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Play-Based Mathematics Activities as a Resource for Changing Educator Attitudes and Practice:

Play-Based Mathematics Activities as a Resource for Changing Educator Attitudes and Practice: This multiple case study explored early childhood educators’ implementation of a suite of play-based mathematics activities with children aged 3 to 5 years in six different early childhood education and care programs in Melbourne, Australia. Educators approached the enactment of the activities differently; however, those educators who used the activities reasonably frequently and with attention to the underpinning mathematical concepts reported an increase in their self-confidence in supporting children’s mathematical thinking. For these educators, increasing self-confidence, in conjunction with children’s enthusiasm, led to increased frequency and further gains in self-confidence. Some educators did not implement the activities and no change in attitude was observed. New ways to support early childhood mathematics teaching practice, as a means to challenge entrenched attitudes and beliefs, are needed. Keywords early childhood, mathematics, teacher attitudes, teacher beliefs, curriculum, maths talk, play-based mathematics When children regularly spend many hours in the company resistant to change, and manifest in their pedagogical prac- of an early childhood educator, the early childhood educator tice. Changing beliefs and attitudes requires an individual to is a proximal and highly influential element of the child’s make personal, cognitive adjustments to incorporate new evolving social and cultural ecology (Bronfenbrenner, 1979). ideas. This is particularly difficult in the teaching environ- Early childhood educators’ attitudes are pervasively impor- ment if the changes do not align with the individual’s per- tant: positive, enthusiastic attitudes to problem solving are sonal beliefs and goals for children’s learning (Curby et al., likely to engender enthusiasm and positivity in children’s 2009). The resistance may be a personal response to negative approaches to learning, but the corollary holds true as well— memories rather than denial that supporting children’s math- negative attitudes and avoidance of concepts are likely to ematical thinking is in children’s interests (Ginsburg, Lee, & lead to negativity and avoidance in children (Bellock, Boyd, 2008). This is important, because studies have found a Gunderson, Ramirez, & Levine, 2010; Connor & Neal, 2014; connection between educators’ attitudes to mathematics and McCray & Chen, 2011; Stipek, Givvin, Salmon, & the attitudes of their students to mathematics (Bellock et al., MacGyver, 2001). In the context of early childhood educa- 2010; Connor & Neal, 2014; Kalder & Lesik, 2011). tion, this influence occurs very early in a child’s learning tra- Changes in recent years in early childhood education in jectory and thus potentially affects children’s perception of Australia have resulted in educators being mandated to imple- their own abilities as they continue into formal school-based ment a recognized early years learning framework (Australian education (Lake & Kelly, 2014; Tschannen-Moran & Children’s Education and Care Quality Authority [ACECQA], Woolfolk Hoy, 2001) and onwards. 2011). This requires educators to support children’s mathe- Much of an educator’s attitude toward teaching mathe- matical thinking and their acquisition of mathematical lan- matics derives from memories and experiences relating to guage. A significant association has been found between the their own mathematics learning, and is likely to influence frequency and duration of play-based mathematics activities their teaching practice in some way (Brown, 2005). Describing the “framing” function of cognitive schemas, The University of Melbourne, Victoria, Australia Bruner (1990) states that the prominent aspect of a memory Corresponding Author: is often the attitude attached to that memory. Educators’ Caroline Cohrssen, Melbourne Graduate School of Education, The beliefs have been defined as “tacit, often unconsciously held University of Melbourne, 4/100 Leicester Street, Melbourne, Victoria assumptions about students, classrooms, and the academic 3010, Australia. material to be taught” (Kagan, 1992, p. 65), which are stable, Email: ccoh@unimelb.edu.au Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 SAGE Open enacted within early childhood programs and children’s Table 1. CLASS Scores (Emotional Support and Instructional Support) Wave 1 E4Kids Study (2010; N = 258). learning outcomes (Cohrssen, Tayler, & Cloney, 2015). However, new ideas are inevitably filtered through existing M SD Median Minimum Maximum Range knowledge structures (Curby et al., 2009; Kagan, 1992) and Instructional 2.06 0.77 1.92 1 4.7 3.7 conceptual change is difficult. Consequently, some aspects of Support educators’ practice remain unaltered (Spillane & Zeuli, 1999; Emotional 5.14 0.91 5.2 2.44 6.94 4.5 Stigler & Herbert, 1998). Variability of early childhood prac- Support titioners’ knowledge, attitudes, and professional practices leads to inconsistency in fidelity of implementation (Zvoch, 2009), a situation which is further confounded by variables Participants specific to individual settings (Durlak, 2010; Zvoch, 2009) such as individual educators’ own mathematics knowledge. This implementation study was positioned within a broader Nonetheless, whereas educators’ attitudes, beliefs, and confi- longitudinal study, the E4Kids study (Tayler, Ishimine, dence in their mathematics abilities affect the extent to which Cleveland, Cloney, & Thorpe, 2013). Potential participants they intentionally teach mathematical ideas (Lee & Ginsburg, were selected according to room-level Instructional Support 2009), educators’ confidence is a variable that can be scores recorded for educators employed at early childhood addressed by targeted professional learning (Chen, McCray, education and care (ECEC) centers in the state of Victoria Adams, & Leow, 2014), and changes to teachers’ practices, during the first round of E4Kids’ data collection. For the pur- when observed to contribute to changes in children’s learning pose of this sample, the room that received the lowest outcomes, have been associated with changes in teachers’ Instructional Support score using the Classroom Assessment beliefs (Guskey, 2002a, 2002b). Scoring System pre-K to K (Pianta, La Paro, & Hamre, 2008) Educators need to have a clear vision of how curriculum was the start of the “low” category and the median score was materials are intended to help children learn and faith that the start of the “mid range” category. Although all room-level the curriculum materials provided will equip them to sup- readings of Instructional Support were relatively low, for the port students achieving the intended learning objectives; mid range category, the first author contacted one center further, curriculum materials need to support teachers’ immediately above the median score, followed by one center learning along with children’s learning (Drake & Sherin, below, repeating this pattern to remain as close to the median 2009). Increased educator self-confidence is likely to be score as possible. The room with the maximum Instructional associated with more frequent mathematics talk in early Support score was the start of the “high” category. Minimum childhood settings. This is important because learning and maximum scores are presented in Table 1. mathematical language is an important tool for exploring Many of the 128 educators involved in the E4Kids study mathematical ideas and the amount of educators’ maths talk in Victoria during the first round of data collection were has been found to be significantly related to growth in chil- excluded. Grounds for exclusion included, for example, the dren’s mathematics knowledge (Klibanoff, Levine, consented educator having resigned or retired, the majority Huttenlocher, Vasilyeva, & Hedges, 2006). One of the aims of the children in the room being aged below 3 years, educa- of this study—and the focus of this article—was to observe tors were employed at family day care centers or sessional the effect of providing teaching materials in the form of a kindergartens, and in one instance, a potential conflict of suite of play-based mathematics activities with clear learn- interest was identified as the lead educator worked with the ing objectives, step-by-step explanations for the activities, first author in a different capacity. and a description of the mathematical thinking that under- After approaching remaining potential participants by pins each activity, on early childhood (EC) educators’ atti- telephone, the first author met with center coordinators and tudes toward mathematics in early childhood. We educators to describe the study and the implications of par- anticipated that supporting educators’ pedagogical prac- ticipating in the study in more detail. Participation consent tices may contribute to an increase in their self-confidence was then sought at center level and from educators. and a more positive attitude toward intentionally support- Five participants were female and one was male. ing mathematical thinking during play-based activities. Educators’ qualifications ranged from a 2-year diploma in early childhood services to a master’s degree in early child- hood education (see Table 2). All participants held full-time Method appointments. The first educator in Room 4 unexpectedly Changes in children’s learning outcomes, observed to be took long leave mid-way through the study; however, the associated with the frequency and duration of the play-based assistant educator in the room stepped up immediately to the activities presented by the educators in this study, have lead role and undertook to continue with the study. None of already been reported (Cohrssen et al., 2015). The aim of this the participants had attended any post-qualification EC article is to explore the mechanisms at work that contributed mathematics professional learning sessions. A remark made to the change in teachers’ attitudes. by the lead educator in Room 5 illuminates this point: Cohrssen et al. 3 Table 2. Educators’ Early Childhood Teaching Qualifications; Activities explicitly encouraged educators to talk about Age Ranges of Children in These Classes. the activity and to encourage children’s problem solving, experimentation, and investigation, for example, Age range of children Teaching in the class qualification Talk about how the patterns are different and how they are the Room 1 3-5 years Bachelor of early same educator childhood education and Room 2 3-5 years Bachelor of arts educator + 1-year post When children are about to place their card on the washing line, graduate diploma in ask questions such as “Is it before or after this number?” and early childhood “Which two numbers should it go between?” Room 3 3-5 years Bachelor of early educator childhood With the exception of a teddy bear, as one activity required a education familiar toy to be used in an activity focusing on language of Room 4, 3-5 years Bachelor of arts Educator 1 + master’s in location, educators were provided with all necessary equip- early childhood ment (from numeral cards to clothes pegs), an instruction education manual that described the delivery of each activity, including Room 4, 3-5 years Bachelor of early learning objectives and the mathematical concepts underpin- Educator 2 childhood ning each activity, and an abbreviated card each educator education could keep beside them as a prompt when presenting an Room 5 3-5 years Diploma of children’s activity. Educators were at liberty to implement the activities educator services. studying in the order that best suited the broader room curriculum. toward a bachelor Although not “free play” activities, the activities were of early childhood education planned, “playful explorations” (Yelland, 2001, p. 6), enacted Room 6 3-4 years Diploma of children’s initially as educator guided, small group learning experi- educator services ences. For example, one counting activity required each child to roll a die, identify the number rolled by subitizing or counting the dots, and count a corresponding number of col- . . . there’s not a lot of professional development for early ored counters from a pile in the center of the table. Players childhood workers in maths, like you know, at the conference then compared how many counters they had “won” and that we went to in June there was none, but there’s sessions talked about who had “more than,” “less than,” and “the about literacy, there’s sessions about incorporating indigenous same as,” articulating their reasoning. Some educators spoke culture, there’s sessions about social emotional development, of playing games with the children and then making the but there’s no sessions about maths or science . . . there’s a lot of games available to children to use independently. Further stuff I suppose that they do in early years in primary schools that examples of the activities are provided in the appendix. would relate to us as well. Play-Based Mathematics Activities Data The play-based mathematics activities included in the study Self-reported data were obtained