reston, VA: Author.

National Council of lbachers of Mathe-matics. (1991). Professional standards forteaching mathematics. Reston, VA:Author.

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

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National Research Council. (1996). Nation-al science education standards. Washing-ton, DC: National Academy of Sciences.

Nowell, L. (1992, April). Rethinking theclassroom: A community of inquiry.Paper presented at the meeting of theNational Conference on Creating theQuality School, Norman, OK.

Ornstein, A. (1995). Strategies for effectiveteaching (2nd ed.). Madison, WI: Brownand Benchmark.

Rosenshine, B. (1995). Advances inresearch on instruction. Journal of Edu-cational Research, 88(5), 262-68.

Roth, W. (1991). Open-ended inquiry. TheScience Rachel; 58(4), 40-47.

Schifter, D. (Ed.). (1996). What's happeningin math class? Envisioning new practicesthrough teacher narratives (Vol. 1). NewYork, NY: Tbachers College Press.

Schifter, D. (Ed.). (1996). What's happeningin math class? Reconstructing profession-al identities (Vol. 2). New York, NY:Thachers College Press.

Seifert, E., & Simmons, D. (1997). Learn-ing centered schools using a problem-based approach. National Association ofSecondary School Principals Bulletin,81(587), 90-97.

Simpson, D. (1996, February). Engagingstudents in collaborative conversationsabout science. Paper presented at themeeting of the American Associationfor the Advancement of Science,Seattle, WA.

BEST COPY AVAILABLE

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

U.S. Department of Education. (1997).Pursuing excellence: A study of U.S.eighth-grade mathematics and scienceteaching, learning, curriculum, andachievement in international context. Ini-tial findings from the Third InternationalMathematics and Science Study (TIMSS)(LACES 97-198). Washington, DC:Author.

University of Northern Iowa. (January15, 1997). PRISMS project overview.[Online]. Available: http://www.prisms.uni.edu/Overview/

van Zee, E., Iwasyk, M., Kurose, A., Simp-son, D., & Wild, J. (1996, February).Teachers as researchers: Case studies ofstudent and teacher questioning duringinquiry-based instruction. Paper present-ed at the meeting of the AmericanAssociation for the Advancement ofScience, Seattle, WA.

Wang, M., & Walberg, H. (1991). Thachingand educational effectiveness:Research synthesis and consensus fromthe field. In H. Waxman, & H. Walberg(Eds.), Effective teaching: Currentresearch (pp. 81-103). Berkeley, CA:McCutchan Publishing Corporation.

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