Fostering Culturally and Developmentally Responsive Teaching Through Improvisational Practice

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Fostering Culturally and DevelopmentallyResponsive Teaching ThroughImprovisational PracticeElizabeth Grauea, Kristin Whytea & Kate Kresin Delaneyaa Department of Curriculum & Instruction, University of WisconsinMadison, Madison, Wisconsin, USAPublished online: 06 Nov 2014.

To cite this article: Elizabeth Graue, Kristin Whyte & Kate Kresin Delaney (2014) Fostering Culturallyand Developmentally Responsive Teaching Through Improvisational Practice, Journal of EarlyChildhood Teacher Education, 35:4, 297-317, DOI: 10.1080/10901027.2014.968296

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Journal of Early Childhood Teacher Education, 35:297317, 2014Copyright National Association of Early Childhood Teacher EducatorsISSN: 1090-1027 print / 1745-5642 onlineDOI: 10.1080/10901027.2014.968296

Fostering Culturally and DevelopmentallyResponsive Teaching Through Improvisational

Practice

ELIZABETH GRAUE, KRISTIN WHYTE,AND KATE KRESIN DELANEY

Department of Curriculum & Instruction, University of Wisconsin Madison,Madison, Wisconsin, USA

In this article we explore an effort to rethink curricular decision-making with a group ofpublic pre-K teachers working in a context of curriculum escalation and commitment toplay-based pedagogy. Through a professional development program designed to supportdevelopmentally and culturally responsive early mathematics, we examine how teacherstook up the idea of engaging in mathematics with 4-year-olds in a way that marriedcontent knowledge and home practices. We look specifically at three teachers as theynegotiated our vision of responsive practice, using the notion of improvisation as ametaphor to understand how they took up this new role. We found that just having theknowledge about developmentally responsive practices, funds of knowledge, or earlymath was a first step but it was not enough. How teachers took up the elements ofthe professional development was contingent on their capacity to improvise in theirteaching, responding to childrens resources and interests in authentic ways.

All children come to school with an array of intellectual resources and dispositions towardlearning. Using childrens existing knowledge as the foundation for instruction makesteaching contingent on their understandings, recognizing their practices, and framing inter-actions from their perspectives (Graue, Rauscher, & Sherfinski, 2009). Such contingentinstruction is a key element of process quality, which has been defined as childrens directexperiences and interactions with teachers and with the instructional content within class-rooms (Howes et al., 2008, p. 29). Consistent with sociocultural perspectives on learning,the richest interactions are based on teacher knowledge of childrens resources acrossdevelopmental domains (Pianta, 2008).

In this article we explore the nature of responsive teacherchild interactions in an effortto rethink curricular decision-making with 4-year-old kindergarten (4K) teachers com-mitted to play-based pedagogy. Through a professional development program designedto support developmentally and culturally responsive early mathematics practices, weexamine how teachers build on childrens resources in their instructional interactions andpractices.

Received 26 July 2013; accepted 4 May 2014.Address correspondence to Elizabeth Graue, Department of Curriculum & Instruction,

University of Wisconsin Madison, 225 N. Mills, Madison WI 53706, USA. E-mail: [email protected]

Color versions of one or more figures in this article are available online at www.tandfonline.com/ujec.

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We begin with reviews of an anthropological approach to responsive teaching, knownas funds of knowledge (Moll, Amanti, Neff, & Gonzalez, 1992), and the knowledge baseof mathematics teaching and learning in early childhood. We then suggest a specific theo-retical frameworkthe notion of teaching as improvisation. Next, we describe the designof the professional development program and methods used to collect and analyze data.We then examine how participants took up the idea of engaging in mathematics in a waythat married their knowledge of content and home practices, asking: How do 4K teacherstake up the idea of teaching math in culturally and developmentally responsive ways? Inaddition, we pose the question: What do instructional strategies based on reciprocal fundsof knowledge look like in practice?

Literature Review

Funds of Knowledge

Initially introduced to respond to deficit perspectives on minoritized families, fundsof knowledge (FoK) is an asset and culturally based framework for understanding theresources children bring to school (Moll & Greenberg 1990). Focusing on historically andculturally developed knowledge and skills that are foundational to household and individ-ual functioning, FoK engages teachers in ethnographic work to better understand studentsand families (Moll et. al., 1992). With this information they design instruction that takes upfamily knowledge in the classroom.

In contrast to static notions of culture that focus on group practices and that ignorethe everyday lived experiences of marginalized families, FoK situates teachers, children,and families as active participants in cultural and curricular processes (Gonzalez, 2005;Moll, 2000). Recognizing the value of cultural knowledge and practices in learning anddevelopment, teachers employing FoK work to link a childs home and school lives bylearning about and building on family practices and knowledge. This has multiple benefitsfor both teachers and children. As teachers learn about and utilize family FoK, they buildon home practices and engage children more deeply with school learning. Relationshipsbetween families and teachers can develop with recognition of mutual expertise and eachhas more informed knowledge to support the children they share (Moll et. al., 1992).

Over time, scholars have critiqued the application of FoK, suggesting that at times theframework has been misunderstood and oversimplified (Gonzalez, Wyman, & OConner,2011). Reviewing extant literature focused on FoK, Hogg (2011) argues that researchersshould articulate how they theorize and operationalize FoK in their work. Recently, somesuggested pairing FoK with notions of social and cultural capital to understand the nature ofpower and agency for teachers, families, and children in education settings (Rios-Aguilar,2010; Rodriguez, 2013).

Mathematics and Young Children

The importance of literacy in early childhood has been drilled into the publics collectiveconsciousness. Parents are frequently told to read and talk to their children about everydayevents. Teachers are expected to thread literacy into all activities, creating environments thatpromote concepts about print and phonemic awareness (Strickland & Schickedanz, 2009).In contrast, mathematics is not typically seen as a key player in the teaching context at homeor school. Math is curiously absent from the repertoire that parents take up as they teach

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Responsive Practice Through Improvisation 299

their children (Tudge & Doucet, 2004), despite the fact that young children develop math-ematical understandings about the world around them (Ginsburg, Lee, & Stevenson Boyd,2008) related to school mathematical content like number sense (Schoenfeld & Stipek,2012).