from two sources— were drawn primarily from the American Navigations Series implementation logs and semi-structured interviews. Semi- (Cavanagh et al., 2004; Findell et al., 2001; Greenes, structured interviews with participants at three points over a Cavanagh, Dacey, Findell, & Small, 2001; Sheffield et al., 7-month period were audio-recorded, transcribed, and ana- 2002) as no early childhood mathematics curriculum had lyzed thematically to explore participants’ reported imple- been formally validated with young children in Australia. mentation approach and to gain insight into the participants’ Additional activities that provided play-based number word attitudes at the start and at the end of the study toward play- and counting activities more appropriate to an Australian fully yet intentionally teaching mathematical concepts in early childhood context were adapted from an additional their programs. early years mathematics text (Wright, Stanger, Stafford, & First-round interview questions were the same for each Martland, 2006). Activities related to number and opera- educator. Second-round interviews explored issues raised by tions; data collection, organization, and display; and geome- different educators or observed mid-way through the study. try and algebra. Mathematical concepts underpinning the Third-round interviews were very similar in content as issues activity were described in each case, and clear learning raised by most participants were in fact similar. objectives facilitated formative assessment of children’s At the start of the study, participants undertook to use one understanding. activity each day with a small group of children. Because it 4 SAGE Open was not possible for the first author to monitor patterns of There was a change in staff in Room 4. The second educator in implementation directly on a week-by-week basis to observe Room 4 set up activities in the room after recalling that they nuances of implementation (Baker, Kupersmidt, Voegler- were in the storeroom; however, the selection of activities Lee, Arnold, & Willoughby, 2010), the second source of data appears to have been unsystematic. The educator in Room 5 was implementation logs. Educators were asked to complete rarely implemented the activities and similarly kept them in the log after the implementation of an activity noting the the storeroom. Finally, the implementation strategy employed date, how many children participated in the activity, how by the educator in Room 6 cannot be established, as this long the activity was sustained, and what changes were teacher did not complete implementation logs. made, if any, to the delivery of the activity. The implementa- Our attention now turns to the educators in Rooms 2 and tion logs provided an indication of frequency, duration, and 3, and the first educator in Room 4. These educators took a fidelity of implementation of the suite of learning activities. systematic approach to implementing the activities. In Room 2, activities were used as an add-on to the program throughout the study, however in response to children’s Results and Discussion demands—and the educator’s recognition that the activities Table 3 provides a summary of the educators’ engage- afforded opportunities for social and emotional learning— ment with the activities and an indication of reported the activities were used with increasing frequency. The edu- self-confidence at various points throughout the project. cator reported that she came to see that learning priorities in Notable is the relationship between the consistency and fre- the broader program were supported by the play-based quency of implementation—that is, engaging small groups mathematics activities. Consequently, not only were they of children in the activities—and educator attitude toward or used more frequently, but the educator also deliberately perception of the merit of the play-based opportunities for revisited some of the activities that had been presented ear- mathematical thinking. Specifically, those educators who lier in the year: used the activities reasonably frequently, intentionally focus- . . . not everyone’s had the opportunity to do every game . . . ing on the underpinning mathematical concepts as set out in because some are here five days, some are here one day, some the description of each activity, reported an increase in their are two days . . . maybe sometimes it’s to give someone else an self-confidence in supporting children’s mathematical think- opportunity to do that. Or maybe . . . I thought, “oh no, I do ing. For these educators, increasing self-confidence com- understand that a bit better now” or what the outcome (should bined with the enthusiasm with which children took part in have been). (Room 2, Round 3 interview) the activities, led to changes in their practice. Activities were implemented more frequently and children’s learning was The educator in Room 3 described uncertainty about how to observed. Supported by growing familiarity with the activi- go about teaching mathematical ideas in her program and ties, implementation frequency increased and further gains in consequently enacted the activities with a high degree of educators’ self-confidence were reported. Educators’ reports fidelity; she followed instructions provided for each activity of self-efficacy are also included in the summary, and the closely. Children’s enthusiastic participation in the activities, implications are considered in the discussion to follow. coupled with the educator’s growing confidence and famil- iarity with the suite of activities resulted in more frequent, flexible, and open-ended use of the materials. Implementation of Activities The first educator in Room 4 incorporated the activities in Wide implementation variability, in enactment and fre- the program plan from the start of the study, selecting activi- quency, was observed among participants in this study ties that aligned with children’s interests: despite their initial undertakings to present at least one activ- ity each day to a small group of children. First, we discuss If the children are really . . . interested in Snakes and Ladders low implementation cases. The discussion will then address and using the dice, so that would be something that comes out, reports from teachers who implemented the play-based and then . . . you can explain to children how you use the dice in activities with greater frequency and consistency. that situation and how you use it when you’re playing Snakes After 4 weeks, the educator in Room 1 withdrew from the and Ladders . . . (Room 4, Educator 1, exit interview) study. In this program, the activities (designed to be small group activities) were presented to groups as large as 17, One activity was set up each week on a designated table in resulting in children spending a lot of time waiting for a turn. the room. Although each activity involved small groups of The educator selected activities based on perceived ease of children, the educator usually waited for children to initiate delivery, rather than their “fit” to children’s observed skills the play at this table and most activities were then teacher and understanding. Taking both characteristics of delivery into directed in their delivery. account, it is not surprising that children’s engagement was Having provided a broad brush stroke description of how sub-optimal and may have contributed to the teacher’s report educators approached the incorporation of the suite of activi- that the children did not “respect the equipment” (see Table 3). ties in their curricula, the next section narrows our focus to Cohrssen et al. 5 Table 3. Educators’ Attitudes and Practices in Implementing Play-Based Mathematics Activities Reported During Semi-Structured Interviews. Reported attitude at start of Reported attitude Implementation study at end of study approach Room 1 Positive. “It will help them go Negative. Withdrew from study after Unsystematic selection of activities educator to school.” four weeks based on those that appeared most “ . . . for these children it’s probably straightforward to implement rather not appropriate, as these children than based on assessment of children’s have no respect for equipment”. existing knowledge and skills. Using the resources complicated the Group sizes too large; led to many transition from centralized franchise- children waiting to participate. level planning to room-level planning. Room 2 Uncertain. Social and Positive. Reported unanticipated Systematic use of activities; selection educator emotional development benefits: activities provided strategy altered from teacher-comfort to were priorities in preparing opportunities for children to perceived interests and learning needs of children for transition to lead activities, turn-taking, peer children. Educator’s responsiveness to school. Reservations about conversations. Unambiguous learning children’s enthusiasm led to increasingly adding to an already full objectives facilitated authentic frequent delivery of activities (a program. assessment that in turn supported morning game and an afternoon game). individualized scaffolding and planning Appropriate group size supported for learning. Supported evidence- children’s engagement. based conversations with families about their children’s learning. Valued being provided with “the right language” to use. Room 3 Apprehensive but willing to Positive. Surprised by extent to Systematic, to-the-letter enactment of educator participate. Time benefits of which children’s understanding/ activities at the start; assessed against receiving a package suite of skill exceeded or did not yet meet learning objectives. activities (high proportion assumptions prior to using clear Children’s enthusiasm positively reinforced of children from non-English learning objectives to observe and educator’s early efforts. speaking backgrounds and assess. Fidelity remained high; frequency increased much time spent liaising Valued being provided with “the right due to children’s demand and educator’s with families); anxious about language” to use. growing confidence. teaching mathematical ideas Growing confidence. “This is not As confidence grew, first modeled and described her personal something that I’m going to stop now intended purpose of the resources then experience of mathematics just simply because we’ve done the made resources available for children as highly teacher directed, study.” to use independently, joining in from remembering extreme time to time to ensure purposeful anxiety, and self-doubt. engagement. Room 4 Positive but contradictory. Educator 1 exit interview Systematically incorporated in the program Educator Resistant to structured Positive but contradictory. Surprised plan and set up at a designated table each 1 implementation of activities; by children’s mastery of mathematical day. Selected according to children’s described benefits of using concepts, but maintained that observed interests. learning objectives when using activities with the purpose of (During first author’s visit, activities observing and assessing assessing children’s understanding presented as small group activities, children’s understanding, but of a mathematics idea was “too goal but highly teacher-directed despite resistant to using observations directed.” purportedly rejecting this approach.) to plan contingent learning experiences. Room 4 (No interview at start of Positive, but contradictory. Resistant Unsystematic: (a) Activities forgotten Educator study.) to scaffolding and extending remained in the storeroom for several 2 understanding: “we just sat back weeks; (b) “ . . . probably just read and observed some of it . . . I think the main section” of the instructions it was just for us to see . . . how and consequently “we didn’t really well they could do (the activities) understand the concept.” independently.” Teacher support contingent upon Observed to deliver activities on highly children’s observed interest. teacher-directed one-to-one basis. (During first author’s visit, question-and- answer style discourse observed during one-to-one interactions.) (continued) 6 SAGE Open Table 3. (continued) Reported attitude at start of Reported attitude Implementation study at end of study approach Room 5 Positive. “I feel really good Positive. Literacy activities privileged Seldom implemented. educator about it . . . it will give us over mathematics activities: “—a Activities available to children at their . . . a greater understanding child can sit down and do a puzzle request as program follows children’s of some of the language and by themselves . . . Like obviously interests. However children did not some of the concepts that there’s no teacher interaction at that request activities. we can use.” experience while they’re doing the Rarely used unless first author attended puzzle and obviously all that extra the center. language is not happening, but the (In response to first author asking child can sit there and do the puzzle where activities were stored, educator by themselves; they can’t as such acknowledged that they were stored in sit there and read a book . . . I’m the office where children could not see more likely to go and sit with the them.) child who’s looking at the book by themselves than to sit with the child who’s doing the puzzle.” Room 6 Positive. Spoke about Positive. “ . . . it’s a lot less scary Verbal report of frequent implementation educator high level of personal because I’m more . . . and because with high fidelity. mathematics anxiety and I think I’m comfortable with it the Used activities to “assess unofficially.” memories of highly teacher- children are more comfortable with (No implementation logs were filled directed teaching and a sense it.” out. In addition, implementation during of inadequacy: “ . . . when Further remarks reflect a contradiction first author’s visits observed to deviate I was at school . . . I’d have between using the play-based markedly from activity instructions.) this massive, ‘Oh my God, activities purposefully to support we’re doing maths.’ So I learning and using the activities to don’t want the children to be keep children occupied. scared of maths.” the use of specific learning objectives for each game to assess . . . they’ve really enjoyed them . . . you know, it’s been challenging for them, and they’ve enjoyed having the play- children’s learning through play. based maths . . . yeah, they’ve enjoyed having the activities. Cause when I pull out a game, I say, “I want to play a game,” they’re very eager to do that. Like, a lot of the board-type games, Formative Assessment of Children’s Learning and then they will . . . I say, “Well, we’re not gonna fight over this pink card” or something, and they have to agree, yes we Educators in Rooms 2 and 3 reflected on the contribution of won’t, because we really want to play the game. (Room 2, the suite of learning experiences to their observation and Round 2 interview) assessment of children’s learning, as well as to curriculum planning. Explicit learning objectives focused the educator’s observa- The educator in Room 2 commented on unanticipated tions and were used to assess whether children had mastered opportunities for turn-taking, peer conversations and for underpinning mathematical concepts and were ready to children to lead activities. explore extension activities, or whether further rehearsal or a drop-back activity would be appropriate. Conversations with . . . I suppose my opinion has changed a little bit, that I didn’t families were informed by the educator’s assessment of the realise, I hadn’t thought how much they might enjoy it and how much they’re still doing all those things I’m wanting them to do, extent to which children achieved learning objectives embed- you know, like the sharing and . . . [interruption] . . . when ded in activities, supporting meaningful conversations with they’re interested in something, often they will put a little bit families about their children’s learning. more effort into that socio-emotional stuff, yeah I will wait for my turn, yeah I will let them have their turn, do you know what Yeah, some have found it easy; others of the same age and same I mean? Cause I want to have my turn. So yeah, I have found skill in counting and making patterns still found that difficult . . . that that’s a real positive. (Room 2, Round 2 interview) they do sort of patterns in music and we do, like, beading. They’ve done a lot of patterns and stuff like that, so I thought In addition, the children’s response to the activities was they had an understanding of patterns, but then sometimes with remarked upon several times during the course of the study: the clowns like sitting there in front of them, it’s almost like . . . Cohrssen et al. 7 they didn’t realise they know how to do it, you know. They No, I didn’t personally, but I think . . . Actually I think (the thought this is more complicated or something. (Room 2, Round assistant) did. Another educator in the room, I think she saw an 2 interview) activity that was happening and some concepts that were being used, I think it was the geometry patterns one. (Teacher 2, Room 4, Round 3 interview) The educator in Room 3 spoke of increasing self-confi- dence and excitement at her growing ability to observe, The second lead teacher commented further: assess, and support children’s learning by using the learn- ing objectives for each activity to assess children’s under- . . . we thought (some of the activities) would be a bit too standing. Encouraged to persevere by the children’s positive difficult in that it would be more one-on-one, like teacher and response to the games, this educator described having pre- child, or we didn’t really understand what the concept . . . or like viously over- or underestimated different children’s how to implement it, or we just didn’t get time because we used competency. the same . . . sometimes we use the same activities later on in each week . . . we feel that in our room it’s just . . . like we’d love I’ve got one child who has been in care [child care] since she to do one on one things but it’s just too busy in our room to be was a baby five days a week, and very proactive at home, very able to sit down and do that with other children . . . (Room 4, proactive here. Whenever we do any of these activities, she Round 3 interview) knows straight away. I watched her the other day. She goes, “You’ve added an extra two there.” She was explaining it to one In summary, the educators in Rooms 2 and 3, and the first of the other children, because they couldn’t quite figure it out. educator in Room 4 remarked that many children’s demon- She goes, “Well, you’ve added an extra two, so that makes six.” strated skills and understanding either exceeded or, con- And I’m just looking at her . . . And then we did the patterning, versely, did not yet meet the educators’ expectations, when and straight away, after, I said, “You can come up with your own assessed against the learning objectives provided for each pattern and picture,” she was the first one to sit there, put all the pieces together, figured out her pattern, drew it up, and said, “It activity. It is well established in research and in practice that reminds me of a mouse” and then continued pattern making. children’s mathematical understanding varies substantially (Room 3, Round 1 interview) and much may be attributed to environmental stimuli (see, for example, Gould, 2012; Klibanoff et al., 2006). But also the children are the ones who are driving it, because Recognizing this variability points to the critical importance they have particular games in there that they love, so they won’t of authentic and accurate assessment to differentiate learning let me do the other ones. (Room 3, Round 2 interview) opportunities for children. At the start of the study, the first educator in Room 4 described intentionally using learning objectives to assess Reported Changes in Attitude children’s mathematical understanding as a new approach: We now consider how enacting the activities impacted on educators’ attitudes toward intentionally teaching mathemat- Writing down all that—how they went and what happened and ics in early childhood. Two participants (Rooms 1 and 2) all that—and observing all that is more what we normally do. raised concerns about incorporating another element in their (Teacher 1, Room 4, Round 1 interview) programs. The educator in Room 1 withdrew from the study. This issue was pursued at the second (exit) interview with The educator in Room 2 recognized that incorporating the first lead educator. It appears that the learning objec- the activities into the program provided opportunities to tives contributed to formative assessment of children’s extend children’s mathematics learning and social and knowledge and using learning objectives to support written emotional learning. Her attitude underwent a significant observations demonstrates a shift in this educator’s teach- change and the activities were enacted more frequently. ing practice: Rather than needing to unlearn existing understanding to learn new ideas (Snider, 2004; Spillane, 2000), which At times, yeah, at times I did feel, oh I didn’t know he could do this, and that kind of helped plan further in the sense how would have required a significant change in cognitive could it be more challenging for that child . . . So would you schema, this educator quickly recognized benefits of imple- write up observations based on what you’d seen from these menting the activities and was open to a more intentional, maths activities? Some of them, yes . . . because we have them evidence-based approach: in daily reflections . . . (Teacher 1, Room 4, Round 2, exit interview) I think I have definitely been more mindful of the mathematics in the children’s play because . . . I know that they understand so The second lead educator in Room 4 reported not having much more about it, about numbers now, so we have been able used the activities as an opportunity to assess children’s to extend a little bit like when we’re playing, you know, in learning: different . . . (Room 2, Round 3 interview) 8 SAGE Open It made me more focused and broadened (my) understanding of it’s a lifelong journey. And I think well if I take this activity, different aspects of maths that can be taught to preschoolers, where can I take it? Can I take it to something else, or can I keep that’s my short answer. (Room 2, Round 3 interview) using it over and over again because it’s a useful tool as well for assessing where children are also, and helping them with numeracy. I’d like to keep going and see when I’ve got that extra The educators in Rooms 2 and 3 expressed concerns at the time that I can make to work on it, what will the difference be for start of the study about using “the right language.” me as a teacher as well? And then for the children, what will Mathematics language-related uncertainty inhibited their happen? (Room 3, Round 3 interview) self-confidence and consequently their willingness to engage children in such activities. Using the activities directly The educators in Rooms 4 and 5 waited for children to initi- addressed these concerns, as examples of questions and rel- ate interactions around the activity or request an activity— evant language to model were provided with each activity. although the activities were not always accessible to the Reading the provided step-by-step explanations of each children as they were stored in a different room. Their atti- activity was reported to equip the educators with sufficient tudes remained unchanged throughout the duration of the knowledge to feel more confident and consequently, to study, reflecting their persistent pedagogical beliefs about model the language in conversations with children. This con- the role of the early childhood educator. Although all three tributed to an upward spiral of increasing self-confidence educators in these rooms stated a belief in the importance of and more frequent enactment of the activities and the educa- supporting children’s emerging mathematics skills, none tors’ practice changed. believed this to include purposeful formative assessment to Echoing Bruner’s (1990) statement that it is frequently plan systematically to support and extend children’s devel- the attitude attached to a memory that persists, the educator oping mathematical thinking. Somewhat ironically, both in Room 3 reflected on her own mathematics education: educators in Room 4 were observed to engage in highly teacher-directed, question-and-answer interaction patterns, . . . it was about right and wrong, and if you were wrong, there thus creating or perpetuating the pressure for children “to get was a consequence for getting it wrong at school with maths, I it right,” an approach that both educators reported intending found. Or they made it very competitive, you know, who could to avoid. Research has demonstrated that educators filter get it quicker could get this, could have this prize, or whatever it was, so that already would put anxiety there about getting it new ideas through existing knowledge (Curby et al., 2009; right, and then . . . I don’t know what everyone else’s experience Kagan, 1992) and when exposed to new ideas, are inclined to is, for me it would be about I just shut down so I wouldn’t think focus on superficial similarities to familiar knowledge and at all. (Room 3, Round 2 interview) unlearning may be required to gain new knowledge (Snider, 2004; Spillane, 2000). However, this process of unlearning is This educator’s personal experience of mathematics differed not always successful and practice may not change (Spillane substantially from the play-based approach in which enact- & Zeuli, 1999; Stigler & Herbert, 1998). In both cases, by ment of the activities demanded, and required, personal choosing to join in with children’s play only when requested, memories and deep-seated, learned attitudes toward mathe- rather than guiding children’s use of the play-based activities matics to be set aside (Bruner, 1990) to learn new ideas in a purposeful manner, these educators limited their oppor- (Snider, 2004; Spillane, 2000). The speed with which the tunities to observe the gains in children’s learning that when educator’s attitude turned around was remarkable. By the coupled with a change in teaching practice, contribute to end of the study, the conversation was more light-hearted changes in teachers’ beliefs and attitudes (Guskey, 2002a, (evidenced by her