Utah State UniversityDigitalCommons@USUTeacher Education and Leadership FacultyPublications Teacher Education and Leadership

2006

Code RED (remediation and enrichment days):The complex journey of a school and universitypartnership's process to increase mathematicsachievementPatricia S. Moyer-PackenhamUtah State University

K. Dockery

S. Jamieson

J. Ross

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Recommended CitationMoyer, P. S., Dockery, K., Jamieson, S., & Ross, J. (2006). Code RED (remediation and enrichment days): The complex journey of aschool and university partnership's process to increase mathematics achievement. Action in Teacher Education, 28(4), 75-91.

Code RED (Remediation and Enrichment

Days): The Complex Journey of a School

and University Partnership's Process to

Increase Mathematics AchievementPatricia S. MoyerGeorge Mason University

Kim DockeryFairfax County Public Schools

Spencer JamiesonFairfax County Public Schools

Julie RossFairfax County Public Schools

ABSTRACT: This study examined a focused remediation and enrichment effort among school

and university faculty to affect the mathematics achievement of a group of third-grade students

in a Title I elementary school. A total of 87 students participated in the Code RED (Remedia-

tion and Enrichment Days) Project. During the Code RED Project, student assessment data

were used to identify high-need areas for mathematics instruction. The Code RED Project ses-

sions occurred in small groups over a 10-week period. Pre- and posttest assessments, as well

as state-standardized tests, were used for data gathering during the project. Pre- and posttest

data indicate that students made significant gains in mathematics achievement during the

Code RED Project overall, in different ability groups, and in different subgroup populations. In

addition, during the Code RED Project, 100% of the third-grade class passed the end-of-grade

state-standardized testing. A comparison of the pass rates for the state-standardized test for

third-grade students before and during the Code RED Project indicates a significant increase

in students labeled in the pass-proficient and pass-advanced categories. In addition to the stu-

dents' increasing their achievement results, teachers adopted new instructional practices, andpreservice teachers participated in the inquiry culture of the school.

School-based inquiry that results in improvedmathematics achievement for all students is acomplex process that requires much more thanimplementing new materials and teachingmethods. This process involves the transforma-tion of individual teachers, resources, andschool goals into a collaboration that is willingto think about teaching and learning in newand different ways. This process is even morecomplex when the goal is undertaken as a pro-

fessional development school collaboration be-tween an elementary school and its universitypartner that trains preservice teacher interns.

This article describes the journey of one suchpartnership and the positive student achieve-ment that resulted in mathematics because ofthis collaboration. First, we provide backgroundinformation on the development of the relation-ship between the elementary school and a uni-versity faculty member who was working in the

Action in Teacher Education Vol. 28, No. 4 75

Address correspondence to Patricia S. Moyer, George Mason University, 4085 University Drive, Suite 200A, Fairfax, VA22030. E-mail: pmoyer@gmu.edu.

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school with preservice teacher interns. We de-scribe how the relationship began with preser-vice teacher internship supervision and how itevolved to focusing on student learning withclassroom teachers in the school. The relation-ship resulted in the growth of a culture of in-quiry for the teachers working at the school, thepreservice teacher interns in field placements atthe school, the university faculty member su-pervising interns in the school, and the school'sadministrators. During the academic schoolyear reported in this article, these colleagues de-veloped the Code RED Project (where RED isan acronym for Remediation and EnrichmentDays) as a way to increase the mathematicsachievement of third-grade students in theschool. This article discusses the impact of theCode RED Project and the complex relation-ships and processes that led to its success.

Professional DevelopmentSchool Relationships

Teacher education researchers have examineda variety of influences on the preserviceteacher's development, including the studentteaching experience, teacher educationcourses, methods in those courses, and teachereducation programs and institutions (Civil,1993; Griffin, 1999; Koehler, 1985; Tabach-nick & Zeichner, 1984). In an effort to takeadvantage of the positive elements offered bya more site-based experience and to betterconnect university students to their futureroles as teachers (Moyer & Husman, 2006),many teacher education programs have re-designed their academic configurations forearning teaching licensure (McKibbin, 1999;Spalding, Wilson, & Sandidge, 2000; Stein,Smith, & Silver, 1999). Some of these changeshave led to professional development schoolpartnerships between universities and localschools that support the preservice teacher'sdevelopment in the context of meeting chil-dren's needs at the school site (NationalCouncil for Accreditation of Teacher Educa-tion, 2001). The school and university faculty

described in this research were engaged insuch a relationship.

Most teacher education programs have ex-amined and articulated what beginning teach-ers should know and be able to do and whattypes of experiences might help them to de-velop teacher skills and dispositions (Reynolds,1992). The professional development schoolinternship experience in this collaboration wasdesigned to prepare student teachers for today'sevolving school culture. The preservice teacherinterns in this collaboration were in the ele-mentary school setting 4 days every week from7:30 a.m. to 3:30 p.m. throughout the entire ac-ademic school year. This gave them many op-portunities to be exposed to the culture, con-text, and community norms of the elementaryschool. Specifically, they were exposed to therhythms and routines of the school day (cul-ture); to the way in which the school subjectswere taught, including the resources, the pacingguides, and the pressures of state assessmentsand mathematics accountability (context); andto understanding the needs of parents and chil-dren (community).

There is a shared belief that teaching re-quires an understanding of the rules and rou-tines of the school culture, the ability to col-laborate with other education professionals,and an awareness of the communities in whichone teaches (Sikula, Buttery, & Guyton,1996). A school that promotes an environ-ment of continuous learning with a shared mis-sion may have a different impact on the preser-vice teacher than one in which individualswork in isolation. Rather than view the prac-tice of teaching as an isolated act, schools havebegun to reframe the work that they do to em-brace this spirit of teacher learning as a contin-uum by engaging teachers in professionallearning communities (Eaker, DuFour, & Bur-nette, 2002; Hord, 1997).

A School's ProfessionalLearning Community

The term professional learning community is aterm that was attributed to Hord in 1997

(Blankstein, 2004; Hord, 1997). This notion ofa professional learning community developedfrom work on organizational theory and fromSenge's writing in The Fifth Discipline (1990).One of Senge's five principles in these writingsinvolved team learning, the concept of whichhas made its way into the educational contextand given rise to the development of theschool-based learning community. The devel-opment of the learning community constructshave come to include such common features asshared norms and values, a focus on studentlearning, collaboration, collective inquiry, andan action orientation (Blankstein, 2004; Du-Four & Eaker 1998). With collaboration, in-quiry, and an action orientation, various activi-ties within the school can affect differentmembers of the school community. For exam-ple, the learning curve for a preservice teacherin a yearlong in-school placement is similar tothat of a 1st-year teacher. Therefore, connect-ing these two groups in ways that provide fortheir development can grow a network of sup-port within the school setting where these twogroups exist.

