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Using E-Mail to Write about MathMercedes S. Tichenor & Mary Jean JewellPublished online: 30 Jan 2008.

To cite this article: Mercedes S. Tichenor & Mary Jean Jewell (2001) Using E-Mail to Write aboutMath, The Educational Forum, 65:4, 300-308, DOI: 10.1080/00131720108984511

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Using E-Mail to Write about Mathby Mercedes S. Tichenorand Mary Jean Jewell

It is uncommon to ask a child, "Whatdid you write about in math today?" In fact,many students and teachers would findthis question awkward, because most donot associate writing with math. However,writing should be an essential componentof any math program. When writing aboutmath topics, children have the opportunityto organize information and reflect on theirknowledge and understanding. Writingalso provides records for the teacher thatassist in the assessment of children's learn­ing and understanding, provides a basis fordiscussion with the child, and aids in plan­ning for upcoming instructional activities(Griffiths and Clyne 1994).

The National Council of Teachers ofMathematics (NCTM 1989)has establishedfive student goals related to math. TheNCTM recommendations indicated thatstudents should learn to value mathemat­ics, become confident in their ability to domathematics, become mathematical prob­lem solvers, learn to reason mathematically,and learn to communicate mathematically.Specifically relating to communication inmathematics, NCTM (1998, 85) declared:

Mathematics instructional pro­grams should use communication tofoster understanding of mathematicsso that all students:

• organize and consolidate theirmathematical thinking to communi­cate with others;

• express mathematical ideas co­herently andclearly topeers, teachers,and others; •

• ext end their mathematicalknowledge by considering the think­ing strategies of others;

• use the language of mathemat­ics asa precise means ofmathematicalexpression .

Intrigued by these ideas, we developeda collaborative writing project between col­lege and elementary students that engagedthem in mathematical discourse via e-mail.We began the "keypal" project with clearpurposes in mind, but we happily discov­ered additional, more personally meaning­ful purposes as the project unfolded. As aneducation professor and a second-gradeteacher, we value the role that literacy playsin mathematical learning and understand­ing . Like others (Kennedy and Tipps 1997),we believe that students learn best whenengaged in authentic, integrated, and per­sonally meaningful experiences. We beganthis project convinced of its potential andcommitted to making it work for our stu­dents at both the college and elementarylevels.

ANCHORED BY PuRPOSE:

TEACHERS IN CONTROL

With any instructional approach, teach­ers must ask themselves, "Why are we do­ing this?" to make sure they are on target

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in accomplishing appropriate goals andobjectives. This first step is particularlyimportant when trying to alter current in­structional practice. Therefore, we beganthis project by discussing why it was im­portant for college and elementary studentsto collaborate. What purpose would ourwork together serve? How could we ensurethat it was most beneficial to our students?Our work began in May at a professional­development conference and continuedduring the summer via e-mail exchangesand occasional phone conversations. Ulti­mately, we agreed that the keypal projectcould help our preservice teachers: gain anawareness of how children learn and thinkabout mathematics; learn the importanceof using writing during math instruction;learn how to encourage children to writeabout mathematics; and teach studentshow to use and enjoy technology. We hopedthe exchanges would help the elementarystudents: organize thinking about math­ematics; express ideas, opinions, feelings,and questions about math; improve writ­ing and math skills; and use and enjoy tech­nology. We were excited about the possi-

bilities inherent in su ch a partnership anddeveloped a specific management plan forimplementation so the project would un­fold as predictably as possible.

PROJECT DESCRIPTION

To implement the project, we con­nected 13 elementary education majors and21 second graders via e-mail at the begin­ning of the school year. The two groups ofstudents were in different states, approxi­mately 600 miles apart. The university stu­dents involved in the project were enrolledin a math methods course for elementaryeducation majors at a private university inFlorida. The second graders attended pub­lic school in a suburban Tennessee commu­nity. Family support for education was evi­dent both at school and at home. The parentclub raised funds that significantly supple­mented the school budget, and participa­tion in volunteer and school-wide eventswas high. Many parents were collegegraduates employed in professional posi­tions. They expected their children to besuccessful in school, and most children metexpectations by performing at or above

Mercedes S. Tichenor is Assistant Professor ofTeacher Education at Stetson University in DeLand,Florida. Her research interests include integratingtechnology into teaching and learning, parent andcommunity involvement, and reflective practice.Dr. Tichenor is a member of the Zeta Tau ChapterofKappa Delta Pi.