laughter). Rather than focusing on a per- 2002b). ceived skills deficit, the educator spoke of improving her The educator in Room 6 did not provide implementation own skills to influence children’s regard for mathematics logs, but reported in interviews that using the activities positively: prompted her awareness that she did not lack the necessary skills and understanding to deliver the resources. This aware- Yes, I think I don’t know enough (about mathematics). (Laughs.) ness proved empowering, and her anxiety at the start of the And also because I don’t have that confidence in mathematics as study was reportedly replaced by an increasing sense of well and I think that’s something I need to work on because I’m self-confidence. trying to give something to the next generation, to give them the groundwork and the interest in maths, not just literacy . . . (Room 3, Round 3 interview) Conclusion Early childhood educators have reported a need for increased A marked change in attitude was apparent at the end of the professional learning in early childhood mathematics study: (Barber, Cohrssen, & Church, 2014). We know that educa- tors’ mathematics content knowledge predicts children’s For me, I think it is because this is not something that I’m going learning and engagement in mathematical thinking (Hill, to stop now just simply because we’ve done the study. So to me, Cohrssen et al. 9 Rowan, & Loewenberg Ball, 2005; Shulman, 1986). Increasingly positive attitudes to the activities and greater Furthermore, educators’ attitudes, beliefs, and confidence self-confidence led to more frequent use of the activities, and impact on how mathematics teaching is (or is not) purpose- thus more systematic implementation. Importantly, an fully incorporated in early childhood programs (Lee & increase in educators’ self-confidence in teaching mathemat- Ginsburg, 2009). Chen and colleagues (2014) have found ics is likely to lead to educators modeling positive attitudes that educators’ confidence can be addressed by targeted pro- about mathematics to children, encouraging children to feel fessional learning. In this study, we observed the impact of positive about mathematics (Kalder & Lesik, 2011). implementing play-based mathematics activities with small Children’s positive responses to educators initiating these groups of children on some early childhood educators’ confi- activities encouraged educators to persevere, and thus, the dence, beliefs, and attitudes toward purposefully teaching cycle of teaching and learning continued. mathematics in early childhood. Familiarity with the learning objectives of activities and When educators persevered with play-based activities increased self-confidence enable educators to approach the that clearly set out the intended mathematics learning and activities in a more purposeful manner, facilitating the provided examples of questions for teachers to ask to suit learning in play-based learning, reflecting an imperative in children’s emerging understanding, their confidence effective early childhood education (ACECQA, 2011; increased. It appeared that this was a collaborative and itera- Cohrssen, Church, Ishimine, & Tayler, 2013; Department tive process: reviewing the objectives of each activity famil- of Education Employment and Workplace Relations, iarized the educators with the underpinning mathematical 2009). Specific learning objectives also provided educa- ideas and supported their ability to recognize when children tors with competencies against which to assess children’s achieved the learning objectives. As their confidence grew, developing understanding in an objective manner. This in and spurred on by children’s enthusiastic response and turn facilitated accurate, evidence-based teaching. In short, observed learning gains, activities were enacted more fre- by providing a range of play-based activities that were rel- quently. When the suite of activities was enacted with rea- evant and interesting to the children, along with accompa- sonable fidelity and frequency, children’s made gains in nying instructions, prompts, and suggestions for extending learning (Cohrssen et al., 2015). activities, educators were better equipped to enact child- Professional learning and change in teacher practice, centered practice. when observed to contribute to change in children’s learn- The over-arching goal of early childhood education is ing outcomes, contributes to change in teacher attitudes and to provide optimal learning opportunities for children. beliefs (Guskey, 2002a, 2002b). Educators who imple- Implementation of a suite of play-based early childhood mented the activities systematically reported a change in mathematics activities provided early childhood educa- attitude and beliefs, as the activities-as-resource (a) demon- tors with the resources needed to support and extend pre- strated opportunities for supporting social and emotional school children’s mathematical thinking and mathematical learning, (b) provided educators with the explicit language language. Implicit in this process is ongoing formative to both enact the activities and to share the aims of this assessment of children’s learning. This not only enables play-based learning with children’s families, (c) equipped educators to tailor learning experiences to support chil- educators with strategies to facilitate children’s learning by dren’s demonstrated interests and skills but also provides providing greater specificity in learning objectives, which educators with regular feedback on the efficacy of their subsequently (d) supported gains in children’s learning efforts, increasing the likelihood that they will persevere (Cohrssen et al., 2015), and (e) facilitated formative assess- with the new practices and contributing to a change in ment of and for learning. teacher beliefs regarding early childhood mathematics Although the suite of activities was not designed as a pro- (Guskey, 2002a, 2002b). fessional development resource per se, providing educators Our findings show that the provision and enactment of with information about specific mathematical concepts as a purposefully designed suite of play-based mathematics well as step-by-step instructions for the implementation of activities may enable educators to develop increasing con- the games, in effect supported the educators’ professional fidence in the intentional teaching of mathematics in early learning. Those educators who implemented the activities learning environments. This is encouraging evidence of changed their teaching practice. When the learning objec- the potential impact of an evidence-based, play-based, val- tives were used to support formative assessment of children’s idated early childhood mathematics curriculum. Finding knowledge, educators observed the efficacy of their practice. ways to challenge educators’ beliefs and to encourage new This positive outcome, coupled with children’s observed ways of thinking about mathematics teaching and learning enthusiasm in taking part in the activities encouraged educa- are crucial if educators are to meet the demands of early tors to change their beliefs and to offer further activities from childhood education and the future learning needs of the provided suite of activities. children. 10 SAGE Open Appendix Excerpt From Instruction Manual Cohrssen et al. 11 Appendix (continued) 12 SAGE Open Appendix (continued) Authors’ Note Funding The author(s) disclosed receipt of the following financial support for E4Kids was led by Professor Collette Tayler at the Melbourne the research and/or authorship of this article: This research was Graduate School of Education, The University of Melbourne, in funded by an Australian Postgraduate Award Industry Scholarship partnership with Queensland University of Technology. as part of E4Kids, a longitudinal study investigating the effective- ness of early learning experiences in early childhood settings in Acknowledgments Australia. E4Kids was funded by the Australian Research Council The authors sincerely thank the ECEC services, directors, teachers/ Linkage Projects Scheme (LP0990200), the Victorian Government staff, children, and their families for their ongoing participation in Department of Education and Early Childhood Development, and this study. the Queensland Government Department of Education and Training. Declaration of Conflicting Interests Notes The author(s) declared no potential conflicts of interest with respect 1. “Family day care—comprises services providing small group to the research, authorship, and/or publication of this article. care for children in the home environment of a registered carer. Cohrssen et al. 13 Care is primarily aimed at children aged 0-5 years, but pri- Curby, T. W., LoCasale-Crouch, J., Konold, T. R., Pianta, R., mary school children may also receive care before and after Howes, C., Burchinal, M., . . . Barbarin, O. (2009). The rela- school, and during school holidays. Educators work in part- tions of observed pre-K classroom quality profiles to children’s nership with scheme management and coordination unit staff” achievement and social competence. Early Education and (Steering Committee for the Review of Government Service Development, 20, 346-372. Provision, 2012). Department of Education Employment and Workplace Relations. 2. Although attendance patterns vary, children attending stand- (2009). Belonging, Being and Becoming: The Early Years alone sessional kindergarten (“Kinder”) programs typically Learning Framework for Australia (EYLF). Canberra: Council attend for several hours per day, 2 or 3 days per week. of Australian Governments. 3. Colored cards are included with the resources for the “What’s Drake, C., & Sherin, M. G. (2009). Developing curriculum vision your favorite color?” activity. and trust: Changes in teachers’ curriculum strategies. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work (pp. 321-337). New York, NY: References Routledge. Australian Children’s Education and Care Quality Authority. Durlak, J. (2010). The importance of doing well in whatever you (2011). Guide to the National Quality Standard. Retrieved from do: A commentary on the special section, “Implementation http://files.acecqa.gov.au/files/National-Quality-Framework- research in early childhood education. Early Childhood Resources-Kit/NQF03-Guide-to-NQS-130902.pdf Research Quarterly, 25, 348-357. Baker, C. N., Kupersmidt, J. B., Voegler-Lee, M. E., Arnold, D. H., Findell, C. R., Small, M., Cavanagh, M., Dacey, L., Greenes, C., & Willoughby, M. T. (2010). Predicting teacher participation & Sheffield, L. J. (2001). Navigating through geometry in in a classroom-based, integrated preventive intervention for Prekindergarten–Grade 2. Reston, VA: National Council of preschoolers. 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Navigating through algebra in prekindergarten–Grade Proceedings of the National Academy of Sciences (PNAS), 107, 2. Reston, VA: National Council of Teachers of Mathematics. 1860-1863. Guskey, T. R. (2002a). Does it make a difference? Evaluating pro- Bronfenbrenner, U. (1979). The ecology of human development. fessional development. Educational Leadership, 59(6), 45-51. Cambridge, MA: Harvard University Press. Guskey, T. R. (2002b). Professional development and teacher Brown, E. T. (2005). The influence of teachers’ efficacy and beliefs change. Teachers and Teaching: Theory and Practice, 8, 381- regarding mathematics instruction in the early childhood 391. doi:10.1080/135406002100000512 classroom. Journal of Early Childhood Teacher Education, Hill, H. C., Rowan, B., & Loewenberg Ball, D. (2005). Effects 26, 239-257. of teachers’ mathematical knowledge for teaching on student Bruner, J. (1990). Acts of meaning. Cambridge, MA: Harvard achievement. American Educational Research Journal, 42, University Press. 371-406. Cavanagh, M., Dacey, L., Findell, C. R., Greenes, C., Sheffield, L. Kagan, D. (1992). Implications of research on teacher belief. J., & Small, M. (2004). Navigating through number and opera- Educational Psychologist, 27, 65-90. tions in prekindergarten—Grade 2. Reston, VA: National Kalder, R. S., & Lesik, S. A. (2011, December). A classification of Council of Teachers of Mathematics. attitudes and beliefs towards mathematics for secondary math- Chen, J., McCray, J., Adams, A., & Leow, C. (2014). A survey ematics pre-service teachers and elementary pre-service teach- study of early childhood teachers’ beliefs and confidence about ers: An exploratory study using latent class analysis. Issues teaching early math. Early Childhood Education Journal, 42, in the Undergraduate Mathematics Preparation of School 367-377. doi:10.1007/s10643-013-0619-0 Teachers (IUMPST): The Journal, 5 (Teacher Attributes). Cohrssen, C., Church, A., Ishimine, K., & Tayler, C. (2013). Klibanoff, R., Levine, S., Huttenlocher, J., Vasilyeva, M., & Hedges, Playing with maths: Facilitating the learning in play-based L. (2006). Preschool children’s mathematical knowledge: The learning. Australasian Journal of Early Childhood, 38, 95-99. effect of teacher “math talk”. Developmental Psychology, 42, Cohrssen, C., Tayler, C., & Cloney, D. (2015). Playing with maths: 59-69. Implications for early childhood mathematics teaching from Lake, V. E., & Kelly, L. (2014). Female preservice teachers and an implementation study in Melbourne, Australia. Education mathematics: Anxiety, beliefs, and stereotypes. Journal of 3-13: International Journal of Primary, Elementary and Early Early Childhood Teacher Education, 35, 262-275. doi:10.1080/ Years Education, 43, 641-652. doi:10.1080/03004279.2013.8 10901027.2014.936071 Lee, J. S., & Ginsburg, H. P. (2009). Early childhood teachers’ mis- Connor, J., & Neal, D. (2014). Maths and numeracy (Vol. 12). conceptions about mathematics education for young children Canberra: Early Childhood Australia. 