The character of the professional learningcommunity is one of inquiry. Lambert (1998,2003) describes the importance of the recipro-cal processes of leadership in a professionallearning community that include reflection,inquiry, dialogue, and action. For example, thekinds of questions that would promote inquiryand dialogue within a school (DuFour &Eaker, 1998) might include "What do we wantstudents to know?" "How will we know if theyknow it?" "What will we do if they don't?" and"What will we do if they already knew it?"This disposition for asking questions aboutstudent learning leads to dialogue and discus-sions among preservice, novice, and experi-enced teachers about effective teaching prac-tices. Research indicates that faculty insuccessful schools continuously question exist-ing instructional practices and do not blamelack of student achievement on externalcauses (Glickman, 2002).

The professional learning communityframework is structured into three critical areas:a collaboratively developed and collectively

Code RED (Remediation and Enrichment Days) 77

shared vision and mission, collaborative teamsthat work interdependently to achieve commongoals, and a focus on results and commitment tocontinuous improvement (Eaker, DuFour, &Bumette, 2002). The collaborative relationshipdescribed in this project embraced these criticalareas for a professional learning community.Posing DuFour and Eaker's (1998) key questionsof a professional learning community providedthe impetus for the school faculty in this studyto document its efforts at increasing mathemat-ics achievement for third graders.

In the sections that follow, we describe theproject and its outcomes, which resulted in asignificant increase in student achievementfor all third-grade students in the school onstate-level standardized tests. We share ourstory to highlight the time, effort, and com-plexities of engaging in this process. We alsodescribe how this process developed the in-structional and data analysis skills of theteachers in the project.

The Code RED Project

The elementary school in this project enteredinto a professional development school relation-ship with the local university in 1999. Theteachers at the school had worked together for 5years with the same university professor, whohad been assigned to that school by the univer-sity, and over that time a culture of inquiry hadslowly evolved. Elementary teachers on the staffat the school were trained as clinical faculty,which meant that they were responsible for su-pervising and coteaching with graduate-levelpreservice teacher interns. This university train-ing process for clinical faculty development cre-ated a core of teachers at the school whocoached preservice teachers using reflectivepractices. At the same time, the school began tolearn about the framework of a professionallearning community. Reflective discussionsabout teaching occurred among preserviceteachers, in-service teachers, and the universityprofessor as part of regularly scheduled meetingsbetween the school faculty and university pro-fessor, as part of regularly scheduled seminars

78 MOYER ET AL.

between the preservice teachers and the univer-sity professor, and informally on a daily basis be-tween the school faculty and the preserviceteachers who were placed in the school. One ofthe elementary teachers described this reflectiveprocess as follows:

If I was constantly coaching a studentteacher to examine his/her practices andrevise them based on student outcomes, Imyself needed to be doing the same things.I needed to have better answers when astudent teacher asked me why I did some-thing in a certain way. I began to buildmore reflection into my own teaching.

The mathematics education professor whoserved as the supervisor for the preserviceteacher interns was in the school every weekinteracting with preservice teacher internsand classroom teachers. Over the course of 5years, the mathematics education professorand the teachers built strong professional rela-tionships that were supported by weekly inter-actions at the school. The university profes-sor's background included 10 years of publicschool teaching at the elementary and middlegrades, which gave her an understanding ofthe routines of the elementary school culturefrom the perspective of a classroom teacher.She had 8 years of experience with beginningteachers, in teaching mathematics methodscourses and in supervising teacher interns infield placements. This experience in class-rooms and work with preservice teacher in-terns gave her a practical school-based per-spective on current classroom practices andhigh-yield strategies for student success.

The preservice teacher interns wereplaced in full-year internships at the elemen-tary school. Because of this long-term place-ment, the preservice teachers learned the cul-ture and routines of the school throughfirsthand interactions with students, teachers,school personnel, and parents. In addition toexperiencing these collaborations, the preser-vice teacher interns benefited professionally.In many cases, the preservice teacher internswere offered positions as classroom teachers inthe school system because they had learned

the culture and expectations of the school sys-tem after working for one full academic year inthe elementary school. The hiring of preser-vice teacher interns at the school who camefrom the university's programs enhanced therelationships among these professionals thatdeveloped over 5 years. For example, the class-room teachers who had been mentors of thepreservice teachers were now the latter's col-leagues; the university professor, who had su-pervised the preservice teachers, was now acollaborator on their classroom projects.

As time passed, the preservice teacher in-terns, the classroom teachers, and the univer-sity professor began working together to con-duct small classroom research projects. Havingthe preservice teacher interns in the schoolprovided additional resource personnel forthese projects and engaged the preserviceteachers in classroom action research practices.The collaborative experiences and the trustthat developed allowed classroom teachers,preservice teachers, and the professor to worktogether to collect data and examine instruc-tion. This shared work included discussionswith classroom teachers about teaching andlearning, with a focus on how teachers mightstudy and write about practices in their ownclassrooms. Some of these projects became pre-sentations and published articles highlightingmathematics teaching and learning in theschool (Kosbob & Moyer, 2004; Mailley &Moyer, 2004; Moyer & Mailley, 2004; Moyer,Niezgoda, & Stanley, 2005; Niezgoda &Moyer, 2005; Sweda, Knotts, & Moyer, 2004).These collaborative publications further en-hanced the positive relationships between theschool and the university.

Expanding the Culture of Inquiry

As the university and school faculty wrote to-gether for publication, they expanded the in-quiry culture to other teachers and promptedthe establishment of a more formal teacher re-search initiative within the school. The expan-sion of teacher research beyond the core ofclinical faculty, who worked with interns, toother school faculty created an inclusive cli-

mate that set the expectation for all teachers tobe engaged in inquiry on effective teachingpractices. The teachers' classroom research re-sulted in the elementary school's holding anevent that it called the Teacher Learning Fair,in which the teachers presented their individ-ual classroom research projects. The fair wasattended by teachers and administrators fromthe rest of the school system. To prepare for thepresentations, teachers developed brief reportsabout their projects, which described their re-search questions, data collection methods, andresulting implications for classroom practices.As a result of this school-based activity, theschool-system administrators enlarged thescope of the Teacher Learning Fair to include acluster of 30 schools. The purpose of this newinitiative was to broaden the collaborative cul-ture of learning from classroom research acrossthe K-12 school-system environment.

Making Plans to AffectStudent Achievement

Although the initial collaborative relationshipwas built on a school-university professionaldevelopment school partnership to supportpreservice teachers, the partnership expandedwell beyond this goal in subsequent years.These changes led to a shared focus on plansto affect students' mathematics achievementat the elementary school. This focus on math-ematics involved the improvement of mathe-matics teaching and learning for preserviceteacher interns, classroom teachers, and theuniversity mathematics education professor,within the context of the school community.