Mary Jean Jewell is a doctoral candidate in readingeducation at Peabody College of VanderbiltUniversity in Nashville. She has been a resourceand elementary classroom teacher in Tennessee'sWilliamson County School System for 11 years.

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grade level. Students were randomlymatched; many preservice teachers hadtwo second-grade keypal partners, due todifferences in class size.

Before the e-mail exchanges began,preservice teachers were familiarized withthe project's purpose and completed coursereadings related to integrating writing withmath. They had several opportunities todiscuss their readings and ideas about theproject in class. Brainstorming sessionsabout types of questions to ask and how toget children to write about math conceptsalso occurred during the college class.Though many of the preservice teacherswere excited about the project, some wereskeptical about using writing as an instruc­tional strategy for teaching math. Thismethodology was not a part of their ownmath backgrounds, and they were con­cerned about how they would get childrento share their thoughts about math in mean­ingful ways.

Groundwork also was laid to ensureadministrative and parental support, buildbackground knowledge, and enhance mo­tivation. The project was discussed withparents during open-house nights and viawritten correspondence. Enthusiastic sup­port for the project was evident. Both theprincipal and parents were glad the chil­dren would be writing to university stu­dents who could effectively model commu­nication skills and pose math questions.Having the opportunity to build writingand math skills simultaneously through useof technology was also particularly appeal­ing. The principal offered access to the com­puter lab through flexible scheduling. Chil­dren were familiarized with letter-writingtechniques in the classroom and keyboard­ing skills in the computer lab. Both instruc­tors exchanged information and photosfrom their respective schools and surround­ing communities to familiarize studentgroups with each other. Many of the sec-

ond graders had vacationed in Florida andrelated fond memories of being there. Thisnew learning experience was approachedwith eager anticipation on both sides.

Participants exchanged e-mail mes­sages on alternating weeks during a 13­week period. Messages from the preserviceteachers were individually e-mailed to theuniversity instructor and then forwardedto the classroom teacher as a collective at­tachment. This method served a record­keeping function, ensuring that all letterswere written and delivered on time. Moreimportantly, it provided a safeguard forstudents. Though we were confident thatall student exchanges would be appropri­ate, having adult mediators alleviated anyapprehensions of parents and childrenabout communicating with "str angers." Atthe end of the project, we learned that atleast one child approached the new rela­tionship with initial discomfort. He said,"1 was writing someone 1didn't know andhad never seen. 1 felt uncomfortable." Wewere glad we had anticipated such con­cerns and were able to allay them. Further­more, because many second graders wereunaccustomed to reading small single­spaced type, font sizes were enlarged andspacing adjusted before letters were printedand distributed to children.

After reading the letters, second grad­ers marked questions posed by theirkeypals with highlighters and drafted writ­ten responses that served as springboardsfor discussion during individual confer­ences with the teacher. The conferencesbecame invaluable over the course of theproject, increasing understanding of stu­dent attitudes, abilities, interests, andneeds. After conferencing, students madefinal revisions before letters were typed inthe computer lab. This correspondence waslikewise collected and sent as an attach­ment via e-mail to the university instruc­tor, who in turn printed and distributed

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letters at the beginning of the methodsclass.

To help preservice teachers learn moreabout the second graders' experiences inschool, the classroom teacher e-mailed bi­weekly updates regarding current topics ofstudy in math and other subjects. Uni ver­sity students became aware of when chil­dren were learning estimation, place value,and computational skills-but they alsolearned about drama performances, holi­day celebrations, and field trips. These up­dates were very helpful to preservice teach­ers as they corresponded with elementarystudents. Frequently, they used this infor­mation to spark communication and relatemathematical questioning to experiences atschool. If preservice teachers wrote to morethan one keypal, they often asked both chil­dren the same questions to understand stu­dent similarities and differences. Conver­sations began with typical penpaldialogues focusing on topics such as hob­bies, interests, and family members andended by posing or answering questions:

College Student:I am glad to hear that you like

music. I love music too, especiallysince I play the piano and the cello.What kind of dog is Ginger? Whatcolor is she? Unfortunately, we can­not have pets at school. At home myparents have two dogs, two cats, andabird. I usedtohavetwo turtles. Yourteacher toldus that you were workingon balancing and weighing. What ex­periments have you done with balanc­ing? Have you done any experimentswith weighing? If an object is big, doyou think it will weigh a lot?