14 SAGE Open in the United States. Australasian Journal of Early Childhood, Tschannen-Moran, M., & Woolfolk Hoy, A. (2001). Teacher effi- 34(4), 37-45. cacy: Capturing an elusive construct. Teaching and Teacher Lobel, A. (1970). Frog and toad are friends. New York, NY: Education, 17, 783-805. Harper & Row. Wright, R. J., Stanger, G., Stafford, A., & Martland, J. (2006). McCray, J., & Chen, J. (2011). Foundational mathematics: A Teaching number in the classroom with 4-8 year-olds. London, neglected opportunity. In B. Atweh, M. Graven, W. Secada, & England: SAGE. P. Valero (Eds.), Mapping equity and quality in mathematics Yelland, N. (2001). Reconceptualising play and learning in the lives education (pp. 253-268). New York, NY: Springer. of young children. Australasian Journal of Early Childhood, Pianta, R., La Paro, K., & Hamre, B. K. (2008). Classroom assess- 36(2), 4-12. ment scoring system (CLASS) manual, pre-K. Baltimore, MD: Zvoch, K. (2009). Treatment fidelity in multisite evaluation: A mul- Paul H. Brookes. tilevel longitudinal examination of provider adherence status Sheffield, L. J., Cavanagh, M., Dacey, L., Findell, C. R., Greenes, and change. American Journal of Evaluation, 30, 44-51. C., & Small, M. (2002). Navigating through data analysis and probability in prekindergarten—Grade 2. Reston, VA: Author Biographies National Council of Teachers of Mathematics. Caroline Cohrssen is a senior lecturer in the Melbourne Graduate Shulman, L. S. (1986). Those who understand: Knowledge growth School of Education at The University of Melbourne. Her research in teaching. Educational Researcher, 15(2), 4-14. investigates children’s diverse demonstrations of mathematical think- Snider, V. E. (2004). A comparison of spiral versus strand curricu- ing and how this informs effective early childhood pedagogical strate- lum. Journal of Direct Instruction, 4, 29-39. gies during the years prior to school. Her current research explores Spillane, J. P. (2000). Cognition and policy implementation: opportunities to support children’s spatial thinking in the context of District policymakers and the reform of mathematics educa- playful preschool curricula. Besides teaching pre-service teacher can- tion. Cognition and Instruction, 18, 141-179. didates, her work is also directed towards supporting the ongoing post- Spillane, J. P., & Zeuli, J. S. (1999). Reform and teaching: Exploring qualification professional learning of early childhood practitioners. patterns of practice in the context of national and state math- ematics reforms. Educational Evaluation and Policy Analysis, Amelia Church is a lecturer in the Melbourne Graduate School of 21, 1-27. Education at The University of Melbourne, where she teaches Steering Committee for the Review of Government Service courses in reesarch methods in early childhood education, applied Provision. (2012). Report on Government Services 2012. conversation analysis and qualitative research methods. Her current Canberra, Australia: Productivity Commission. research involves children’s talk, classroom interactions, and how Stigler, J. W., & Herbert, J. (1998, Winter). Teaching is a cultural misunderstanding is resolved in talk-in-interaction. activity. American Educator, 1-10. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyver, V. Collette Tayler holds the Chair in Early Childhood Education and L. (2001). Teachers’ beliefs and practices related to math- Care in the Melbourne Graduate School of Education at The ematics instruction. Teaching and Teacher Education, 17, University of Melbourne and co-authored the OECD Report 213-226. “Starting Strong II”, an international analysis of ECEC policy and Tayler, C., Ishimine, K., Cleveland, G., Cloney, D., & Thorpe, K. provision. Her work addresses program access and engagement; (2013). The quality of early childhood education and care ser- program standards and quality, the curriculum and pedagogy vices in Australia. Australasian Journal of Early Childhood, applied in different services, leadership and staff development, 38(2), 13-21. child and family involvement, and program outcomes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SAGE Open SAGE

Play-Based Mathematics Activities as a Resource for Changing Educator Attitudes and Practice:

SAGE Open , Volume 6 (2): 1 – May 31, 2016

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Abstract

This multiple case study explored early childhood educators’ implementation of a suite of play-based mathematics activities with children aged 3 to 5 years in six different early childhood education and care programs in Melbourne, Australia. Educators approached the enactment of the activities differently; however, those educators who used the activities reasonably frequently and with attention to the underpinning mathematical concepts reported an increase in their self-confidence in supporting children’s mathematical thinking. For these educators, increasing self-confidence, in conjunction with children’s enthusiasm, led to increased frequency and further gains in self-confidence. Some educators did not implement the activities and no change in attitude was observed. New ways to support early childhood mathematics teaching practice, as a means to challenge entrenched attitudes and beliefs, are needed. Keywords early childhood, mathematics, teacher attitudes, teacher beliefs, curriculum, maths talk, play-based mathematics When children regularly spend many hours in the company resistant to change, and manifest in their pedagogical prac- of an early childhood educator, the early childhood educator tice. Changing beliefs and attitudes requires an individual to is a proximal and highly influential element of the child’s make personal, cognitive adjustments to incorporate new evolving social and cultural ecology (Bronfenbrenner, 1979). ideas. This is particularly difficult in the teaching environ- Early childhood educators’ attitudes are pervasively impor- ment if the changes do not align with the individual’s per- tant: positive, enthusiastic attitudes to problem solving are sonal beliefs and goals for children’s learning (Curby et al., likely to engender enthusiasm and positivity in children’s 2009). The resistance may be a personal response to negative approaches to learning, but the corollary holds true as well— memories rather than denial that supporting children’s math- negative attitudes and avoidance of concepts are likely to ematical thinking is in children’s interests (Ginsburg, Lee, & lead to negativity and avoidance in children (Bellock, Boyd, 2008). This is important, because studies have found a Gunderson, Ramirez, & Levine, 2010; Connor & Neal, 2014; connection between educators’ attitudes to mathematics and McCray & Chen, 2011; Stipek, Givvin, Salmon, & the attitudes of their students to mathematics (Bellock et al., MacGyver, 2001). In the context of early childhood educa- 2010; Connor & Neal, 2014; Kalder & Lesik, 2011). tion, this influence occurs very early in a child’s learning tra- Changes in recent years in early childhood education in jectory and thus potentially affects children’s perception of Australia have resulted in educators being mandated to imple- their own abilities as they continue into formal school-based ment a recognized early years learning framework (Australian education (Lake & Kelly, 2014; Tschannen-Moran & Children’s Education and Care Quality Authority [ACECQA], Woolfolk Hoy, 2001) and onwards. 2011). This requires educators to support children’s mathe- Much of an educator’s attitude toward teaching mathe- matical thinking and their acquisition of mathematical lan- matics derives from memories and experiences relating to guage. A significant association has been found between the their own mathematics learning, and is likely to influence frequency and duration of play-based mathematics activities their teaching practice in some way (Brown, 2005). Describing the “framing” function of cognitive schemas, The University of Melbourne, Victoria, Australia Bruner (1990) states that the prominent aspect of a memory Corresponding Author: is often the attitude attached to that memory. Educators’ Caroline Cohrssen, Melbourne Graduate School of Education, The beliefs have been defined as “tacit, often unconsciously held University of Melbourne, 4/100 Leicester Street, Melbourne, Victoria assumptions about students, classrooms, and the academic 3010, Australia. material to be taught” (Kagan, 1992, p. 65), which are stable, Email: ccoh@unimelb.edu.au Creative Commons CC-BY: This article is distributed under the terms of the Creative Commons Attribution 3.0 License (http://www.creativecommons.org/licenses/by/3.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/open-access-at-sage). 2 SAGE Open enacted within early childhood programs and children’s Table 1. CLASS Scores (Emotional Support and Instructional Support) Wave 1 E4Kids Study (2010; N = 258). learning outcomes (Cohrssen, Tayler, & Cloney, 2015). However, new ideas are inevitably filtered through existing M SD Median Minimum Maximum Range knowledge structures (Curby et al., 2009; Kagan, 1992) and Instructional 2.06 0.77 1.92 1 4.7 3.7 conceptual change is difficult. Consequently, some aspects of Support educators’ practice remain unaltered (Spillane & Zeuli, 1999; Emotional 5.14 0.91 5.2 2.44 6.94 4.5 Stigler & Herbert, 1998). Variability of early childhood prac- Support titioners’ knowledge, attitudes, and professional practices leads to inconsistency in fidelity of implementation (Zvoch, 2009), a situation which is further confounded by variables Participants specific to individual settings (Durlak, 2010; Zvoch, 2009) such as individual educators’ own mathematics knowledge. This implementation study was positioned within a broader Nonetheless, whereas educators’ attitudes, beliefs, and confi- longitudinal study, the E4Kids study (Tayler, Ishimine, dence in their mathematics abilities affect the extent to which Cleveland, Cloney, & Thorpe, 2013). Potential participants they intentionally teach mathematical ideas (Lee & Ginsburg, were selected according to room-level Instructional Support 2009), educators’ confidence is a variable that can be scores recorded for educators employed at early childhood addressed by targeted professional learning (Chen, McCray, education and care (ECEC) centers in the state of Victoria Adams, & Leow, 2014), and changes to teachers’ practices, during the first round of E4Kids’ data collection. For the pur- when observed to contribute to changes in children’s learning pose of this sample, the room that received the lowest outcomes, have been associated with changes in teachers’ Instructional Support score using the Classroom Assessment beliefs (Guskey, 2002a, 2002b). Scoring System pre-K to K (Pianta, La Paro, & Hamre, 2008) Educators need to have a clear vision of how curriculum was the start of the “low” category and the median score was materials are intended to help children learn and faith that the start of the “mid range” category. Although all room-level the curriculum materials provided will equip them to sup- readings of Instructional Support were relatively low, for the port students achieving the intended learning objectives; mid range category, the first author contacted one center further, curriculum materials need to support teachers’ immediately above the median score, followed by one center learning along with children’s learning (Drake & Sherin, below, repeating this pattern to remain as close to the median 2009). Increased educator self-confidence is likely to be score as possible. The room with the maximum Instructional associated with more frequent mathematics talk in early Support score was the start of the “high” category. Minimum childhood settings. This is important because learning and maximum scores are presented in Table 1. mathematical language is an important tool for exploring Many of the 128 educators involved in the E4Kids study mathematical ideas and the amount of educators’ maths talk in Victoria during the first round of data collection were has been found to be significantly related to growth in chil- excluded. Grounds for exclusion included, for example, the dren’s mathematics knowledge (Klibanoff, Levine, consented educator having resigned or retired, the majority Huttenlocher, Vasilyeva, & Hedges, 2006). One of the aims of the children in the room being aged below 3 years, educa- of this study—and the focus of this article—was to observe tors were employed at family day care centers or sessional the effect of providing teaching materials in the form of a kindergartens, and in one instance, a potential conflict of suite of play-based mathematics activities with clear learn- interest