During the year of this project, the im-provement of student achievement scores onthe state mathematics assessment surfaced asan important goal of the third-grade teacherteam. Meeting adequate yearly progress goalsin subgroup populations was critical in this Ti-tle I school because of accountability require-ments of No Child Left Behind. This legisla-tion mandates that all public schools be heldaccountable for the yearly progress of all stu-dents, including subgroup populations of stu-dents. Based on past state mathematics test

Code RED (Remediation and Enrichment Days) 79

scores, the third-grade team selected the im-provement of mathematics performance as itscollaborative goal. As part of the school's pro-fessional learning community goals during theyear of the project, each grade-level teamworked to collect student assessment data thatcould inform instruction. The use of releasedtest items from the state's assessments allowedthe teachers to develop common mathematicsassessments for their grade level. Developingthese common assessments enabled the schoolto identify students in need of mathematics re-mediation or enrichment.

During the fall of the project year, theschool principal and the university professorhad a crucial conversation. The school princi-pal related to the university professor her con-cern about critical mathematics needs in theschool and her vision for having a broad im-pact on student achievement. The two talkedabout how to put this vision into practice byusing existing school structures and resources.These ideas focused on the use of high-yieldstrategies that would have a profound impacton mathematics achievement (Marzano, Pick-ering, & Pollock, 2001). The principal wasaware that the research that the teachers andthe professor had conducted had built confi-dence in individual teachers in using teacherresearch in their own classrooms. The principalbelieved that this relationship could be the ba-sis for a move from individual teacher researchto grade-level or schoolwide action research.She also understood that she was asking theuniversity professor to work with classroomteachers beyond her role as a coach and super-visor for the preservice teacher interns; there-fore, the principal committed school resourcesto this professional development work.

Professional DevelopmentWith a Purpose

As a result of the conversation between theuniversity professor and the principal, the uni-versity professor began working with the third-grade teachers as a team. The professor pre-pared to take on a coaching role with theteachers that would include looking at student

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data and talking about instructional practices inmathematics that were based on those data. Asa framework for designing the professional de-velopment, the university professor structuredher planning around the research regardingwhat makes professional development effectivefor teachers of mathematics (Garet, Porter, Des-imone, Birman, & Yoon, 2001; Loucks-Horsley,Hewson, Love, & Stiles, 1998; Smith, 2001).Results from a national sample of mathematicsand science teachers indicate that six structuraland core features of professional developmenthave the greatest impact on teacher learning(Garet et al., 2001). The structural features in-clude the form of the activity, duration, andcollective participation. The core features in-clude the content focus of the activity, activelearning, and coherence.

Research indicates that the form of theprofessional development activity can maketeachers more or less responsive to changingteaching practice (Darling-Hammond, 1995,1996). The university professor chose reformtypes of professional development, such as ateacher study group with follow-up coaching,rather than a more traditional type of profes-sional development, such as a teacher work-shop. During the teacher study-group session,the university professor facilitated discussionamong the teachers, the mathematics special-ist, and herself. Although the professor did notmake a presentation to the group, she did pre-pare manipulative materials and other hand-outs that could be used as examples to discussthe mathematics topics that arose as part ofthe group discussion. When questions aroseabout mathematics instruction, the professorshared ideas in the role of a coach and col-league rather than an "ivory tower expert."

Professional development that is sus-tained over time, or that has duration, has thehighest likelihood of making lasting changesin classroom practice. Because of the long-term relationship of collegial work in theschool, the transition into the Code REDProject was a natural extension of the workthat was already being done. During the CodeRED Project, the teachers and university pro-fessor continued their interactions both for-mally (in a study group and in grade-level

meetings) and informally (in hallway conver-sations). Throughout the school year, thesediscussions provided teachers with opportuni-ties to test instructional strategies and discussthe results with their colleagues and the uni-versity professor.

A third structural feature of the profes-sional development during the Code REDProject was collective participation. Whenprofessional development is designed forteachers from one school who are teaching atthe same grade level, they have many moreopportunities than otherwise to discuss theconcepts they are learning and the instruc-tional strategies they are finding effective intheir classrooms. In this case, the teachersshared curriculum materials, assessments, andstandards, and they were able to share ideasabout the needs of the third-grade studentswhom they were teaching.

To the university professor, the focus onmathematics content was one of the most im-portant features of the professional develop-ment. When professional development has aspecific content focus, such as the Code RedProject's focus on third-grade mathematics, itcan have a significant effect on changingteachers' practices (Corcoran, 1995). Duringthe study-group discussions, the universityprofessor shared mathematics problems, andthe group discussed the mathematics contentknowledge that students would need to solvethose problems. After the mathematics con-tent in a problem was identified, the group dis-cussed strategies for teaching that content,common error patterns that students experi-ence in learning that particular content(Ashlock, 2006), and how to extend the con-tent for advanced learners. These discussions,focusing primarily on the mathematics, re-vealed that teachers did not always understandhow to develop a particular mathematicaltopic, because of gaps in their own learning.Through these mathematics discussions, theclassroom teachers' mathematical contentknowledge was strengthened.

A feature of effective professional devel-opment that is particularly important toclassroom teachers is coherence. Coherenceinvolves how the teachers perceive the pro-

fessional development in connection withother school goals, as aligned with their stateand school-system standards and assessments,and as a catalyst for ongoing discussion andcommunication among the group and beyondthe group to other members of the school fac-ulty. The goals of the Code RED Project wereclearly embedded in the school's goals andthe teachers' goals as a third-grade team.Their efforts to improve student learningwere aligned with the content of the statestandards and included an in-depth examina-tion of the state-standardized assessmentitems for their third graders. Because of thiscoherence, the Code RED Project promptedmany discussions about mathematics topicsamong teachers, administrators, preserviceteacher interns, the university professor, andthe mathematics specialist.

The core feature of active learning was ev-ident throughout the Code RED Project. Theuniversity professor and the school's mathe-matics specialist were actively engaged in dis-cussing types of data available at the schooland data that they needed to collect and ana-lyze. The university professor learned how thedata in the school were aggregated by subpop-ulations and how these were important to theschool's yearly goals. The mathematics spe-cialist learned strategies that the universityprofessor used to organize the data and deter-mine focus areas where students were repeat-edly having difficulty on the school's assess-ments. During the study-group sessions withthe teachers, participants examined the third-grade data and collaboratively identifiedmathematics content that was particularly dif-ficult for students. An important part of thisprocess was that the teachers were actively en-gaged in learning to read the student data, inidentifying the mathematics content in thedata, and in determining priorities for address-ing areas of weakness for the third-grade class.Having teachers analyze the data was a muchmore powerful process than if the professorhad announced the weakness areas to theteachers. Learning how to conduct an analysisof student mathematics data enabled theteachers to use the process on their own insubsequent years to identify students' needs.