This lack of attention has especially serious implications for children of poverty, par-ticularly those of color, and English Learners (National Research Council [NRC], 2009).Coming into kindergarten with mathematics skills and knowledge that lag behind theirmore affluent peers (Denton & West, 2002; Ginsburg et al., 2008; Lee & Burkham, 2002),these children frequently work with teachers who are often uncomfortable with mathemat-ics, have not learned rich strategies for supporting mathematics learning, and who mayinterpret the learning gap as a deficit based in the home (NRC, 2009). As a result, theirteachers favor lower-level mathematics skills like memorizing and rote tasks with a basicskills orientation over problem solving (Stipek & Byler, 1997).

In addition, early childhood curriculum often relegates mathematics to counting, fail-ing to consider how naturalistic play experiences lend themselves to broader mathematicalthinking and understanding for young children (NRC, 2009; Parks & Bridges-Rhoads,2012). The balance between making math explicit in the early childhood classroom andletting children play their way into math is a delicate one (Parks, 2010). A skilled earlychildhood teacher can utilize childrens play to leverage learning that builds on the interestsand choices of each child (Jones & Reynolds, 2011). To effectively teach both content andpractices teachers should tap into childrens foundational mathematical understandings andthen develop rich mathematical activities that build on that prior knowledge (Schoenfeld &Stipek, 2012).

Responsivity Through Improvisation

Responsive teachers are attentive to childrens interests (Bredekamp & Copple, 1997;Kontos, 1999). They enhance childrens play by adding to the activity at hand and giv-ing directions that follow from the activity in which the children are already engaged(Lobman, 2005). Responsive teaching requires content knowledge and teacher recognitionof childrens resources, interests, experiences, and skills. But equally important, it requiresaction contingent on that knowledge (Hamre et al., 2012). Because of the multidimen-sional nature of this knowledge/action, responsive teaching cannot be scripted. Instead, itis improvisational.

In her foundational work, Lobman (2006) defined improvisation as the joint produc-tion of meaning created through a story. Improvisation is synergisticwhat it creates isgreater than what each person contributes individually. Teachers plan for improvisation butthe plans are flexible and contingent on what students bring to an activity. Through impro-visation workshops, Lobman (2006) found that experiences with basic improv practicesmade the teachers more aware of the quality of their listening and helped them create col-lective activities. Further, she argued that improv is a critical analytic tool to understandthe joint production of meaning in teacherchild interaction. Across a variety of settings,Sawyer (1997, 2004) has also examined improvisation. Sawyer (1997) has used the notionof improvisation to understand how young children create joint meaning, to argue forimprovisational teaching as a counter to scripted curriculum, as a unit of analysis for activ-ity systems, and as a tool to understand the tension between structure and improvisation inteaching and learning.

In teaching, improvisation focuses attention on the critical importance of teacherchild interactions, making improvisation primarily a relational activity; the means by which

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teachers and children connect through meaningful, content-rich interactions. Further, it is aconcrete enactment of work in the zone of proximal development, allowing teachers to actresponsively to stretch their students understanding. Finally, it serves as a tool for think-ing about the kinds of micromoves that teachers need to engage in when they facilitateplay-based programs. Professional knowledge is critical to improvisation:

. . . to create an improvisational classroom, the teacher must have a highdegree of pedagogical content knowledgeto respond creatively to unexpectedstudent queries, a teacher must have a more profound understanding of thematerial than if the teacher is simply reciting a preplanned lecture or script(Sawyer, 2004, as cited in Reeves, 2010, p. 254).

We build on both Sawyer and Lobmans work in our research but we approach theconstruct in a slightly different way. We build our analysis around work by critical con-structionists (Holland, Lachicotte, Skinner, & Cain, 1998) who argue that improvisation isthe space that creates the potential for new identities, where culture and individual interactresponsively to create change:

Improvisations are the sort of impromptu actions that occur when our past,brought to the present as habitus, meets with a particular combination ofcircumstances and conditions for which we have no set response. Such impro-visations are the openings by which change comes about from generation togeneration. (Holland et al., 1998, pp. 1718)

This perspective on improvisation resonated with us as we worked to understand the com-plex processes of shifting strongly held ideas about practice in early childhood education.Skilled teachers in 4K classrooms must draw on their understandings of high-quality andresponsive early childhood practices, childrens home cultures, and deep content knowl-edge to provide optimal learning experiences for diverse groups of young children (Brown& Lee, 2012). Our professional development, a form of teacher education for in-serviceteachers, was designed to support this process.

Methods

The 4KPD Professional Development Project

The catalyst for this project was the start of a local public 4K program and the prospectof educating over 1,500 four-year-olds. After years of local debate and negotiation,Oscarburg1 began a 4K program in the 20112012 school year, enrolling in the states long-running universal 4K program. A collaborative effort of child care centers, Head Start, andthe public school district, the half-day program was free to all children who were 4 yearsold by September 1.

Anticipating that teachers would need support, a team of researchers at Universityof Wisconsin Madison developed a proposal to the National Science Foundation to pro-vide professional development for 4K teachers focused on culturally and developmentallyresponsive teaching in early mathematics. This focus was chosen in response to the

1All names for locations and individuals are pseudonyms.

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growing cultural gap between teachers and students and the idea that building on chil-drens home resources could serve to make teaching more responsive (Ladson-Billings,1995). We oriented our work to mathematics, based on recent research that indicates thatearly mathematics knowledge is more predictive of later achievement than early literacy(Duncan et al., 2007). We received funding for the project and developed a series ofcourses2 focused on developmentally and culturally responsive early mathematics teaching.We designed our program in line with research-based frameworks for successful pro-fessional development (Desimone, 2009) with a coherent theme (responsive practices),specific disciplinary content (early mathematics) through active learning and collectiveparticipation in a professional learning community.