was identified as the lead educator worked with the ing objectives, step-by-step explanations for the activities, first author in a different capacity. and a description of the mathematical thinking that under- After approaching remaining potential participants by pins each activity, on early childhood (EC) educators’ atti- telephone, the first author met with center coordinators and tudes toward mathematics in early childhood. We educators to describe the study and the implications of par- anticipated that supporting educators’ pedagogical prac- ticipating in the study in more detail. Participation consent tices may contribute to an increase in their self-confidence was then sought at center level and from educators. and a more positive attitude toward intentionally support- Five participants were female and one was male. ing mathematical thinking during play-based activities. Educators’ qualifications ranged from a 2-year diploma in early childhood services to a master’s degree in early child- hood education (see Table 2). All participants held full-time Method appointments. The first educator in Room 4 unexpectedly Changes in children’s learning outcomes, observed to be took long leave mid-way through the study; however, the associated with the frequency and duration of the play-based assistant educator in the room stepped up immediately to the activities presented by the educators in this study, have lead role and undertook to continue with the study. None of already been reported (Cohrssen et al., 2015). The aim of this the participants had attended any post-qualification EC article is to explore the mechanisms at work that contributed mathematics professional learning sessions. A remark made to the change in teachers’ attitudes. by the lead educator in Room 5 illuminates this point: Cohrssen et al. 3 Table 2. Educators’ Early Childhood Teaching Qualifications; Activities explicitly encouraged educators to talk about Age Ranges of Children in These Classes. the activity and to encourage children’s problem solving, experimentation, and investigation, for example, Age range of children Teaching in the class qualification Talk about how the patterns are different and how they are the Room 1 3-5 years Bachelor of early same educator childhood education and Room 2 3-5 years Bachelor of arts educator + 1-year post When children are about to place their card on the washing line, graduate diploma in ask questions such as “Is it before or after this number?” and early childhood “Which two numbers should it go between?” Room 3 3-5 years Bachelor of early educator childhood With the exception of a teddy bear, as one activity required a education familiar toy to be used in an activity focusing on language of Room 4, 3-5 years Bachelor of arts Educator 1 + master’s in location, educators were provided with all necessary equip- early childhood ment (from numeral cards to clothes pegs), an instruction education manual that described the delivery of each activity, including Room 4, 3-5 years Bachelor of early learning objectives and the mathematical concepts underpin- Educator 2 childhood ning each activity, and an abbreviated card each educator education could keep beside them as a prompt when presenting an Room 5 3-5 years Diploma of children’s activity. Educators were at liberty to implement the activities educator services. studying in the order that best suited the broader room curriculum. toward a bachelor Although not “free play” activities, the activities were of early childhood education planned, “playful explorations” (Yelland, 2001, p. 6), enacted Room 6 3-4 years Diploma of children’s initially as educator guided, small group learning experi- educator services ences. For example, one counting activity required each child to roll a die, identify the number rolled by subitizing or counting the dots, and count a corresponding number of col- . . . there’s not a lot of professional development for early ored counters from a pile in the center of the table. Players childhood workers in maths, like you know, at the conference then compared how many counters they had “won” and that we went to in June there was none, but there’s sessions talked about who had “more than,” “less than,” and “the about literacy, there’s sessions about incorporating indigenous same as,” articulating their reasoning. Some educators spoke culture, there’s sessions about social emotional development, of playing games with the children and then making the but there’s no sessions about maths or science . . . there’s a lot of games available to children to use independently. Further stuff I suppose that they do in early years in primary schools that examples of the activities are provided in the appendix. would relate to us as well. Play-Based Mathematics Activities Data The play-based mathematics activities included in the study Self-reported data were obtained from two sources— were drawn primarily from the American Navigations Series implementation logs and semi-structured interviews. Semi- (Cavanagh et al., 2004; Findell et al., 2001; Greenes, structured interviews with participants at three points over a Cavanagh, Dacey, Findell, & Small, 2001; Sheffield et al., 7-month period were audio-recorded, transcribed, and ana- 2002) as no early childhood mathematics curriculum had lyzed thematically to explore participants’ reported imple- been formally validated with young children in Australia. mentation approach and to gain insight into the participants’ Additional activities that provided play-based number word attitudes at the start and at the end of the study toward play- and counting activities more appropriate to an Australian fully yet intentionally teaching mathematical concepts in early childhood context were adapted from an additional their programs. early years mathematics text (Wright, Stanger, Stafford, & First-round interview questions were the same for each Martland, 2006). Activities related to number and opera- educator. Second-round interviews explored issues raised by tions; data collection, organization, and display; and geome- different educators or observed mid-way through the study. try and algebra. Mathematical concepts underpinning the Third-round interviews were very similar in content as issues activity were described in each case, and clear learning raised by most participants were in fact similar. objectives facilitated formative assessment of children’s At the start of the study, participants undertook to use one understanding. activity each day with a small group of children. Because it 4 SAGE Open was not possible for the first author to monitor patterns of There was a change in staff in Room 4. The second educator in implementation directly on a week-by-week basis to observe Room 4 set up activities in the room after recalling that they nuances of implementation (Baker, Kupersmidt, Voegler- were in the storeroom; however, the selection of activities Lee, Arnold, & Willoughby, 2010), the second source of data appears to have been unsystematic. The educator in Room 5 was implementation logs. Educators were asked to complete rarely implemented the activities and similarly kept them in the log after the implementation of an activity noting the the storeroom. Finally, the implementation strategy employed date, how many children participated in the activity, how by the educator in Room 6 cannot be established, as this long the activity was sustained, and what changes were teacher did not complete implementation logs. made, if any, to the delivery of the activity. The implementa- Our attention now turns to the educators in Rooms 2 and tion logs provided an indication of frequency, duration, and 3, and the first educator in Room 4. These educators took a fidelity of implementation of the suite of learning activities. systematic approach to implementing the activities. In Room 2, activities were used as an add-on to the program throughout the study, however in response to children’s Results and Discussion demands—and the educator’s recognition that the activities Table 3 provides a summary of the educators’ engage- afforded opportunities for social and emotional learning— ment with the activities and an indication of reported the activities were used with increasing frequency. The edu- self-confidence at various points throughout the project. cator reported that she came to see that learning priorities in Notable is the relationship between the consistency and fre- the broader program were supported by the play-based quency of implementation—that is, engaging small groups mathematics activities. Consequently, not only were they of children in the activities—and educator attitude toward or used more frequently, but the educator also deliberately perception of the merit of the play-based opportunities for revisited some of the activities that had been presented ear- mathematical thinking. Specifically, those educators who lier in the year: used the activities reasonably frequently, intentionally focus- . . . not everyone’s had the opportunity to do every game . . . ing on the underpinning mathematical concepts as set out in because some are here five days, some are here one day, some the description of each activity, reported an increase in their are two days . . . maybe sometimes it’s to give someone else an self-confidence in supporting children’s mathematical think- opportunity to do that. Or maybe . . . I thought, “oh no, I do ing. For these educators, increasing self-confidence com- understand that a bit better now” or what the outcome (should bined with the enthusiasm with which children took part in have been). (Room 2, Round 3 interview) the activities, led to changes in their practice. Activities were implemented more frequently and children’s learning was The educator in Room 3 described uncertainty about how to observed. Supported by growing familiarity with the activi- go about teaching mathematical ideas in her program and ties, implementation frequency increased and further gains in consequently enacted the activities with a high degree of educators’ self-confidence were reported. Educators’ reports fidelity; she followed instructions provided for each activity of self-efficacy are also included in the summary, and the closely. Children’s enthusiastic participation in the activities, implications are considered in the discussion to follow. coupled with the educator’s growing confidence and famil- iarity with the suite of activities resulted in more frequent, flexible, and open-ended use of the materials. Implementation of Activities The first educator in Room 4 incorporated the activities in Wide implementation variability, in enactment and fre- the program plan from the start of the study, selecting activi- quency, was observed among participants in this study ties that aligned with children’s interests: despite their initial undertakings to present at least one activ- ity each day to a small group of children. First, we discuss If the children are really . . . interested in Snakes and Ladders low implementation cases. The discussion will then address and using the dice, so that would be something that comes out, reports from teachers who implemented the play-based and then . . . you can explain to children how you use the dice in activities with greater frequency and consistency. that situation and how you use it when you’re playing Snakes After 4 weeks, the educator in Room 1 withdrew from the and Ladders . . . (Room 4, Educator 1, exit interview) study. In this program, the activities (designed to be small group activities) were presented to groups as large as 17, One activity was set up each week on a designated table in resulting in children spending a lot of time waiting for a turn. the room. Although each activity involved small groups of The educator selected activities based on perceived ease of children, the educator usually waited for children to initiate delivery, rather than their “fit” to children’s observed skills the play at this table and most activities were then teacher and understanding. Taking both characteristics of delivery into directed in their delivery. account, it is not surprising that children’s engagement was Having provided a broad brush stroke description of how sub-optimal and may have contributed to the teacher’s report educators approached the incorporation of the suite of activi- that the children did not “respect the equipment” (see Table 3). ties in their curricula, the next section narrows our focus to Cohrssen et al. 5 Table 3. Educators’ Attitudes and Practices in Implementing Play-Based Mathematics Activities Reported During Semi-Structured Interviews. Reported attitude at start of Reported attitude Implementation study at end of study approach Room 1 Positive. “It will help them go Negative. Withdrew from study after Unsystematic selection of activities educator to school.” four weeks based on those that appeared most “ . . . for these children it’s probably straightforward to implement rather not appropriate, as these children than based on assessment of children’s have no respect for equipment”. existing knowledge and skills. Using the resources complicated the Group sizes too large; led to many transition from centralized franchise- children waiting to