Code RED (Remediation and Enrichment Days) 81

Instructional Practices That Focuson Representations

During the group sessions, the professor distrib-uted copies of mathematics problems from thestate assessment tests so that teachers could an-swer the questions and discuss strategies andcontent. As teachers reviewed the test items,they realized that they had not taught a partic-ular concept in the format that was presented tostudents on the state assessment, even thoughthey had taught the mathematics content ofthe test item. Teachers recognized that studentswould need exposure to a variety of visual andpictorial representations of mathematics con-tent to understand and correctly respond to amathematical question. Through this recogni-tion, teachers used grade-level meetings and in-formal discussions to talk about how best toteach a particular mathematics topic.

The university professor worked with theteachers to recognize the importance of con-nections among various forms of representa-tions (such as manipulatives, pictures, andsymbols) and how those representationsmight appear as test items. Mathematical rep-resentation is one of five process standards inthe Principles and Standards for School Mathe-matics (National Council of Teachers ofMathematics, 2000). In the teaching andlearning of mathematics, teachers and stu-dents use a variety of representations to or-ganize, communicate, and record mathemati-cal ideas. The teachers here therefore beganusing more nonlinguistic representations(Marzano et al., 2001) in their teaching, in-cluding graphic representations (graphic or-ganizers), physical models (manipulatives),mental pictures, drawing pictures, and kines-thetic activity, to expose students to variousrepresentations for a mathematical concept.Teachers also provided more opportunitiesfor students to translate among various repre-sentational forms, including physical models,visual or pictorial models, and symbolic nota-tion. An example of this translation from onerepresentation to another may occur amongthe following: a picture of a fraction region,words or numerals for that fraction amount,and a 10 X 10 decimal-grid representation

82 MOYER ET AL.

equivalent to that amount. To engage stu-dents in this new way of thinking about themathematics, teachers used more questioningduring instruction to promote student think-ing.

Teachers also began using a problem of theday in which the teacher talked through herthinking and solution routes when solving aproblem, and she encouraged students to dothe same. The third-grade teachers and math-ematics specialist collaborated to select andcreate these problems of the day so that theywould focus on weakness areas identified fromthe third-grade assessment data. Verbalizingtheir solution routes for students and preser-vice teacher interns allowed the classroomteachers to examine their own thinking,which influenced how they viewed their in-structional practices. This verbalization, in aneffort to make their thinking more transpar-ent, was a shift in instructional practices forthe teachers on the third-grade team. Theprincipal and the university professor realizedthat these shifts in thinking would be requiredacross the grade levels for changes to be madethroughout the school. By the end of the aca-demic year and into the summer months, theuniversity professor worked with the entire el-ementary staff to focus on grade-specific math-ematics topics, nonlinguistic and visual liter-acy, and the use of representations for teachingmathematics.

Third-Grade Team Takes Ownershipof Student Achievement

The school's professional learning communitywas a noticeable shift from teachers' focus onteaching to their focus on student learning. Itwas evident that the third-grade team hadtaken ownership when it decided to name theproject Code RED. Giving the initiative aname signified the importance of the projectto the team, and it was one of the third-gradeteachers who created the name. The teacherswere especially concerned about students'mathematics achievement in Grade 3 becausethis was the first grade level where children inthe state took the state-level standardized test.

The teachers knew that this content was animportant benchmark in mathematical learn-ing for subsequent grades.

Method

In the sections that follow, we describe the re-search conducted by the team for the CodeRED Project-including the participants, pro-cedures, data sources, analysis, and results-which focused on the following overarchingresearch question: What is the impact of theCode RED Project's focused remediation andenrichment on the mathematics achievementof students in Grade 3?

Participants

This project was conducted at an elementaryschool on the East Coast near the Washing-ton, DC, Metropolitan area. The school is adesignated EXCEL school, which means thatit receives Title I mathematics and readingsupport. After-school programs include After-School Remediation and School Age-ChildCare (SACC). There were 580 students at-tending the school during the project. Thestudent population was comprised of studentsfrom over 29 countries with major concentra-tions of Hispanic and Vietnamese popula-tions. Schoolwide populations were reportedwith the following demographics: Asian 25%,Black 2%, Hispanic 44%, White 24%, andother 5%. There were 34% English-as-a-second-language students, 43% fee-waiverstudents (free/reduced lunch), 4% gifted serv-ices, and 23% special education services. Ofthese students, 20% were classified with littleor no English proficiency.

Third-grade students. A total of 84 third-grade and 3 second-grade accelerated studentsparticipated in the Code RED Project. Thestudents in the five 3rd-grade classes rangedin age from 7 years to 10 years. Twelve specialeducation students participated. The ratio offemales to males in the Code RED Project was42 to 45. The students varied in their degreesof mathematics proficiency, from high levels

of achievement to low levels of achievement.During the Code RED Project activities, stu-dents were placed in 10 heterogeneous groupsof approximately 8 or 9 students for their par-ticipation in the remediation and enrichmentdays.

Code RED Project faculty. A total of 15educators were involved in the design andimplementation of the Code RED Project.Of the 15 educators involved in the project,11 served as instructors for the Code REDProject. These individuals included thethird-grade teachers, school administrators,and instructional support staff. Each teacherwas asked or had volunteered to participatein the Code RED Project. Some instructorstaught lessons every session, whereas otherinstructors took turns teaching the 10 iden-tified weakness areas for remediation and en-richment. These instructors varied in theiryears of experience in education, from 2years to 21 years. Three individuals servedas substitutes in cases where a teacher wasabsent.

Procedures

At the beginning of the project, students inthird grade completed a mathematics pretest.The pretest was a 50-item measure based onreleased items from the state's learning stan-dards test. The assessment was administered inJanuary as a pretest and again in May as aposttest. The university mathematics educa-tion professor and the school mathematicsspecialist collaborated to disaggregate the datagathered from the pretest.

We analyzed the pretests to identify pat-terns in the test items that were missed by over70% of the students in each of the five 3rd-grade classes. We first identified these testitems by individual class and then lookedacross the classes to identify items most fre-quently missed in all of the classes. An analy-sis of the pretest showed that there were com-mon areas that over 70% of the third-gradestudents answered incorrectly.

After determining these key areas of weak-ness, the university mathematics education

Code RED (Remediation and Enrichment Days) 83

professor and the school mathematics special-ist shared the data with the third-grade teamof teachers in a half-day study-group session.During the session, the group collaborativelydecided to focus on 10 key areas for the CodeRED Project. These 10 key areas were inte-grated into daily mathematics instruction inall third-grade classrooms and were used for fo-cus lessons on the Code RED Project days.The 10 key focus areas included probabilityand interpreting outcomes, fraction denomi-nators/numerators, rounding, problem-solvingstrategies, using/interpreting visual images,translating from pictures to word text andword text to pictures, recognizing test dis-tracter items, vocabulary used for subtraction,keys on graphs and different types of graphs,and decimals/fractions and their relationshipto one whole.