The Participants

We invited all 4K teachers in Oscarburg to participate in the professional developmentproject and interested parties completed an application that detailed their teaching certifica-tion, years teaching, experience with mathematics and working with families, and rationalefor participation. Only teachers not certified to teach 4K were excluded from the program.This paper focuses on our work with the second of three cohorts of teachers in the first year4K was implemented in the community. It included 19 school-based and three community-site 4K teachers. All participants had early childhood licensure and undergraduate degreesin education, with the exception of two teachers with emergency certifications and one earlychildhood special educator. The teachers ranged from first-year novices to educators closeto retirement. With the exception of a teacher who was Vietnamese American, all our par-ticipants were White women. While this is not a diverse sample, it does reflect the realityof the current degreed early childhood work force, which continues to be largely Whitewomen (Saluja, Early, & Clifford, 2002).

The Professional Development Courses

Central to our design was the goal of building on the FoK tradition by adding a reciprocalelement. To do this, we created a series of courses that asked teachers to focus on childrenshome resources when they designed instructional activities. In addition we urged teachersto develop culturally responsive strategies to help families understand how to mathematizetheir home practices. From the perspective of FoK, we know that family members can learnfrom teachers and teachers can learn from families. Our goal was that teachers and familieswould link the specific cultural practices exemplified by FoK with generalized knowledgeof childrens mathematical understanding to respond in authentic ways to childrens skillsand experiences. To do this, we asked teachers to reconceptualize their relationships withfamilies by building on family FoK (Gonzalez, 2005) and to buy into the idea that earlymathematics is a powerful tool for taking up childrens resources in the classroom.

Another key element was an effort to shift teachers to the unfamiliar role of ethnogra-pher by developing an appreciation of culture and the anthropological tools of participantobservation, interviews, and artifact analysis. Our objective was to help teachers developthe skills that would allow them to access, understand, and utilize knowledge of childrens

2The professional development program was delivered through a series of four courses that werea hybrid of traditional graduate courses and ongoing professional development. Teachers receiveduniversity credit for participation and could transfer the credits if they were interested in pursuing amasters degree.

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home lives as they designed culturally and developmentally responsive curriculum focusedon mathematics. To that end, we asked them to work with a focal child and family acrossthe school year. With their focal child, they conducted multiple ethnographic home vis-its. In class, the teachers designed home visits and interviews that would illuminate familymathematics practices. Reflective assignments were organized to connect teacher practicewith the readings and what they were learning through home visits. In turn, the teacherstranslated what they found out about their focal child into educational activities, workingwith their colleagues who provided support. Additionally, the teachers developed child-centered assessments called learning stories (Carr, 2001). Learning stories are descriptionsof children engaged in a moment of learning. These stories document in situ assessmentsand communicate to the child and family the process of learning.

We focused on balancing intentional math teaching and responsive participation inplay-based activities. This balance required teachers to identify and understand the devel-opmental patterns in early mathematics, the specific resources children brought into theirplay, and the ability to be a master playersomeone who could engage in childrens playto enrich rather than squash it (Reynolds & Jones, 1997). We then asked teachers to thinkabout what this meant for their role in childrens play in 4K classrooms.

Data Collection and Analysis

Over four semesters, we audiotaped large and small group class discussions and collectedartifacts such as teacher assignments and our planning documents. We conducted individualinterviews with each teacher at the beginning and end of each school year resulting in fourinterviews across the 2-year program. We administered the Classroom Assessment ScoringSystem (CLASS) three times in each classroom to gather data about classroom quality(Pianta, LaParo, & Hamre, 2008). In addition, we selected six participants as case studiesof practice. We chose these case study teachers to represent variation in site (e.g., school vs.community), practice (e.g., play based vs. didactic), and teacher characteristics (e.g., juniorvs. senior). Researchers conducted bimonthly classroom observations of these teachers andtheir practice, taking detailed ethnographic field notes. All data were entered into NVivofor analysis. The Appendix provides examples of interview questions and course readings.We present descriptions of three cases in this article.

We3 began our analysis by reading through the data, approaching the data in two ways.First, each of us closely examined at least 1 month of data from the courseincluding alltranscripts and notes from that period. Second, we analyzed one teachers data through thethree main themes of our project as coding tools: early childhood education, early mathe-matics, and FoK. Following this initial cycle, we met to discuss emerging themes. Usingthese discussions, we identified emerging subcodes and began reading and coding recur-sively. Using a Project Journal, we continued to link joint understanding. This, in additionto our weekly discussions helped us to identify and focus in on developing themes. Themesthat were supported in/by two or more sources were included in subsequent analyses.We triangulated our assertions across data sources and analyses. Collaborative writing alsoserved as an important tool for continued analysis (Graue, 1998).

We were keenly interested in how the teachers knowledge and the professional devel-opments strands (of mathematics, developmentally appropriate practices, and funds of

3Initial analysis included a large research team. We are grateful to Anita Wager, Sonia Ibarra,Bridget Christiansen, Anne Karabon, Jiwon Kim, and Kate Delaney for their help to understand thisrich data set.

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knowledge) came together to create curriculum in responsive spaces. It was clear that theresources provided by this knowledge were necessary, but not sufficient for high-qualityteaching. They needed to be activated in context to be of use (Cohen, Raudenbush, & Ball,2003). It was at this point that we turned to the metaphor of improvisation to understandand explain how teachers took up the strategies offered by the professional development.For us, improvisation embodies the nimble and knowledge-informed decision-making of aculturally and developmentally responsive teacher of early mathematics. Using improvisa-tion was a natural tool in the context of our project to build knowledge in multiple domains.To understand how they took up the ideas presented in the professional development we useimprovisation as frame to examine three teachers practice. We chose these particular casesto illustrate the variation in the teachers enactment of the professional developments keyconstruct and how they translated these ideas in their practice.

Findings

Wanda: Assessing Where Children Should Be

A veteran kindergarten teacher, Wanda is patient and gregarious, her voice quiet even whenher school-based 4K classroom is on the edge of control. She is quick to laugh with childrenand wants to know each child and family in a meaningful way. That being said, movingfrom the structured kindergarten curriculum to a more responsive and fluid 4K curriculumwas more difficult than Wanda had anticipated:

4-K is definitely child-directed, the teacher following the kid. Whereas, unfor-tunately, the 5-K that I had been teaching has turned into a first grade fromtwenty years ago. And its really teacher-led depending on the levels of the stu-dents. So Im really trying to think of how I can do this without doing it theway I used to where it was all planned out ahead and I just followed each day.(Initial interview)

As a kindergarten teacher, Wanda felt pressure to get her students ready for first grade.She carried this into her 4K teaching, despite the districts stated commitment to a child-centered program. Teaching to grade-level standards was something she understood. Ivedone twelve years of kindergarten. I can sit down still and tell you what the beginning andend of the year goals are for kindergarten. I have no clue for 4K so its even harder causeIm trying to figure out how to get them there (Small group, January 25, 2012).