participate. level planning to room-level planning. Room 2 Uncertain. Social and Positive. Reported unanticipated Systematic use of activities; selection educator emotional development benefits: activities provided strategy altered from teacher-comfort to were priorities in preparing opportunities for children to perceived interests and learning needs of children for transition to lead activities, turn-taking, peer children. Educator’s responsiveness to school. Reservations about conversations. Unambiguous learning children’s enthusiasm led to increasingly adding to an already full objectives facilitated authentic frequent delivery of activities (a program. assessment that in turn supported morning game and an afternoon game). individualized scaffolding and planning Appropriate group size supported for learning. Supported evidence- children’s engagement. based conversations with families about their children’s learning. Valued being provided with “the right language” to use. Room 3 Apprehensive but willing to Positive. Surprised by extent to Systematic, to-the-letter enactment of educator participate. Time benefits of which children’s understanding/ activities at the start; assessed against receiving a package suite of skill exceeded or did not yet meet learning objectives. activities (high proportion assumptions prior to using clear Children’s enthusiasm positively reinforced of children from non-English learning objectives to observe and educator’s early efforts. speaking backgrounds and assess. Fidelity remained high; frequency increased much time spent liaising Valued being provided with “the right due to children’s demand and educator’s with families); anxious about language” to use. growing confidence. teaching mathematical ideas Growing confidence. “This is not As confidence grew, first modeled and described her personal something that I’m going to stop now intended purpose of the resources then experience of mathematics just simply because we’ve done the made resources available for children as highly teacher directed, study.” to use independently, joining in from remembering extreme time to time to ensure purposeful anxiety, and self-doubt. engagement. Room 4 Positive but contradictory. Educator 1 exit interview Systematically incorporated in the program Educator Resistant to structured Positive but contradictory. Surprised plan and set up at a designated table each 1 implementation of activities; by children’s mastery of mathematical day. Selected according to children’s described benefits of using concepts, but maintained that observed interests. learning objectives when using activities with the purpose of (During first author’s visit, activities observing and assessing assessing children’s understanding presented as small group activities, children’s understanding, but of a mathematics idea was “too goal but highly teacher-directed despite resistant to using observations directed.” purportedly rejecting this approach.) to plan contingent learning experiences. Room 4 (No interview at start of Positive, but contradictory. Resistant Unsystematic: (a) Activities forgotten Educator study.) to scaffolding and extending remained in the storeroom for several 2 understanding: “we just sat back weeks; (b) “ . . . probably just read and observed some of it . . . I think the main section” of the instructions it was just for us to see . . . how and consequently “we didn’t really well they could do (the activities) understand the concept.” independently.” Teacher support contingent upon Observed to deliver activities on highly children’s observed interest. teacher-directed one-to-one basis. (During first author’s visit, question-and- answer style discourse observed during one-to-one interactions.) (continued) 6 SAGE Open Table 3. (continued) Reported attitude at start of Reported attitude Implementation study at end of study approach Room 5 Positive. “I feel really good Positive. Literacy activities privileged Seldom implemented. educator about it . . . it will give us over mathematics activities: “—a Activities available to children at their . . . a greater understanding child can sit down and do a puzzle request as program follows children’s of some of the language and by themselves . . . Like obviously interests. However children did not some of the concepts that there’s no teacher interaction at that request activities. we can use.” experience while they’re doing the Rarely used unless first author attended puzzle and obviously all that extra the center. language is not happening, but the (In response to first author asking child can sit there and do the puzzle where activities were stored, educator by themselves; they can’t as such acknowledged that they were stored in sit there and read a book . . . I’m the office where children could not see more likely to go and sit with the them.) child who’s looking at the book by themselves than to sit with the child who’s doing the puzzle.” Room 6 Positive. Spoke about Positive. “ . . . it’s a lot less scary Verbal report of frequent implementation educator high level of personal because I’m more . . . and because with high fidelity. mathematics anxiety and I think I’m comfortable with it the Used activities to “assess unofficially.” memories of highly teacher- children are more comfortable with (No implementation logs were filled directed teaching and a sense it.” out. In addition, implementation during of inadequacy: “ . . . when Further remarks reflect a contradiction first author’s visits observed to deviate I was at school . . . I’d have between using the play-based markedly from activity instructions.) this massive, ‘Oh my God, activities purposefully to support we’re doing maths.’ So I learning and using the activities to don’t want the children to be keep children occupied. scared of maths.” the use of specific learning objectives for each game to assess . . . they’ve really enjoyed them . . . you know, it’s been challenging for them, and they’ve enjoyed having the play- children’s learning through play. based maths . . . yeah, they’ve enjoyed having the activities. Cause when I pull out a game, I say, “I want to play a game,” they’re very eager to do that. Like, a lot of the board-type games, Formative Assessment of Children’s Learning and then they will . . . I say, “Well, we’re not gonna fight over this pink card” or something, and they have to agree, yes we Educators in Rooms 2 and 3 reflected on the contribution of won’t, because we really want to play the game. (Room 2, the suite of learning experiences to their observation and Round 2 interview) assessment of children’s learning, as well as to curriculum planning. Explicit learning objectives focused the educator’s observa- The educator in Room 2 commented on unanticipated tions and were used to assess whether children had mastered opportunities for turn-taking, peer conversations and for underpinning mathematical concepts and were ready to children to lead activities. explore extension activities, or whether further rehearsal or a drop-back activity would be appropriate. Conversations with . . . I suppose my opinion has changed a little bit, that I didn’t families were informed by the educator’s assessment of the realise, I hadn’t thought how much they might enjoy it and how much they’re still doing all those things I’m wanting them to do, extent to which children achieved learning objectives embed- you know, like the sharing and . . . [interruption] . . . when ded in activities, supporting meaningful conversations with they’re interested in something, often they will put a little bit families about their children’s learning. more effort into that socio-emotional stuff, yeah I will wait for my turn, yeah I will let them have their turn, do you know what Yeah, some have found it easy; others of the same age and same I mean? Cause I want to have my turn. So yeah, I have found skill in counting and making patterns still found that difficult . . . that that’s a real positive. (Room 2, Round 2 interview) they do sort of patterns in music and we do, like, beading. They’ve done a lot of patterns and stuff like that, so I thought In addition, the children’s response to the activities was they had an understanding of patterns, but then sometimes with remarked upon several times during the course of the study: the clowns like sitting there in front of them, it’s almost like . . . Cohrssen et al. 7 they didn’t realise they know how to do it, you know. They No, I didn’t personally, but I think . . . Actually I think (the thought this is more complicated or something. (Room 2, Round assistant) did. Another educator in the room, I think she saw an 2 interview) activity that was happening and some concepts that were being used, I think it was the geometry patterns one. (Teacher 2, Room 4, Round 3 interview) The educator in Room 3 spoke of increasing self-confi- dence and excitement at her growing ability to observe, The second lead teacher commented further: assess, and support children’s learning by using the learn- ing objectives for each activity to assess children’s under- . . . we thought (some of the activities) would be a bit too standing. Encouraged to persevere by the children’s positive difficult in that it would be more one-on-one, like teacher and response to the games, this educator described having pre- child, or we didn’t really understand what the concept . . . or like viously over- or underestimated different children’s how to implement it, or we just didn’t get time because we used competency. the same . . . sometimes we use the same activities later on in each week . . . we feel that in our room it’s just . . . like we’d love I’ve got one child who has been in care [child care] since she to do one on one things but it’s just too busy in our room to be was a baby five days a week, and very proactive at home, very able to sit down and do that with other children . . . (Room 4, proactive here. Whenever we do any of these activities, she Round 3 interview) knows straight away. I watched her the other day. She goes, “You’ve added an extra two there.” She was explaining it to one In summary, the educators in Rooms 2 and 3, and the first of the other children, because they couldn’t quite figure it out. educator in Room 4 remarked that many children’s demon- She goes, “Well, you’ve added an extra two, so that makes six.” strated skills and understanding either exceeded or, con- And I’m just looking at her . . . And then we did the patterning, versely, did not yet meet the educators’ expectations, when and straight away, after, I said, “You can come up with your own assessed against the learning objectives provided for each pattern and picture,” she was the first one to sit there, put all the pieces together, figured out her pattern, drew it up, and said, “It activity. It is well established in research and in practice that reminds me of a mouse” and then continued pattern making. children’s mathematical understanding varies substantially (Room 3, Round 1 interview) and much may be attributed to environmental stimuli (see, for example, Gould, 2012; Klibanoff et al., 2006). But also the children are the ones who are driving it, because Recognizing this variability points to the critical importance they have particular games in there that they love, so they won’t of authentic and accurate assessment to differentiate learning let me do the other ones. (Room 3, Round 2 interview) opportunities for children. At the start of the study, the first educator in Room 4 described intentionally using learning objectives to assess Reported Changes in Attitude children’s mathematical understanding as a new approach: We now consider how enacting the activities impacted on educators’ attitudes toward intentionally teaching mathemat- Writing down all that—how they went and what happened and ics in early childhood. Two participants (Rooms 1 and 2) all that—and observing all that is more what we normally do. raised concerns about incorporating another element in their (Teacher 1, Room 4, Round 1 interview) programs. The educator in Room 1 withdrew from the study. This issue was pursued at the second (exit) interview with The educator in Room 2 recognized that incorporating the first lead educator. It appears that the learning objec- the activities into the program provided opportunities to tives contributed to formative assessment of children’s extend children’s mathematics learning and social and knowledge and using learning objectives to support written emotional learning. Her attitude underwent a significant observations demonstrates a shift in this educator’s teach- change and the activities were enacted more frequently. ing practice: Rather than needing to unlearn existing understanding to learn new ideas (Snider, 2004; Spillane, 2000), which At times, yeah, at times I did feel, oh I didn’t know he could do this, and that kind of helped plan further in the sense how would have required a significant change in cognitive could it be more challenging for that child . . . So would you schema, this educator quickly recognized benefits of imple- write up observations based on what you’d seen from these menting the activities and was open to a more intentional, maths activities? Some of them, yes . . . because we have them