There were 10 Code RED Project daysthat occurred over a 10-week period. On eachCode RED Project day, third-grade classroomteachers did not teach a regular mathematicslesson. Instead, students participated in aCode RED Project-day mathematics lessonthat focused on 1 of the 10 key areas of identi-fied weakness for the third-grade students. Thestudents participated in the Code RED days in10 small groups, with approximately 8 or 9 stu-dents in each group. The lessons were taughtin classrooms and other locations throughoutthe school. The distribution of students tothese groups was based on their performanceon the pretest assessment, as well as otherclassroom performance indicators from the fallsemester. The distribution of students in the10 groups included two groups of advancedstudents and eight groups of students with anequal distribution of low- and average-abilitystudents. Students in the eight groups partici-pated in instructional sessions that focused onremediation and enrichment of the key focusareas. Students in the two advanced groupsparticipated in instruction with a greater focuson enrichment. All of the sessions focused ondeveloping students' mathematical profi-ciency and fluency by working with skills, con-tent, and strategies. The focus of the remedia-tion was on conceptual understanding and

84 MOYER ET AL.

common student error patterns. The focus ofthe enrichment was on extending the con-cepts beyond grade level and to deeper levelsof understanding.

One instructor was assigned to each of the10 key focus areas. In addition to the five 3rd-grade classroom teachers, instructional aides,administrators, and other support staff servedas five additional instructors so that studentscould participate in Code RED days in smallgroups. Each instructor taught one key focusarea every week for 10 weeks. For the instruc-tors, this reduced the amount of their prepara-tion time for the 10 lessons. Instead of prepar-ing 10 different lessons, each instructor couldprepare an in-depth lesson on one focus area(e.g., different types of graphs). In preparingthis lesson on different types of graphs, for ex-ample, the instructor found numerous types ofgraphs with different presentation orienta-tions, examined error patterns that studentsmake when reading and interpreting graphs,and reviewed advanced types of graphs withmultiple points of information and complexkeys. This enabled the instructor to become anexpert on understanding graphs and the devel-opmental progression of students when theylearn to read and interpret graphs. The instruc-tor prepared basic lessons on graphs to supportstudents who were just learning to read graphs,as well as complex lessons for the more ad-vanced students. This deep level of engage-ment with the content strengthened teachers'own mathematics knowledge and gave thempractice in creating lessons that differentiatedfor various levels of student learning.

The nature of the instruction during thelessons included the use of physical models(manipulatives), visual/pictorial models, andsymbolic notation, in an effort to make con-nections among these various forms of repre-sentation. The interactions among studentsand instructors focused on questioning anddiscussing mathematics topics and on studentsand instructors sharing their thinking throughwriting and drawing.

During the Code RED Project, studentshad a different teacher every week for 10weeks on each project day. Students focusedon content during the Code RED days differ-

ent from that of some of their classmates, andthe instruction was more interactive for thestudents. Because the students were participat-ing in lessons taught by nine instructors plustheir third-grade classroom teachers, theywere exposed to a variety of representationsand presentations of the mathematics. Be-cause the students were learning content dif-ferent from that some of their classmates, stu-dents discussed the mathematics with oneanother when they returned to their class-rooms. And because they were in smallergroups, they had more interaction with the in-structor and were able to have more discus-sions about mathematics with their smallgroups.

As part of their participation in the proj-ect, the third-grade teachers received addi-tional released time to collaborate and to planthe Code RED days. These opportunities toplan and collaborate prompted discussionabout instructional strategies. These discus-sions supported changes in instructional prac-tices during the daily mathematics lessons andgave instructors ideas for the 10 CodeRED-day experiences. Preservice teacher in-terns participated in the professional develop-ment activities and discussions, learned newinstructional strategies to use for support inthe classrooms, and provided instructionalsupport to release teachers from their class-rooms for some of the grade-level team plan-ning times, and they participated in otherteam planning sessions.

The first Code RED Project day started inearly March and occurred every Tuesday untilthe end of May for a period of 10 weeks. Themathematics specialist, school principal, andmathematics education professor documentedactivities during the project. They believed thatthe results of the Code RED Project may havethe potential to provide the information neededto implement the process of remediation andenrichment in other grades at the school.

Data Sources

The first source of data for this project was thepretest and posttest assessments of students'mathematics content knowledge in the five 3rd-

grade classrooms. Both the pretests and posttestswere forms of the same mathematics assessment.This assessment was a 50-item multiple-choicetest composed of the mathematics release itemsfrom the third-grade state mathematics test.

A second source of data for the project wasan informal teacher ranking by each teacherto identify student achievement levels in eachclass. Students were ranked by teachers ashigh, average, or low achievement, dependingon their in-class performance in mathematicsduring the first half of the academic year.

The third source of data was compiledfrom the annual pass-rate scores on the state-level mathematics standards test for the third-grade students at the elementary school. Passrates were examined from the third graderstested the years before, during, and after theCode RED Project. These scores allowedteachers to make comparisons between thethird-grade Code RED Project students andstudents who completed third grade the yearbefore and had not participated in the project.It also allowed the teachers to see how studentperformance on the test was affected the yearafter the Code RED Project, when teacherswere using instructional strategies during regu-lar instruction that were based on the use ofmultiple forms of representation.

Data Analysis and Results

Analysis 1. The first analysis examined the re-sults from the pretest and posttest measures toanswer the following question: What was theoverall impact of the Code RED Project treat-ment on the mathematics achievement of stu-dents in Grade 3?

To answer this question, we used a paired-samples t test to determine the effect of the treat-ment on students' posttest scores. The individualstudent scores served as the dependent variable.Because of student mobility at the school, thenumber of students that are reported here withcomplete data points equals 70. The analysisshowed a statistically significant gain betweenthe pretest (M = 66.9, SD = 15.2) and posttest(M = 80.9, SD = 14.8), t(69) = -11.882, p =.000. The result indicates that students' scores onthe posttest measure of mathematics achieve-

Code RED (Remediation and Enrichment Days) 85

ment increased significantly following the CodeRED Project treatment.

Analysis 2. The second analysis examinedthe gain scores between the pretest andposttest measures using a comparison of thegain scores among the three teacher-identifiedgroups of students (high, average, and low) toanswer the following question: Following theCode RED Project treatment, were there dif-ferences in the mathematics achievement gainscores among the three teacher-identifiedgroups of students (high, average, and low)?