AlthoughWandas identity as a kindergarten teacher might have constrained her abilityto enact a child-centered approach, it also left her with a wealth of mathematical contentknowledge. Wanda embraced the early childhood mathematics content presented in theprofessional development, something we could see during classroom observations. One ofWandas greatest strengths is her ability to deeply engage children in mathematical thinkingin whole-group settings. At the start of the day, we would often see Wanda and the childrenworking through counting challenges:

Kwame whisper counts his way around the circle of children. Eleven, helisps when he gets to the last child. Yes, we have eleven friends here today.So how many of our friends are not here today? Wanda asks as she writes aneleven on the white board. Two! most of the children call out, though somesay three and one says nine. Thats right, says Wanda, two children

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are absent today. How do you know? Simon? Simon smiles and responds,Because we have 13 friends in our class. Wanda smiles too, Right! Solets seeI think we can make this a story problem . . . does anyone wantto try? Tsheej raises his hand. I have thirteen friends in my class, but twogot sick, so they stayed home, says Tsheej. Wowgood one. Anyone else?Several children share story problems. When children struggle, Wanda asksquestions, supporting them to the correct answer. She is deeply engaged, andso are the children, who want to show how they can manipulate these numbers.(Observation, January 25, 2012)

Wandas ability to scaffold mathematical thinking allows her students to try out new waysof thinking about numbers and counting. Wanda told her colleagues how she used this timeto push their number knowledge to get them ready for kindergarten. She is proud of howmath excites her students and enjoys watching their skills grow.

Wanda used developmentally appropriate practices as a tool to understand 4K andparticularly the social/emotional elements of this approach. She saw the main differencebetween 4K and kindergarten as the added social and emotional support that 4-year-oldsneeded in their transition to school:

It caught me totally off guardhow different the kids are. In their development,and also what we are supposed to be doing in the classroom. They need me tohelp them solve problems, to like model. And to give hugs, and hold hands.We didnt have time to do that in K5. (Observation, December 8, 2012)

Wanda sees meeting the social and emotional needs of the children as an important aspectof her role as a 4K teacherthis was evident in both her reflections from the professionaldevelopment and from how she ran her classroom. She brought this lens to her under-standings of FoK. While the cultural element of FoK was difficult for Wanda, she did takeup other information from her home visits to inform her practice to meet the social andemotional needs of her students. For example, Wanda used her knowledge of one of herstudents position as youngest brother to provide opportunities for him to be a leader, to lethim make decisions in whole group, and to remind herself to have extra patience when hehad difficulty sharing with other children. For Wanda, thinking in terms of home resourcesgave her tools to support social/emotional practices.

One assignment for the professional development course involved creating a mathactivity using their focal childs FoK in combination with the childs mathematics knowl-edge for a family math night event. Wanda created a board game that would help improveher focal childs, Jess, mathematics skills with a kitty theme because of Jesss love forher cat:

Jess can rote count to 11, identify more than half the numbers 010, and countobjects up to 10 (1:1 correspondence). Unfortunately, these are not all consis-tent. Jess has a cat at home that . . . she loves. She also loves to create thingsin the art center. I am calling my game Kittys Walk Home. The student willstart by rolling a dice. The number rolled is how many spaces the kitty willwalk on the board. Instead of using an object to move around the spaces, Jesswill use the paint dotters. This will allow Jess to better see how many spacesshe has gone. . . . This activity is a combination of some ideas I have used in thepast. . . . I am changing this game to cater to Jesss needs and interest. Therewill be no numbers on the game board, so it doesnt confuse the player with

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number he/she is working on during each count. If she is trying to concen-trate on 1:1 correspondence with the number she has rolled, having preprintednumbers may be confusing. (Family math night assignment)

Wanda easily created an activity that connected to Jesss mathematical needs. Whenattempting to tap into Jesss FoK she connected with something Jess liked from home, hercat. In a sense, Wanda used Jesss interest to create a theme for the game. Generating themesfrom childrens interests is a classic early childhood practice, but does not necessarilyconnect to FoKs focus on the home practices children engage in.

Unlike many of the other teachers in the professional development program, teach-ing math came easily for Wanda. As a kindergarten teacher, she had experience engagingchildren in whole-group and center-based math activities. In class discussions, Wanda wasa leader, helping to familiarize other teachers with the district math curriculum. She oftenlaughed about this, saying that even when she wanted to learn about what other teachers did,they wanted her to talk about math. However, finding ways to join math play in less struc-tured situations was a challenge. As a kindergarten teacher, Wandas improvisation wasmuch more scripted so that she would ready children for first grade. This focus on wherechildren should be continued to be a pressure. In a conversation with the other 4K teacherat her school, Wanda noted that she knew that if the kids didnt do well in kindergarten, shewould hear about it from the teachers upstairs.

At the onset of the school year, without her familiar kindergarten script, improvisationwas finding a new thing to count, or a new way to introduce counting at a center. Over thecourse of the year, Wanda began to find ways to join in math play with her students and touse knowledge of their home resources to inform her practice. After an observation in herclassroom late in March, Wanda noted: It has been hard, trying to catch them using mathin play. But if I sit long enough, I do see it, and sometimes I can get to know what theyknow if I just play along (Observation, March 28, 2012). Uniting FoK, developmentallyresponsive practices, and math content into a curriculum that could be improvised in playwith young children is a work in progress for Wanda, but one in which she actively engagesin developing.