Second Grader:Ginger is a golden lab. She is the

color of gingerbread. She is eightmonths old, and she is a big dog. An

object that is big is not alwaysheavy.Yes, I have done experiments withweighing. I haven't done very manyexperiments with balancing.

Generally, preservice teachers posedtwo types of math questions to secondgraders. Open-ended questions focused ontopics: "What did you learn in math thisweek?" "What do you like about math?"and "What do you not like about math?"Some preservice teachers used sentencestarters or sentence stems to get childrenstarted: "My favorite activity in math is ..." or "Math is like ..." They also asked chil­dren to solve very specific problems deal­ing with shapes, weights, mileage, count­ing, patterns, and sequencing. When asked,second graders explained how they solvedproblems and described alternative waysto find solutions.

WAS THE PROJECT SUCCESSFUL?

At the end of the project, preserviceteachers reflected on the experience by re­sponding to a set of questions in a writtenessay:

• How do you believe writing fits intothe math curriculum? Into the classroom?

• How do you think teachers can andshould engage children in talking and writ­ing about math?

• What kinds of questions did you askyour keypal? What kinds of responses didyou receive? How do you think the tworelate?

• What have you learned about teach­ing and learning math from this experi­ence?

• What have you learned about yourstudent(s) and math?

• How will you use this experiencewhen teaching elementary school math?

We reviewed and categorized re­sponses to identify common themes. Over­all, the education students enjoyed the

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project. The preservice teachers were al­ways excited to hear back from theirkeypals. In fact, they looked forward to re­ceiving students' letters and were disap­pointed when letters did not arrive becauseof technical difficulties or student absences.

Preservice Teachers' PerspectivesMany preservice teachers recognized

the difficulty in getting second graders to"discuss math" through writing. Some feltthey asked too many questions and ex­pected the second graders to answer themall. It was also difficult for preservice teach­ers to recognize students' ability levels.Furthermore, some university students haddifficulties getting their keypals to focus onmath; many second graders wanted towrite about other things.

Preservice teachers often thought theirkeypals knew more about math than thechildren could put into written language.As one participant noted, "I learned thatboth of my keypals know a lot about math,but neither of them realized it or claimedto like it all that much. One student saidthat he didn't know what balancing wasyet, but he answered one of my questionsconcerning weight beautifully." Anotherwrote that his keypal "does not like mathbecause it is hard. But he couldn't tell meexactly what was hard." These responsesmay be due to children not naturally con­necting math with writing or defining mathas just completing algorithms, which indi­cates the importance of combining verbaland written language processes duringmath instruction at all grade levels.

The college students learned how im­portant is it to be specific when asking ques­tions. Most children only answered whatwas asked; when asked yes/no questions,responses were very brief. Preservice teach­ers also recognized the difficulty in askingstudents to explain or answer how and whyquestions; in many instances, no explana-

tions were given, even when asked.Preservice teachers remarked that writ­

ing can help teachers check for conceptualunderstanding. One wrote, "Our goal is tomake sure that students understand thereason behind the answer as well as howto work through it. One way we can do thisis by incorporating writing into our mathcurriculum." As another noted, "In havingstudents write about the computations theydo, teachers can benefit by seeing how thestudents organize thoughts, move throughthe process of a proble~, and most impor­tantly reason."

Finally, preservice teachers made in­sightful inferences about student develop­ment. Because preservice participants hadthe chance to share letters received fromkeypals with one another, they soon recog­nized the diverse ability levels of childrenin one classroom.