To answer this question, we used an analy-sis of variance to compare the gain scores ofthe three groups to determine the effect of thetreatment on students' mathematics achieve-ment. The mean gain scores served as the de-pendent variable. The analysis showed no sta-tistically significant differences among thegain scores of the three groups, F(2, 67) =1.97, p > .05. The results shown in Table 1 in-dicate that the gain score of each group wasnot statistically different from the others. Al-though there is numerical evidence to suggestthat the students identified as low achieve-ment made the greatest gains of the threegroups, there is no statistical evidence support-ing this trend. In small sample sizes such asthis one, it may be difficult to reveal statisticaldifferences using these analyses.

Analysis 3. The next analysis examinedthe results from the pretest and posttest meas-ures to answer the following three questions:What was the impact of the Code RED Pro-ject treatment on the mathematics achieve-ment of students in the teacher-identified lowgroup? The teacher-identified average group?And the teacher-identified high group?

To answer these questions, we conductedthree separate paired-samples t tests to deter-mine the effect of the treatment on students'posttest scores for each of the three groups,with the individual student scores serving asTable 1. Mean Gain Scores for Teacher-Identified

Student Groups

Student group Score

Low achievement 16.45Average achievement 14.71High achievement 10.60

86 MOYER ET AL.

Table 2. Pre- and Posttest Score Means for Low, Average, and High Achievement Students

Group n Pretest M Posttest M M Gain p Value

Low 22 52.64 69.09 16.45 .000*Average 28 66.86 81.57 14.71 .000*High 20 82.50 93.10 10.60 .000*

.p <.001.

the dependent variable. Table 2 presents theresults of this analysis. These analyses showeda statistically significant gain between thepretest and posttest measures for all three ofthe individual groups. These results indicatethat each of the teacher-identified abilitygroups earned scores on the posttest of mathe-matics achievement that increased signifi-cantly following the Code RED Project treat-ment.

Analysis 4. Another analysis examined theresults from the pretest and posttest measuresto answer the following five questions: Whatwas the impact of the Code RED Project treat-ment on the mathematics achievement of stu-dents in Teacher A's class? In Teacher B's class?In Teacher C's class? In Teacher D's class? InTeacher E's class?

To answer these questions, we conductedfive separate paired-samples t tests to deter-mine the effect of the treatment on students'posttest scores for each of the third-gradeclassrooms, where the individual studentscores served as the dependent variable. Table3 shows the results of this analysis. This analy-sis shows a statistically significant gain be-tween the pretest and the posttest in four ofthe five 3rd-grade classrooms.

The results indicate that four of the fiveclassrooms earned scores on the posttest ofmathematics achievement that increased sig-nificantly following the Code RED Projecttreatment. Although students in Teacher D's

classroom showed numerical gains on theposttest, these gains did not reach statisticalsignificance. The students in Teacher B's andC's classes showed the most significant averagegains following the Code RED Project treat-ment.

Analysis 5. In the final analysis, we exam-ined the following question: How did the stan-dardized state-level test scores of students inthird grade who participated in the Code REDProject compare with the test scores of stu-dents who completed the third-grade stan-dardized test the year before and the year afterthe Code RED Project?

To answer this question, we examined theoverall scores of students in Grade 3 at the el-ementary school who participated in thestate-level assessment in spring 2003 with stu-dents who participated in spring 2004 (theyear of the Code RED Project) and spring2005 (the year after the Code RED Project).In essence, this gave us a control group forcomparison of the state-level testing data. Italso allowed us to examine how the newteaching strategies being used by teachers dur-ing regular instruction, with a focus on repre-sentations and visual/pictorial models, carriedover into the next year of instruction after theCode RED Project had ended. We disaggre-gated these data to further examine the scoresof students in several subgroups. Table 4 pres-ents pass rates for all students and subgrouppopulations.

Table 3. Pre- and Posttest Score Means for Each Third-Grade Class by Teacher

Teacher n Pretest M Posttest M M Gain p Value

A 16 67.00 81.38 14.38 .000*B 14 58.43 74.86 16.43 .000*C 13 69.85 86.46 16.61 .000*D 12 68.00 76.67 8.67 .074E 15 71.07 84.80 13.73 .000*

*p <.001.

Code RED (Remediation and Enrichment Days) 87

Table 4. Third-Grade Pass Rates on the State Mathematics Assessment in 2003, 2004, and 2005

Control Code RED After Code RED

Group 2003 2004 2005

All third-grade students 79% 100% 91%

White 83 100 100

Hispanic 74 100 84

Limited English proficient 68 100 83Economically disadvantaged 75 100 86Disabled 67 100 92

These pass rates show that 100% of thestudents-that is, every student in the third-grade class-passed the state-level mathemat-ics assessment during the Code RED Project.As the table shows, in the year before theCode RED Project, 21% of the third grade didnot pass the state mathematics assessment.Table 4 also shows that only 9% of all thirdgraders did not pass the state assessment theyear after the Code RED Project. In addition,there were overall increases in the pass ratesfor all subgroups between the 2003 and 2005academic years. The largest populations of stu-dents who did not pass the mathematics as-sessment in 2003 were in the limited-English-proficient and disabled subgroups. As the tableindicates, there were strong numerical in-creases in these pass rates following the CodeRED Project.

It is also significant to note the number ofstudents who tested in the pass-proficient andpass-advanced achievement categories whencomparing the 2003, 2004, and 2005 results.Figure 1 reports numbers of students in thefail, pass-proficient, and pass-advanced report-ing categories for 3 years. Not only does itshow that the number of students who failedthe test in 2003 dropped to zero in 2004, but italso illustrates that students testing in the pro-ficient category increased by 48% and those inthe advanced proficiency category increasedby 48%. These percentages represent signifi-cant increases in student achievement for thethird-grade students during the year of theCode RED Project. The distribution in 2005 isalso an improvement in all categories whencompared with the 2003 baseline data.

A final note that is important to consideris the 100% pass rate on the state assessment,

as well as the performance of students on thepre- and posttests in the five classes. Althoughthe pre- and posttest assessments designed bythe Code RED Project team revealed that fourof the five classes demonstrated significantgains on the posttest, one of the classes (thatof Teacher D) did not. However, when the stu-dents in Teacher D's class completed the statestandardized testing later that spring, the stu-dents in Teacher D's class, like the students inthe other four 3rd-grade classes, all passed thestate test.

Discussion: IncreasingStudent Achievement

These findings show that the Code RED Pro-ject had a positive impact on students' mathe-matics achievement scores in Grade 3 duringthe year of the project. The pre- and posttestresults showed significant improvements forthird-grade students when the team focused onstudents' needs based on the data they hadgathered. The 100% pass rate on the state-level mathematics assessment for all third-grade students during the year of the CodeRED Project was a second source of data toconfirm these conclusions. We believe that animportant part of this project was the teachers'learning to interpret student data and their us-ing that data to focus on remediation and en-richment. Students participated in mathemat-ics sessions that targeted their needs for aperiod of 10 weeks. Rather than review or re-mediate using general concepts, the Code REDProject days were focused on identified weak-nesses for this group of third-grade students.