Emma: Observing Where Children Are

Emma works in a child care site and her style of improvisation is tied closely to how sheconstructs her 4K environment, which carefully avoids any externally scripted curriculum.Except for a couple short meetings when the children talk about their day and she readsthem a book, Emma avoids teacher-directed/structured lessons. Rather than focusing onspecific academic skills via calendar time, worksheets, or teacher-directed activities, Emmabelieves children will acquire skills (ABCs and 1,2,3s) through play. She worries aboutstandards being pushed down from kindergarten programs. She thinks children should beallowed to explore freely, taking ownership over their own improvisation; she facilitatesthis by following their lead.

Emma came to the professional development activities with an impassioned sense ofher educational philosophy. Although she does not speak explicitly about the NationalAssociation for the Education of Young Childrens Developmentally Appropriate Practices(DAP), Emmas work with young children reflects DAP ideals. Emma focused on develop-mentally appropriate practices and inquiry-based learning through a play-based curriculum.Within that, she sees three main tools to create good early childhood teaching: observingindividual children within the classroom, careful construction of the environment by the

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teacher, and interactions with the children while theyre playing. Emma trusts that childrenwill engage with the environment she constructs based on her knowledge of child develop-ment and childrens interest. She derives this knowledge through play-based observationsand open-ended questions that ask children to reflect on their own learning. Families areinvited to share traditions and photos with the whole class, providing information abouttheir childrens uniqueness. Emma sees her work with families as a way to further herknowledge about individual children.

Emma questioned how the professional developments version of early math teach-ing connected to play-based learning because she saw it as explicit math instruction. Istruggledthe night that we were playing all those math games . . . we just got donediscussing these articles about the importance of child-initiated activities, and now werenotI just dont see the connection (End of year 1 interview, May 2012). There is roomfor games in Emmas practice, but they are games the children ask to play and games thatare not explicitly teaching academic skills. Here Emma and a small group of children figureout who is going to go first in a board game the children asked to play:

Emma sits near to a board game while the children play. The children are decid-ing who should go first. Emma tells the children, So you each need threepatientsmake sure you have three. Belle asks, Can I go first? She is fol-lowed quickly by Bette, Can I go second? Emma tells them, The oldestperson goes first. How old are you? The children excitedly shout out theirages, 5 1/2, 4, 4 3/4! Miles, the youngest child in the group, has not said any-thing yet. Emma asks him, Are you t? He responds enthusiastically, Im 3!Bette asks Emma, Am I second? Emma tells her that she is because they aregoing to go in a circle. Bette adds, Yes, and because Im 4 3/4. (Classroomobservation, January 20, 2013)

In this scenario Emma saw mathematical language as a natural part of setting up the game.She believes strongly in child-initiated practices; activities she sees as direct teachingare a clear pedagogical conflict for her. Emmas mathematical content knowledge couldbe a resource for children, but only if she sees mathematical content embedded in chil-drens interactions and activities. For this reason, Emma resisted some of the professionaldevelopments new math content and pedagogical approaches.

It is hard to say how Emmas math content knowledge was deepened because she didnot see value in altering how she taught math. Since so much of her teaching has to dowith setting up the environment and expecting children to take it to the next step, Emmasworking math knowledge in her classroom was difficult to observe. Even though Emmaquestioned the value in the ideas presented about how to teach math, she was gratefulfor this new information because she did not feel well educated in the language of math.However, she was tentative about what she thinks she gained:

It was giving language to those [math] skills that we were already doing, that Iwas already seeing, but just didnt exactly know how to speak to it. It was def-initely the language . . . it goes back to the whole critical thinking that youretrying to develop and with your kids, if you cant fully speak to something, Idont think you fully process it out yourself. So, it cemented it more for me.(End of year 1 interview, May 2012)

Emmas construction of developmentally appropriate framed her skepticism of the pro-fessional developments approach to early math, however, her perspective did allow the

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language of mathematics to be mapped onto her already established practices. Her mathe-matics knowledge was deepened and her practices were affirmed, but she did not think itchanged how she taught.

Emmas philosophy was reinforced in the focal child assignment. Though she part-nered with a family who was not from the U.S. the more important thing was that theirapproach to child-rearing was compatible with her teaching philosophy. Elis parents placedhim at Emmas preschool because they wanted him in a play-based program. Their rejec-tion of explicit academic training was a turn away from their own childhood experiencesand favored instead a focus on fun. When Emma was asked to reflect on what she learnedabout Elis FoK from her home visit with his family one of the things she talked about washis love of games, which is what she pulled from to plan an activity for family math night:

At home, Eli and his family play a lot of games. He especially likes to playcard games at home and counting activities that are active such as jumping onthe bed and counting each jump. He and his brother like to do active activitiesat home and love to be silly together. His parents prefer to encourage explo-rative activities at home that are not so formal and allow their children to playand feel they are playing. I call this activity Counting Sillies. You can use aregular deck of playing cards or a deck of cards created by you with numbersthat go as high as needed. If you just have a deck of regular cards, the firstplayer picks a card, says the number on it and then tells the other players whatthey need to do such as: jump, nod their head, clap their hands, wiggle for thatmany counts, etc. . . . his parents value child initiated and inspired activities touse as family learning activities so I wanted to create an activity that honoredthose values. (Family math night assignment)

From Emmas observations of Eli in the classroom, she thought he could benefit fromengaging in numeral recognition and rote counting activities. She took this information andmarried it with what she learned about activities Eli likes to do at home along with hisparents beliefs about education and childhood. Emma created a game, which ordinarilywould have been too teacher directed for her to be comfortable with, but using Elis familysFoK allowed her to see the game as being responsive to Eli, making the game somewhatmore acceptable in her eyes. Emma saw value in the idea of funds of knowledge, but wewonder, if those funds conflicted with her understanding of developmentally appropriatepractices, would the professional knowledge win out? She avoided this potential conflictwhen she chose a family with whom she could easily connect. Emmas views of appropriatepractice were reflected in Elis parents orientation to parenting and education, which shesaw as distinct from their own cultural norms.

With DAP as a foundation, Emma attends to individual children through her knowledgeof development and the opportunities available in the carefully constructed environment.As a result, improvisational teaching is scripted by her notions of DAP and the possibilitiesfor children that are bound up in the teacher-created, developmentally oriented, observableenvironment. This leads to a focus on where children are.