Overall, college students concludedthat the information gained through thisexperience was valuable. They recognizedthe importance of integrating writing andmath. According to the responses, everypreservice teacher plans to use writing asan instructional tool when teaching mathand plans to encourage verbal and writtencommunication from their students as well .This exchange allowed preservice teachersto gain a better understanding of how chil­dren learn, think, feel, and write-a lessonlearned best through experience. Onewrote, "The whole assignment was a joy,but I felt in the end that I may not haveachieved all that was expected. Through theexperience I was able to talk about mathwith a student, see the ability level of a sec­ond grader, and work on problem-solvingskills. If there had been more time, I thinkthat I could have really seen how she wascoming to her solutions. Despite that, thekeypal project afforded me the opportunityto begin my experience with math, writing,and the elementary student."

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According to the

responses, every preservlce

teacher plans to use

writing as an

instructional tool when

teaching math.

Second Graders' PerspectivesElementary students also benefited

from the project in both expected and un­expected ways. The classroom teacher toldher students that they were helping thesefuture teachers by participating in thekeypal project. She emphasized to themthat there were often no"corr ect" answers to theirquestions. Children weresimply told to do theirbest to answer the collegestudents' questions andknow that their responseswere appreciated . Theywere encouraged to seekhelp from one anotherand their teacher ifneeded. Children workedthrough their letter writ­ing as if they were devel-oping personal relation-ships, occasionally seeking advice from theirteacher, but very much in control of the writ­ten conversation. In fact, when they indicatedthat too many questions had been asked, theysimply declined to answer all questions.

After the project ended, the classroomteacher conducted private interviews withstudents to understand the keypal projectfrom their perspective.As with the responsesfrom the education students, we analyzedthese responses individually and thengrouped them according to common themes.

The children exuded enthusiasm forthe keypal project. Many came to the inter­view with smiles on their faces and did nothesitate in telling why they liked theproject. Their perspectives were helpful tous in evaluating the experience.

Second graders primarily enjoyed thekeypal project because they felt they hadmade "new friends" who shared commoninterests and experiences. Learning withkeypals had been a fun opportunity to: getto know someone far away who shared

similar interests and experiences, writemore about themselves personally, and usecomputers in a meaningful way. Interestwas piqued for several children because ofthe college-elementary age match.

Though some students had difficultymaking the math connection, several stu­

dents indicated that theylearned math-related con­cepts . Whether theylearned how to solve spe­cific problems, improvecomputational skills, in­crease attention to detail,or improve attitude to­ward math, they felt theirmath performance wasbetter because of thekeypal experience.

Several second grad­ers also said that writingand computer-related

skills had improved. Word-processingprocedures were followed with more confi­dence, written expression was more fluent,and use of writing mechanics more correct.Paragraph and letter-writing skills weremore evident than at the beginning of theschool year. Because children were corre­sponding with others regularly, they seemedto pay closer attention to detail by interpret­ing and responding to questions withgreater care. These young children, who atthe beginning of the school year seemedunsure of where to begin writing on the pageand what to say, were much more indepen­dent. Children said that writing was "hardwork, but fun!" Many expressed a sense ofpride in their accomplishments and interestin continued growth.

When asked what would have madethe keypal project better, children expresseda variety of ideas. The long-distance natureof the relationship was limiting for a fewsecond graders. Three children said theywould like to see and talk with their new

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friends . Others likely did not suggest thischange because they knew it would be im­possible to implement.

Several writing activities in the class­room were more open-ended, allowing chil­dren the opportunity for more freedom ofexpression, but the keypal experience was amore traditional independent-writing pro­cess exercise. All correspondence was writ­ten in traditional form (date, greeting, body,etc.), and children edited their work to fa­cilitate reading and response by preserviceteachers. The only requirement was thatchildren make efforts to answer the ques­tions posed. Children were free to movearound the room and work alone or withclassmates of choice during writing times.The computer lab was used by the entireclass during regularly scheduled times.

Seven children wished something couldhave been done to make the task easier orless time consuming. One student said hewould like to omit the writing part of theexercise and go directly to the computer lab,and a few others would have done viceversa. Early in the year, the elementaryteacher noticed a great deal of variation infine motor development among children.Little hands need time to become strongerfor extended periods of writing and typing,and this was the case for several students. Itwas important to realize the physical de­mands placed on young children by writ­ing and typing, so tasks were completedover several days in feasible chunks.