88 MOYER ET AL.

50-45-40-35-30-25-20-15-10-5-0- 1Lll���

Fail

M 200302004l 2005

Pass Pass Adv.Prof.

Figure 1. Number of third graders in the fail, pass-proficient, and pass-advanced categories on the 2003, 2004, and2005 state mathematics assessments.

Another important component of the in-crease in student achievement was that theclassroom teachers were focusing on a deeperunderstanding of the mathematics and on var-ious representations for the mathematics dur-ing regular instruction as well as during theCode RED Project days. Rather than focus onthe teaching of a lesson, teachers shifted theirfocus to student needs, student thinking, andhow students were learning. This shift meantthat the culture for teaching among the mem-bers of the team moved from planning forteaching to planning for learning. The teach-ers were learning planning, instead of lessonplanning. A culture of learning planningmeans that teachers are more apt to ask ques-tions about learning outcomes and examinetheir own role in those outcomes. We believethat the teachers seriously examined how theymight have a positive impact on student learn-ing in this project.

The resulting increase in student achieve-ment launched other school teams to engage inmore reflection, inquiry, dialogue, and ac-tion-all hallmarks of a successful school cul-ture (Jolly, 2005). As teachers in other grade

levels observed the efforts and outcomes oftheir colleagues' work, this embedded profes-sional practices associated with inquirythroughout the school. As a result of the CodeRED Project, all grade levels began schoolwideplanning that focuses on improving mathemat-ics achievement for all students in the school.

Enhancing Teachers' InstructionalPractices and Leadership Attributes

The evidence of students in the third gradecontinuing to be successful on the state-standardized assessments following the CodeRED Project demonstrates how teachers em-bedded what they learned during the projectinto their daily instructional practices. Webelieve that these persisting improvementscan be attributed to a change in teachers'mathematical content knowledge, use ofmore representational forms (including vi-sual/pictorial), and strategies for differentiat-ing instruction for students of differing abil-ity levels. Teachers worked together with theuniversity mathematics education professorand the school mathematics specialist to tar-

. I

get specific mathematics content strands andconcepts, and develop strategies that wouldincrease students' understanding of thoseconcepts. In particular, teachers engaged inexamining mathematics items and under-standing the mathematical thinking thatwould be required of students for respondingto those items.

When the teachers worked backward fromthe test items, it allowed them to focus on themathematics content in the items, the variousforms of representation (including numbers,symbols, pictures, graphs) that were used toconvey mathematical ideas in items, and thecomplexity of the multistep thinking that wasrequired for a response. For example, whenteachers examined one of the fraction items,they found that the question stem was pre-sented in the form of a fraction numeral withfraction words; the picture that accompaniedthe problem was presented as a set model forfractions; and the response items were pre-sented in decimal form. When teachers exam-ined this question format, they began to thinkabout how they were teaching the conceptsand whether their instructional strategies wereaddressing the knowledge that studentsneeded to respond accurately to these types oftest items. This shift in focus enabled theteachers to, rather than teach to a test, focuson the types of teaching strategies required forteaching mathematical concepts in ways thatbuild students' mathematical thinking.

Another important distinction in their in-struction was that, from a developmental per-spective, teachers had a deeper understanding ofthe mathematics. They recognized students' er-ror patterns as well as how to extend and enricha concept for advanced students. This type ofanalysis of mathematics problems carried overinto teachers' regular instruction, and viewingconcepts from remediation through enrichmentbecame a part of regular practices following theCode RED Project. By incorporating these pro-fessional strategies into their daily mathematicsinstruction, teaching and learning in third graderegularly included differentiated learning withplanned remediation and enrichment that sup-ported students. In the year following CodeRED, these instructional practices continued,

Code RED (Remediation and Enrichment Days) 89

and students' scores on the state-standardizedassessment positively reflected these changes inteachers' instructional patterns.

Preservice Teacher Development

When a school develops common practices,they become institutionalized by the com-mon language that all parties begin to use.That then becomes the way in which theschool conducts its business. In this elemen-tary school, the practice of using data to in-form instruction and plan for learning in col-laborative teams was modeled by theclassroom teachers (Reeves, 2004). Examin-ing student data together provided a contextfor the preservice teachers to be engaged inprofessional planning and reflection as mem-bers of the school community. Preserviceteachers embedded in grade-level teams wereengaged in the daily dialogue of the project.These conversations allowed them to partici-pate in the culture of inquiry modeled by theteachers, acquire the language of the profes-sional community for which they will bemembers, and practice professional learningplanning in the real-life context of theschool. The classroom teachers made theirthinking and planning transparent to thepreservice teachers throughout the CodeRED Project. This openness allowed the pre-service teachers to observe and discuss theprocess with their supervising classroomteachers and the university professor. It alsodeveloped the classroom teachers as bettermentors for the preservice teachers.

The preservice teachers at this schoolwere able to see firsthand how their supervis-ing classroom teachers participated in aprocess of their own professional learning anddevelopment. They saw how the teachers tookownership of a school concern and developeda solution that they implemented and howthis implementation yielded positive learningresults for the students. This systematic exam-ination and inquiry process on the part of theclassroom teachers showed good instructionalpractices in mathematics. It also modeled forthe preservice teachers the processes used byprofessionals to engage in collective inquiry

90 MOYER ET AL.

and achieve the common goal of affecting stu-dent achievement for the entire grade level.

Concluding Remarks

This study highlights the broader impacts ofhow a partnership among school and univer-sity faculty and students can result in mean-ingful mathematical learning for everyone in-volved in the process. Although the results forthe third-grade students on the state mathe-matics assessment were an impressive outcomeof this project, even more significant were thelessons that the teachers learned about math-ematics and the analysis of student data, theinstructional shifts that the teachers made intheir focus on learning planning (rather thanlesson planning), and the benefits for the pre-service teachers whom they were supervising.These shifts in thinking are the kind of resultsthat can change a school's culture and have aresounding impact on professional practicesfor years to come. These changed practiceswill not simply affect the outcome of oneyear's standardized mathematics test resultsbut will influence the way that teachers ap-proach student learning throughout their ca-reers. A current reality of public schooling isstudent accountability. We encourage our col-leagues in education to think about accounta-bility beyond our standardized testing resultsand to use our creative partnership as an impe-tus to focus more on the actions that schoolscan take to create a culture of inquiry that re-sults in sustained learning for teachers and stu-dents. U

References

Ashlock, R. B. (2006). Error patterns in computa-tion: Using error patterns to improve instruction(9th ed.). Upper Saddle River, NJ: Pearson/Merrill/Prentice Hall.