Chela: Imagining What Children Could Be

Chela is a quiet, thoughtful school-based 4K teacher who is independent but collaborative;playful, but serious. The implementation of 4K allowed her to move from the more struc-tured program of grade 2 to a more responsive approach of preschool. I think play-basedand child-initiated is my big philosophy. Taking my teaching from them, letting them direct

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me where to go which this is a program that will allow me to do that (Initial interview,September 2011). This move set the stage for the type of teaching that third-generationDAP describedbringing together knowledge of development, knowledge of individualchildren, and knowledge of cultural practices (Copple & Bredekamp, 2009).

Chela saw play-based pedagogy as the perfect vehicle for developmentally responsiveteaching. Initially she was a strong play advocate, but she worried that entering play mightdampen childrens activity, That line of how much do I push, do I keep questioning orhow much do I just kind of step back and watch and observe . . . each kids different (Endof year 1 interview, May 2012). Chela was a master of identifying a teachable momentin play and turning it into a tailored learning opportunity. The need to control materialsand activities, something that many teachers mistake for classroom management, was notpart of Chelas professional identity. She assumed that children would make good choicesif she provided good instruction. A family math night that included activities developedin the professional development provided a paradigm example of following the childrenslead:

[In the block area] I sat down with about 4 kids and a few parents. I guidedthem through the activities to see if there would just be some excitement andthen takeoff. Throughout the activities, a couple kids just kept asking, Can webuild now? I thought for a minute and then said yes and chatted briefly aboutknocking down small towers only because of the number of people in the room.This block situation stands out for me because I have similar moments duringthe school day. I find that from time to time, I stop myself for a minute, listen towhat the kids are telling me, and make changes. (Family math night reflection)

In addition to a commitment to play, Chela loved math. Chela turned this passion formath into a professional strengthshe took advantage of all math professional develop-ment opportunities and she made mathematics a central part of her practice. Unlike manyof her peers, Chela didnt have a math center or a math timethat seemed silly to her,as math was everywhere. Weaving math into daily activities was what Chela did best.As she designed different games or visual supports she looked for the math hook. Forexample, Chela used 10 frames in attendance (see Figure 1), a typical opportunity for namerecognition and counting; extending the activity in several ways that deepened learningopportunities:

As they talk about attendance, Mrs. C reminds the group that Derek has movedand his name is no longer on the board. Sherices name is still on the board how-ever. Mrs. C asks how they knew that Sherice wasnt at school today? Someonesays, We cant see her? Mrs. C asks how many children are NOT here today?They agree 1. She then asks how many are at school. Someone replies, Alot. Mrs. C asks how they could find outthey reply, count. They count thenumber of name cards. 1, 2, 3 . . . 11. Eleven kids at school today. They figureout that Angelas name isnt thereits over on one of the tables. Angela goesto get her name and they count the names again12! Mrs. C pulls out a coupleof ten frames with flip covers and tells them that they know the first one. Sheopens the first flap and they begin counting, 1, 2, 3, 4, 5 opening a flap upfor each one. She then asks what they think comes next, touching the first flapon the second track. Someone guesses 6. Together they count the remainingnumbers. They then count up to 20. They also count up to ten in SpanishandAngela continues on to 20. (Classroom observation, November 29, 2012)

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Figure 1. Ten frame with flaps.

Counting can become a fetish in some classrooms (NRC, 2009; Parks & Bridge-Rhoads,2012), but Chela uses routines as a context for real problem solvingasking children totalk about how they knew that someone was not at school and to recount when anothername card is added. The ten frame uses multiple visual supports for learningthe flapspromote rote and authentic counting, number recognition, and support the development ofvisual memory. Its ten frame format scaffolds subitizing and the use of both English andSpanish provides two sources of counting. A variation on this theme had Chela droppingmarbles into a metal can and the children counting the sounds, then showing her how manyshe dropped on a ten frame fashioned from a cookie sheet.

The final source of knowledge that enlivened Chelas teaching was funds of knowl-edge. In many ways, Chela was a typical U.S. elementary teacherWhite, female, andmiddle class (Strizek, 2006). She had a 2-year-old son who was cared for at home by herhusband. Choosing a focal child, she inverted the assignment that asked her to work withsomeone different from herself. She chose Kiki, the middle of five children under the ageof 8 whose father was a Mexican immigrant and his mother a U.S. born Latina. While mostteachers would perceive this as difference, Chela saw herself reflected in Kikis family andthought she would learn more if she felt comfortable and that would pay off later:

I wanted to really push myself to step out and get to know a family that isquite different from me. However, I was worried that if I was too nervous, Imay spend most of my time and energy focusing on that, versus the reflectionon the practices that I really want to learn or improve upon. I decided somelevel of comfort from a relationship already established would be beneficial tome and Kikis family had that. Even after deciding on Kiki, part of me is stilltorn, as I know eventually nerves would fade and working with a family andculture that I know little about would be very valuable to me as a teacher andas a person. In the end, I decided that Kiki and his family would help provideme the skills I need to later delve into a family that may be much different thanI am accustomed. (Focal child reflection)

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While we are not sure how Chela would conceptualize a family that is quite different fromme, we are struck by how she framed the notion of difference. Her ability to see herself inthem was more a matter of her saying, Yes, Im like them than Yes, they are like me.This allowed her to take up the relationship in a more collaborative manner.

On her home visit, Ernesto excitedly tells Chela that he can count cookies. He brings abox of cookies from the kitchen and tells us that there are only a few and he counts them inEnglish. Then he says, We had donuts but we ranned out. To get the donuts you go straightand then this way (pointing as if to give directions). His mom then tells us that they getdonuts at the grocery and that Ernesto helps her find groceries at the store, telling him toget five of something because there are 5 children. Chela brought the sources of knowledgetogether in her family math night activity, developed to reflect Ernestos interests, resources,and skills:

Ernesto enjoys games and regularly keeps track of items. His mother shared heis always counting food and comparing with his siblings. In discussions at theplay-dough table and the home visit, it was made known that my focal childhas a love of doughnuts!4 This game is a ten-frame take on the classic, Hi-HoCherrio game. The game includes four ten-frame donut boxes, a spinner, and40 donut game pieces. Each player gets a ten-frame and takes turn spinning thespinner. The player may add donuts or may have to eat (take away) donuts totheir ten-frame. The first to have a full box is the winner. I designed this activitybecause I wanted to work on part-part-whole relationships, as my focal seemedto have a natural interest in it. A ten-frame is a great tool to build connectionsto five and within tens facts as well as practice counting on and/or countingback. (Family math night assignment)

In this activity, Chela pulls from her knowledge of early childhood practices, the develop-ment of counting, and observations of Ernestos funds of knowledge. Chela states that oneof the reasons she created this activity is because of Ernestos love for donuts, but upon fur-ther investigation her reasoning seems deeper than a love of donuts. Chela also consideredthe mathematical nature of the home practices Ernesto participates in when shopping fordonuts. The FoK connection represents Ernestos hybrid identity as an emerging bilingualwho is focused on counting things, particularly donuts.