Many children indicated an interest indoing more to learn. One girl said shewould like to have more "math quizzes"from her keypal to help her learn. Anotherstudent said she would like to write "a biglong letter because it would help you withtyping and handwriting, and you'd getmore information." These children seemedto enjoy challenge and realize the potentialthese efforts hold. Each child's writing wascompleted and kept in a personal pocket

folder that contained blank paper, a pen­cil , and a spelling reference guidebook.Keypal letters were accumulated in thepockets, so over time children could reviewall correspondence. This organizationalsystem seemed to facilitate second graders'developing sense of accomplishment.

The Teacher's PerspectiveIn reviewing our original purposes for

the keypal project, how it developed, andour students' reactions, we have comeaway with a deeper understanding ofteaching and learning for our students andourselves. The structure of this project wasan anchor in terms of implementation;more importantly, it forced us to considerthe reasons for our actions, enabling us togain insights that have the potential to af­fect our teaching in positive ways.

We are more convinced than ever thatwriting is a valuable instructional tool(Burns 1995; Countryman 1992). Thisproject organized the classroom teacher'sthinking about planning and assessinglearning. She became more aware of strat­egies she used and encouraged from herstudents and how she was integrating in­struction in general. She learned how stu­dents solved or did not solve problems andthat they did not regularly use the strate­gies taught in school. One university stu­dent wrote to her keypal, "You said thatyou use your fingers to help you in math.That is a great way to find answers to mathproblems. What other ways can you findout answers to math problems?" The sec­ond grader responded, "I don't know anyother ways to do math problems." Yet thesecond graders had been taught to usestrategies such as making doubles, count­ing on and back, and using a number line.This was a powerful awakening for theclassroom teacher; she needed to providemore effective strategy instruction.

The biweekly lesson-plan updates writ-

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ten for college students provided an outletthat encouraged reflection about assign­ments an d activities being planned. Theteacher told university stud en ts w ha t chil­dren would be doing at school each w ee kand provided rationale for her instruction.This project p rovided a w riting outlet thatencouraged more thoughtful planning onthe teacher 's part, an important first stepin providing more effective instruction.

More thoughtful planning also tookplace because of the project's assessmentcomponent. Frequently, teachers get caughtup in the daily routine of walking throughcontent without fully considering how in­struction influences children's motivationfor learning (Turner, Meyer, Cox, Logan,DiCintio, and Thomas 1998). Ass essmentoften focuses on cognition w ithou t fullyconsidering how learning experiences in­fluence children's beliefs about themselvesas learners (M oon and Schulman 1995 ).Regular conferencing was a ke y componentoriginally designed to help s tu d en ts im­prove their writing skills, but it served afar greater unexpected purpose. Throughongoing regular conferences, the teacherlearned a great deal about stu d en ts' mathconcepts and self-percep tions. By discov­ering how stu d en ts reacted to questionsand topics, she got to know her students inmore personal ways . She learned whatkinds of strategies students used to solveproblems and how often they used them.She learned what interested and confusedthem, how comfortable they were withmath, and how empowered they felt to askmath questions of "b ig" college stu d en ts.

She also learned the importance ofmaking learning fun, particularly for stu­dents w ho lack confidence and feel unsuc­cessful. She was reminded that students, ata very early age, have already decided thatthey have particular strengths and needs.One second grader wrote, "Ma th is hardbecause I do not like math. What you can

do for me is help me with math." The uni­vers ity stud en t struggled in dealing withthis message and spent the entire semestertr ying to find w ays to help the student be­come more positive toward learning math.More important, the teacher became awareof the student's feelings and was able toaddress them in school on a regular basis.With time, this student decided, "Math isn'ttha t hard after all. " Discovering thestudent's attitude, and her difficulty ex­plaining her attitude, motivated the teacherto ensure that the student would have posi­tive experiences and become more inter­ested in math. Perhaps the interaction withher keypal and the teacher helped improveher confidence in this area. This importanceof self-efficacy for learning is well docu­mented (Deci and Flaste 1995) .