Blankstein, A. (2004). Failure is not an option.Thousand Oaks, CA: Corwin Press.

Civil, M. (1993). Prospective elementary teachers'thinking about teaching mathematics. Journalof Mathematical Behavior, 12, 79-109.

Corcoran, T. B. (1995). Transforming professionaldevelopment for teachers: A guide for state policy-

makers. Washington, DC: National GovernorsAssociation.

Darling-Hammond, L. (1995). Changing concep-tions of teaching and teacher development.Teacher Education Quarterly, 22(4), 9-26.

Darling-Hammond, L. (1996). What matters most:A competent teacher for every child. Phi DeltaKappan, 78(3), 193-201.

DuFour, R., & Eaker, R. (1998). Professional learn-ing communities at work: Best practices for en-hancing student achievement. Bloomington, IN:National Educational Services.

Eaker, R., DuFour, R., & Bumette, R. (2002). Get-ting started: Reculturing schools to become profes-sional learning communities. Bloomington, IN:National Educational Service.

Garet, M. S., Porter, A. C., Desimone, L., Birman,B. F, & Yoon, K. S. (2001). What makes pro-fessional development effective? Results froma national sample of teachers. American Educa-tional Research Journal, 38(4), 915-945.

Glickman, C. (2002). Leadership for learning.Alexandria, VA: Association for Supervisionand Curriculum Development.

Griffin, G. A. (1999). The education of teachers:Ninety-eighth yearbook of the National Society forthe Study of Education. Chicago: University ofChicago Press.

Hord, S. (1997). Professional learning communities:Communities of continuous inquiry and improve-ment. Austin, TX: Southwest Educational De-velopment Laboratory.

Jolly, A. (2005). A facilitators guide to professionallearning teams. Greensboro: University ofNorth Carolina, SERVE Center.

Koehler, V. (1985). Research on preservice teachereducation. Journal of Teacher Education, 36(1),23-30.

Kosbob, S., & Moyer, P. S. (2004). Picnicking withfractions. Teaching Children Mathematics, 10(7),375-381.

Lambert, L. (1998). Building leadership capacity inschools. Alexandria, VA: Association for Su-pervision and Curriculum Development.

Lambert, L. (2003). Leadership capacity for lastingschool improvement. Alexandria, VA: Associa-tion for Supervision and Curriculum Develop-ment.

Loucks-Horsley, S., Hewson, P. W, Love, N., &Stiles, K. E. (1998). Designing professional de-velopment for teachers of science and mathemat-ics. Thousand Oaks, CA: Corwin Press.

Mailley, E., & Moyer, P. S. (2004). The mathemat-ical candy store: Weight matters. Teaching Chil-dren Mathematics, 10(8), 388-393.

Marzano, R. J., Pickering, D. J., & Pollock, J. E.(2001). Classroom instruction that works:Research-based strategies for increasing studentachievement. Alexandria, VA: Association forSupervision and Curriculum Development.

McKibbin, M. D. (1999). Alternative certificationin action: California's teaching internships.Kappa Delta Pi Record, 36(1), 8-11.

Moyer, P. S., & Husman, J. (2006). Integratingcoursework and field placements: The impacton preservice elementary mathematics teach-ers' connections to teaching. Teacher EducationQuarterly, 33(1), 37-56.

Moyer, P. S., & Mailley, E. (2004). Inchworm anda half: Developing fraction and measurementconcepts using mathematical representa-tions. Teaching Children Mathematics, 10(5),244-252.

Moyer, P. S., Niezgoda, D., & Stanley, J. (2005).Young children's use of virtual manipulativesand other forms of mathematical representa-tions. In W. J. Masalski & P. C. Elliott (Eds.),Technology-supported mathematics learning envi-ronments: Sixty-seventh yearbook (pp. 17-34).Reston, VA: National Council of Teachers ofMathematics.

National Council for Accreditation of Teacher Ed-ucation. (2001). Standards for professional de-velopment schools. Washington, DC: Author.

National Council of Teachers of Mathematics.(2000). Principles and standards for school math-ematics. Reston, VA: Author.

Niezgoda, D. A., & Moyer, P. S. (2005). Hickorydickory dock: Navigating through data analysis.Teaching Children Mathematics, 11 (6), 292-300.

Reeves, D. (2004). Accountability for learning.Alexandria, VA: Association for Supervisionand Curriculum Development.

Reynolds, A. (1992). What is competent begin-ning teaching? A review of the literature. Re-view of Educational Research, 62(1), 1-35.

Senge, P. M. (1990). The fifth discipline: The art andpractice of the learning organization. New York:Doubleday/Currency.

Sikula, J., Buttery, T. J., & Guyton, E. (Eds.).(1996). Handbook of research on teacher educa-tion (2nd ed.). New York: Simon & Schuster.

Code RED (Remediation and Enrichment Days) 91

Smith, M. S. (2001). Practice-based professional de-velopment for teachers of mathematics. Reston,VA: National Council of Teachers of Mathe-matics.

Spalding, E., Wilson, A., & Sandidge, R. (2000).Piecing a quilt: Redesigning secondary teachereducation in the context of statewide educa-tional reform. Teacher Education Quarterly,27(4), 25-44.

Stein, M. K., Smith, M. S., & Silver, E. A. (1999).The development of professional developers:Learning to assist teachers in new settings innew ways. Harvard Educational Review, 69(3),237-269.

Sweda, J. R., Knotts, L. A., & Moyer, P. S. (2004).Mr. Greenthumb's garden. Teaching ChildrenMathematics, 1 1(4), 217-225.

Tabachnick, B. R., & Zeichner, K. M. (1984). Theimpact of the student teaching experience onthe development of teacher perspectives. Jour-nal of Teacher Education, 35(6), 28-36.

44440. **.

Patricia S. Moyer is the mathematics educa-

tion program coordinator and MathematicsEducation Center director at George Mason

University, Fairfax, Virginia. Her research fo-cuses on uses of representations in mathemat-ics and mathematics teacher development.

Kim Dockery is the principal of Westlawn El-ementary School in Falls Church, Virginia.She is interested in school improvement fordiverse school populations.

Spencer Jamieson is the mathematics special-ist at Westlawn Elementary School in FallsChurch, Virginia. He serves as a mathematicsinstructor and coach in the school.

Julie Ross is a first-grade teacher and the on-site internship supervisor at Westlawn Ele-mentary School in Falls Church, Virginia.

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TITLE: Code RED (Remediation and Enrichment Days): TheComplex Journey of a Sc

SOURCE: Action in Teacher Education 28 no4 Wint 2006PAGE(S): 75-91

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