Chelas practice is responsive, building on her knowledge of her students, her strongcontent knowledge, and her disposition as a learner. She is committed to play-based peda-gogy and sees herself as a master player, someone who must engage with her students ontheir terms. Learning about FoK provides her another tool to be a responsive teacher so thatshe can imagine what children could be.

Discussion and Implications

We designed this project on the premise that if we supported teachers understanding ofearly mathematics development and their disposition to view families as rich sources ofcurriculum, we could help them build a developmentally and culturally responsive curricu-lum.We hoped to enhance knowledge and skill through readings, discussions, and activitiesamong teachers sharing an interest and a professional learning community, and through

4There was a discussion of whether donuts were developmentally appropriate given theirnutritional status. Their connection to Ernestos interests outweighed concern about their caloricvapidness.

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Figure 2. Donut game.

working with a focal child and family who were different from the teacher. What we foundis that having the knowledge about developmentally responsive practices, funds of knowl-edge, or early math is a first step, but it is not enough. How teachers take up the elements ofthe professional development is contingent on their capacity to improvise in their teaching,and to respond to childrens resources and interests in authentic ways.

Wanda, Emma, and Chela were responsive teachers who drew on extensive profes-sional expertise. They were attracted to different strands of the professional developmentand they improvised differently in their teaching. Wandas standards-based perspective,honed as a kindergarten teacher in a period of curriculum escalation, set the stage forhigh-quality math instruction in large groups. She was challenged by the spontaneity ofplay-based teaching, which involves responding to childrens knowledge and experienceon the fly. Emmas finely developed sense of inquiry-based teaching made her skepticalabout a planned approach to introducing mathematics content that she saw as too teacher-directed. Chela integrated the elements of the professional development most fully in herpractice, embracing play-based pedagogy, weaving early math into her teaching in authenticways, and partnering with a family to bridge home and school for her focal child. Althougheach teacher had the resourcesmathematical content knowledge, FoK, and knowledge ofearly childhood tenetsthey needed to act on these bodies of knowledge. Activating theseresources while playing with children added another level of complexity to their practice.

As we worked to understand the overall experience of the professional development,two constructs served to enhance our thinking. Improvisation helped to portray the kind ofcontingent interaction that helped teachers respond to childrens ideas and experience athome and school. Many of the teachers had drifted away from responsive, child-centeredteaching; improvisation was an apt metaphor to describe the types of practice we hoped tosupport. Through our analysis we began to see how an identity of teacher as expert, whichwas reinforced by understanding of standards and DAP, was a role in a script that con-strained the possibilities for improvisation. These narrower scripts of improvisation madethe idea of reciprocal funds of knowledge, a practice in which home and school mutuallycontributed expertise that could be used to support learning, difficult to conceptualize in theprofessional development and in some participants practice.

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The second was the new theorization of FoK that explores how agency is leveraged inpractice. Particularly for marginalized communities, implementing FoK in instruction hasthe capacity to give voice to children and families (Rodriguez, 2013). Rodriguez (2013)sees a gap in time, space, action, and student agency because,

. . . households are described as possessing a range of strategic cultural knowl-edge that students bring to the classroom and that teachers can tap for thepurposes of developing curriculum and instructional practice. What is left out isthe process by which the students themselves engage in the types of transforma-tion processes . . . relative to how parents FoK evolve, expand, get discarded,or get recontextualized for a different set of family and societal conditions.. . . [This] produces a form of student agency that is still circumscribed by theextent to which adults (parents or educators) allow for students/children/youthto integrate the knowledge(s) for themselves and contribute that knowledgedirectly in ways that make sense to them as learners within the classroomsetting and beyond. (p. 108)

This more child-centered view of FoK has been echoed by Hedges (2011), who arguesthat childrens popular culture is a site of agency in which they transform the knowledgeof home and school into a new cultural currency. The critical perspective that impelledthe original FoK work includes a redistribution of authority in learning that makes teach-ers, families, and children agents in learning. Something as simple as a donut game canbe an example of this kind of cultural currency. This dynamic view of practice is essen-tially improvisational and stands in contrast to the increasingly scripted curriculum usedwith young children today (Parks & Bridges-Rhoad, 2012). This conceptualization of FoKallowed us to see how more possibilities for improvisational teaching were created whenteachers saw children and families as coconstructors of knowledge in the classroom.

We see potential in the notion of culturally and developmentally responsive practicesin early mathematics, but now understand that its potential is circumscribed by the abilityto bring together the elements synergistically so that new forms of power and experiencecan find their way into the early childhood classroom. Improvisation is a way of conceptu-alizing teachers practices that creates room for thinking about how to connect pedagogicalcontent knowledge, teachers knowledge of child development, and families knowledgeand skills in teacherchild interactions. Improvisational interactions orient teachers towardsmaking children active agents in the classroom. As teachers learn about childrens funds ofknowledge curricular decisions are made together.

How does this paper connect to the practice of teacher education? The first connectionis that the key elements of our professional development, FoK, early mathematics, andhigh quality early childhood practices are intertwined in ways that illustrate the notion ofsynergy. Synergy is created when the combination of elements produces effects that aregreater than the sum of the components. While all three teachers are talented professionals,the degree to which they enacted the ideas presented in the professional development wasrelated to the ways that belief, experience, and knowledge served as a fertile context fortheir development. This means that a curriculum for teacher preparation or developmentneeds to be contingently constructedwith conscious attention to the ways that elementsinteract and with knowledge of participants background and beliefs.5

5An analysis of how we took up the teachers funds of knowledge is the subject of another paper.