Finally, the project allowed the second­grade teacher to become more sensitive tostudents' developmental needs. She deter­mined that elementary students must:

• experience a sense of ownership andcontrol of learning;

• experience more effective strategy in­struction in math;

• find personal relevance in what theydo and make learning meaningful;

• feel nurtured and challenged; and• freely express their feelings and opin­

ions about math and learning.Several of these findings are consistent

with recommendations of other educators(Oldfather and Dahl 1994). It is a monu­mental task to meet these needs for all chil­dren, especially considering the diversityof abilities, attitudes, and interests of chil­dren. The ke ypal project increased aware­ness of these issues and provided manyexpected and unexpected outcomes for allinvolved. Finally, the penpal project pro­vid ed a structure for a great deal of com­munication to take place between childrenand their teacher, and between children andfuture teachers. Effective communication is

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the key to continued development for stu­dents and teachers of all ages.

RECOMMENDATIONS

Math partnerships can be great learningexperiences that encourage communicationin mathematics. However, all participantsmust be willing to commit the necessary time,resources, and energy. After implementingthis project, we offer the following recom­mendations for classroom teachers wan tingto begin similar partnerships:

1. Find wa ys for students to communi­cate in writing about math with a varietyof audiences. Similar projects can be imple­mented through dialogue journals betweenteachers and students or between studentsat different grade levels.The writing shouldbe reinforced through open classroom dis­cussions allowing children to verbalizethe ir thinking and reasoning.

2. Establish a nonthreatening classroomenvironment before implementing this typeof project. Allow children to write with free­dom, and do not expect polished and for­mal writing. Also, allow child ren to get ac­quainted wi th their ke ypals throughpersonal correspondence before integrating

REFERENCESBickmo re-Brand, J..ed . 1990. Language in mathematics. Ports­

mouth, N.H.: Heinemann.Burn s, M. 1995. Writing in math class:A resourcefor grades 2­

8. Sausa lito, Calif. : Math Solutions Publications .Country man, J. 1992. Writing to learn mathematics: Strategies

that work, K-12. Portsm outh, N.H.: Heinema nn.Deci, E. L., and R. Flaste. 1995. Why we do what we do: The dy­

namics of personal autonomy. New York: Putna m's Sons .Griffiths, R., and M. Clyn e. 1994. Language in the mathematics

classroom: Talking, representing, recording. Portsmouth,N.H.: Heinema nn .

Kennedy, L. M., and S. Tipps . 1997. Guiding children's learn­ing of mathematics, 8th ed . Belmont, Cali f.: Wadsworth .

Moon , J., and L.Schulma n. 1995. Finding the cOll/lections:Link­ing assessment, instruction, and curriculum in elementary

math concepts and questions.3. Be sensitive to the developmental

levels of students in forming partnerships.Writing and typing for some children in thisproject were labor intensive. Young chil­dren ma y ha ve difficulty writing and us­ing the keyboard. Also, it was challengingfor some children to express their thinkingabout math. Modeling this process throughthink-aloud exercises would be beneficial.

4. Build in time for conferencing. Thiswas a crucial part of the success for theclassroom teacher and allowed for manyunexpected discoveries about students. Theconferencing was originally designed tohelp stu dents improve their writing, but itprovided wonderful opportunities to get toknow students better.

5. Do not forget that writing in mathclass is not to demonstrate writing ability;students should think, reflect, record, andunderstand concepts and processes aboutmathematics (Bickmore-Brand 1990).

We are pleased with the outcome of thisproject. Our goal to create meaningful, au­thentic learning experiences for both el­ementary students and preservice teachersbenefited all those who participated.

mathematics. Portsm outh, N.H.: Heinemann .National Council of Teach ers of Mathemat ics. 1989. Curricu­

lum and evaluation standards for school mathematics.Reston, Va.: NCTM.

Na tiona l Council of Teach ers of Mathemat ics. 1998. Prin­ciples and standa rds for school mathematics: Discus­sion draft. Reston, Va.: NCTM. ERIC ED 429 844.

Ol d fat he r, P., and K. Dahl. I 994 . Toward a socia lconst ruc tivis t reconceptua liza tion of in trins ic motiva­tion for literacy learning . Journal of Reading Behavior26(2): 139-58 .

Turner, J. C , D. K. Meye r, K. E. Cox, C Logan, M. DiCint io,an d C T. Thomas. 1998. Creating contexts for involve­men t in math ematics. Journal of Educational Psychology90(4): 730-45 .

IlF,© Kappa Delta Pi

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