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This project highlights the complexities of early childhood teaching. Through theprofessional development, we asked the teachers to weave together substantive contentknowledge and FoK from diverse families, and then activate this knowledge throughresponsive practices in play-based curriculum. If we want teachers to enact play-basedcurriculum, we need to integrate play as a medium for learning and development into allmethods courses, rather than relegating it to early childhood methods courses. If profes-sionals are to traverse the tremendous gap between home and school and base their practiceon their students funds of knowledge, it is more likely to be embraced if it is presentacross coursework and field study. And the notion of mathematics teaching can be linkedto both home and school contexts with a more elastic view of teaching through play. Thisresponsive model of teaching includes interplay between building on childrens interestsand providing experiences that are explicitly designed to create particular kinds of learn-ing. This requires early childhood teacher educators conversant across multiple domains ofknowledge.

Future research can explore the diverse forms that improvisation can take with particu-lar attention to its contingent nature. We need to understand more about how improvisationserves to enhance responsive teaching and its characteristics in different domains of knowl-edge and with diverse children. Particularly important for teacher education are models forimprovisation, illustrating how it can be taught to and taken up by early childhood teachersfrom different perspectives. It will be challenging in the current accountability context withincreasing standardization to help teachers embrace improvisation but given our knowledgeof the importance of instructional support to learning, it is a tool worth developing.

There will be variation in how teachers enact new approaches to curriculum(McLaughlin, 1987). By exploring how teachers applied culturally and developmentallyresponsive teaching to their work with children and families, we have begun to see howthe idea of improvisation is a part of enacting this type of curriculum in 4K. We admitthat improvisational teaching is rigorousasking teachers to deeply know their childrensfamilies, have a great deal of knowledge about pedagogical content and childrens devel-opment, and then bring all of these understandings together into interactions during play isno easy task. However, early childhood classrooms are dynamic, complex spaces and theircurricula should reflect this complexity. Improvisational teaching is a worthy undertakingbecause it speaks to the type of responsiveness that is at the heart of high-quality teaching.

Acknowledgements

We are grateful to Anne Karabon for her insights about Funds of Knowledge and to theteachers who shared their practice with us.

Funding

The writing of this article was supported in part by a grant from the National ScienceFoundation (1019431). The opinions expressed in this paper do not necessarily reflect theposition, policy, or endorsement of the National Science Foundation.

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Appendix

Brief Selection of the Questions Researchers Asked Teachers During the Beginning andEnd of the Year Interviews

Tell me about yourself. How would you describe your philosophy of teaching young children? What kinds of messages have you gotten about the goals of the 4K program from thedistrict?

What have you learned from families that you have successfully incorporated intoyour practice?

What kinds of barriers have you seen or experienced in working with families? Are there different ways that you find out what kids know about mathematics? When you started the program last year, what were you imagining it would be about?What were you hoping to get out of it?

How would you describe your role in the group?What roles did others play?

How do you think the courses might have influenced your teaching?

Brief Selection of the Questions Teachers (Participants) Created and Asked FamiliesDuring Home Visits

Tell me about what kinds of things you do for work. Describe a typical weekday night. What do you do on the weekends? What places do you go in your community as a family? Who are the people who care for your child? How does your child help out around the house? What kinds of hobbies or activities does your family enjoy doing? What was school like for you growing up? What do you remember about math from your childhood? How do you see math as a part of your adult life? (Ask about artifacts in the home). Who is in the pictures? Where was the picturetaken?

Brief Selection of Course Readings

Amanti, C. (2005). Beyond a beads and feathers approach. In N. Gonzlez, L. C. Moll & C.Amanti (Eds.), Funds of knowledge: Theorizing practices in households, communities,and classrooms (pp. 13141). Mahwah, NJ: Erlbaum.

Copley, J. V., Jones, C., Dighe, J., Bickart, T. S., & Heroman, C. (2007). Mathematics: TheCreative Curriculum approach. Washington, DC: Teaching Strategies.

Eisenhauer, M. J., & Feikes, D. (2009). Dolls, blocks, and puzzles: Playing with mathemat-ical understandings. Young Children, 64(3), 1824.

Ginsberg, M. B. (2007). Lessons at the kitchen table. Educational Leadership,64(6), 5661.

Graue, M. E., & Oen, D. (2008). You just feed them with a long-handled spoon: Familiesevaluate their experiences in a class size reduction reform. Educational Policy, 23(5),685713.

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Griffiths, R. (2007). Young children counting at home. Mathematics TeachingIncorporating Micromath, 203(July), 2426.

Leong, D. J., & Bodrova, E. (2012). Assessing and scaffolding: Make-believe play. YoungChildren, 67(1), 2834.

Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching:Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31,132141.

Moomaw, S. (2011). Integrating curricula to mathematics goals: Putting it all together.In Teaching mathematics in early childhood (pp. 163190). Baltimore, MD: Paul H.Brooks.

Pound, M. L. (2008). Thinking and learning about mathematics in the early years.New York, NY: Routledge.

Tenery, M. F. (2005). La visita. In N. Gonzlez, L. C. Moll & C. Amanti (Eds.),Funds of knowledge: Theorizing practices in households, communities, and classrooms(pp. 119130). Mahwah NJ: Lawrence Erlbaum.

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AbstractLiterature ReviewFunds of KnowledgeMathematics and Young ChildrenResponsivity Through Improvisation

MethodsThe 4KPD Professional Development ProjectThe ParticipantsThe Professional Development CoursesData Collection and Analysis

FindingsWanda: Assessing Where Children Should BeEmma: Observing Where Children AreChela: Imagining What Children Could Be

Discussion and ImplicationsAcknowledgementsFundingReferencesAppendixBrief Selection of the Questions Researchers Asked Teachers During the Beginning and End of the Year InterviewsBrief Selection of the Questions Teachers (Participants) Created and Asked Families During Home VisitsBrief Selection of Course Readings

Documents

Fostering Culturally and Developmentally Responsive Teaching Through Improvisational Practice