evidence-based approach: in daily reflections . . . (Teacher 1, Room 4, Round 2, exit interview) I think I have definitely been more mindful of the mathematics in the children’s play because . . . I know that they understand so The second lead educator in Room 4 reported not having much more about it, about numbers now, so we have been able used the activities as an opportunity to assess children’s to extend a little bit like when we’re playing, you know, in learning: different . . . (Room 2, Round 3 interview) 8 SAGE Open It made me more focused and broadened (my) understanding of it’s a lifelong journey. And I think well if I take this activity, different aspects of maths that can be taught to preschoolers, where can I take it? Can I take it to something else, or can I keep that’s my short answer. (Room 2, Round 3 interview) using it over and over again because it’s a useful tool as well for assessing where children are also, and helping them with numeracy. I’d like to keep going and see when I’ve got that extra The educators in Rooms 2 and 3 expressed concerns at the time that I can make to work on it, what will the difference be for start of the study about using “the right language.” me as a teacher as well? And then for the children, what will Mathematics language-related uncertainty inhibited their happen? (Room 3, Round 3 interview) self-confidence and consequently their willingness to engage children in such activities. Using the activities directly The educators in Rooms 4 and 5 waited for children to initi- addressed these concerns, as examples of questions and rel- ate interactions around the activity or request an activity— evant language to model were provided with each activity. although the activities were not always accessible to the Reading the provided step-by-step explanations of each children as they were stored in a different room. Their atti- activity was reported to equip the educators with sufficient tudes remained unchanged throughout the duration of the knowledge to feel more confident and consequently, to study, reflecting their persistent pedagogical beliefs about model the language in conversations with children. This con- the role of the early childhood educator. Although all three tributed to an upward spiral of increasing self-confidence educators in these rooms stated a belief in the importance of and more frequent enactment of the activities and the educa- supporting children’s emerging mathematics skills, none tors’ practice changed. believed this to include purposeful formative assessment to Echoing Bruner’s (1990) statement that it is frequently plan systematically to support and extend children’s devel- the attitude attached to a memory that persists, the educator oping mathematical thinking. Somewhat ironically, both in Room 3 reflected on her own mathematics education: educators in Room 4 were observed to engage in highly teacher-directed, question-and-answer interaction patterns, . . . it was about right and wrong, and if you were wrong, there thus creating or perpetuating the pressure for children “to get was a consequence for getting it wrong at school with maths, I it right,” an approach that both educators reported intending found. Or they made it very competitive, you know, who could to avoid. Research has demonstrated that educators filter get it quicker could get this, could have this prize, or whatever it was, so that already would put anxiety there about getting it new ideas through existing knowledge (Curby et al., 2009; right, and then . . . I don’t know what everyone else’s experience Kagan, 1992) and when exposed to new ideas, are inclined to is, for me it would be about I just shut down so I wouldn’t think focus on superficial similarities to familiar knowledge and at all. (Room 3, Round 2 interview) unlearning may be required to gain new knowledge (Snider, 2004; Spillane, 2000). However, this process of unlearning is This educator’s personal experience of mathematics differed not always successful and practice may not change (Spillane substantially from the play-based approach in which enact- & Zeuli, 1999; Stigler & Herbert, 1998). In both cases, by ment of the activities demanded, and required, personal choosing to join in with children’s play only when requested, memories and deep-seated, learned attitudes toward mathe- rather than guiding children’s use of the play-based activities matics to be set aside (Bruner, 1990) to learn new ideas in a purposeful manner, these educators limited their oppor- (Snider, 2004; Spillane, 2000). The speed with which the tunities to observe the gains in children’s learning that when educator’s attitude turned around was remarkable. By the coupled with a change in teaching practice, contribute to end of the study, the conversation was more light-hearted changes in teachers’ beliefs and attitudes (Guskey, 2002a, (evidenced by her laughter). Rather than focusing on a per- 2002b). ceived skills deficit, the educator spoke of improving her The educator in Room 6 did not provide implementation own skills to influence children’s regard for mathematics logs, but reported in interviews that using the activities positively: prompted her awareness that she did not lack the necessary skills and understanding to deliver the resources. This aware- Yes, I think I don’t know enough (about mathematics). (Laughs.) ness proved empowering, and her anxiety at the start of the And also because I don’t have that confidence in mathematics as study was reportedly replaced by an increasing sense of well and I think that’s something I need to work on because I’m self-confidence. trying to give something to the next generation, to give them the groundwork and the interest in maths, not just literacy . . . (Room 3, Round 3 interview) Conclusion Early childhood educators have reported a need for increased A marked change in attitude was apparent at the end of the professional learning in early childhood mathematics study: (Barber, Cohrssen, & Church, 2014). We know that educa- tors’ mathematics content knowledge predicts children’s For me, I think it is because this is not something that I’m going learning and engagement in mathematical thinking (Hill, to stop now just simply because we’ve done the study. So to me, Cohrssen et al. 9 Rowan, & Loewenberg Ball, 2005; Shulman, 1986). Increasingly positive attitudes to the activities and greater Furthermore, educators’ attitudes, beliefs, and confidence self-confidence led to more frequent use of the activities, and impact on how mathematics teaching is (or is not) purpose- thus more systematic implementation. Importantly, an fully incorporated in early childhood programs (Lee & increase in educators’ self-confidence in teaching mathemat- Ginsburg, 2009). Chen and colleagues (2014) have found ics is likely to lead to educators modeling positive attitudes that educators’ confidence can be addressed by targeted pro- about mathematics to children, encouraging children to feel fessional learning. In this study, we observed the impact of positive about mathematics (Kalder & Lesik, 2011). implementing play-based mathematics activities with small Children’s positive responses to educators initiating these groups of children on some early childhood educators’ confi- activities encouraged educators to persevere, and thus, the dence, beliefs, and attitudes toward purposefully teaching cycle of teaching and learning continued. mathematics in early childhood. Familiarity with the learning objectives of activities and When educators persevered with play-based activities increased self-confidence enable educators to approach the that clearly set out the intended mathematics learning and activities in a more purposeful manner, facilitating the provided examples of questions for teachers to ask to suit learning in play-based learning, reflecting an imperative in children’s emerging understanding, their confidence effective early childhood education (ACECQA, 2011; increased. It appeared that this was a collaborative and itera- Cohrssen, Church, Ishimine, & Tayler, 2013; Department tive process: reviewing the objectives of each activity famil- of Education Employment and Workplace Relations, iarized the educators with the underpinning mathematical 2009). Specific learning objectives also provided educa- ideas and supported their ability to recognize when children tors with competencies against which to assess children’s achieved the learning objectives. As their confidence grew, developing understanding in an objective manner. This in and spurred on by children’s enthusiastic response and turn facilitated accurate, evidence-based teaching. In short, observed learning gains, activities were enacted more fre- by providing a range of play-based activities that were rel- quently. When the suite of activities was enacted with rea- evant and interesting to the children, along with accompa- sonable fidelity and frequency, children’s made gains in nying instructions, prompts, and suggestions for extending learning (Cohrssen et al., 2015). activities, educators were better equipped to enact child- Professional learning and change in teacher practice, centered practice. when observed to contribute to change in children’s learn- The over-arching goal of early childhood education is ing outcomes, contributes to change in teacher attitudes and to provide optimal learning opportunities for children. beliefs (Guskey, 2002a, 2002b). Educators who imple- Implementation of a suite of play-based early childhood mented the activities systematically reported a change in mathematics activities provided early childhood educa- attitude and beliefs, as the activities-as-resource (a) demon- tors with the resources needed to support and extend pre- strated opportunities for supporting social and emotional school children’s mathematical thinking and mathematical learning, (b) provided educators with the explicit language language. Implicit in this process is ongoing formative to both enact the activities and to share the aims of this assessment of children’s learning. This not only enables play-based learning with children’s families, (c) equipped educators to tailor learning experiences to support chil- educators with strategies to facilitate children’s learning by dren’s demonstrated interests and skills but also provides providing greater specificity in learning objectives, which educators with regular feedback on the efficacy of their subsequently (d) supported gains in children’s learning efforts, increasing the likelihood that they will persevere (Cohrssen et al., 2015), and (e) facilitated formative assess- with the new practices and contributing to a change in ment of and for learning. teacher beliefs regarding early childhood mathematics Although the suite of activities was not designed as a pro- (Guskey, 2002a, 2002b). fessional development resource per se, providing educators Our findings show that the provision and enactment of with information about specific mathematical concepts as a purposefully designed suite of play-based mathematics well as step-by-step instructions for the implementation of activities may enable educators to develop increasing con- the games, in effect supported the educators’ professional fidence in the intentional teaching of mathematics in early learning. Those educators who implemented the activities learning environments. This is encouraging evidence of changed their teaching practice. When the learning objec- the potential impact of an evidence-based, play-based, val- tives were used to support formative assessment of children’s idated early childhood mathematics curriculum. Finding knowledge, educators observed the efficacy of their practice. ways to challenge educators’ beliefs and to encourage new This positive outcome, coupled with children’s observed ways of thinking about mathematics teaching and learning enthusiasm in taking part in the activities encouraged educa- are crucial if educators are to meet the demands of early tors to change their beliefs and to offer further activities from childhood education and the future learning needs of the provided suite of activities. children. 10 SAGE Open Appendix Excerpt From Instruction Manual Cohrssen et al. 11 Appendix (continued) 12 SAGE Open Appendix (continued) Authors’ Note Funding The author(s) disclosed receipt of the following financial support for E4Kids was led by Professor Collette Tayler at the Melbourne the research and/or authorship of this article: This research was Graduate School of Education, The University of Melbourne, in funded by an Australian Postgraduate Award Industry Scholarship partnership with Queensland University of Technology. as part of E4Kids, a longitudinal study investigating the effective- ness of early learning experiences in early childhood settings in Acknowledgments Australia. E4Kids was funded by the Australian Research Council The authors sincerely thank the ECEC services, directors, teachers/ Linkage Projects Scheme (LP0990200), the Victorian Government staff, children, and their families for their ongoing participation in Department of Education and Early Childhood Development, and this study. the Queensland Government Department of Education and Training. Declaration of Conflicting Interests Notes The author(s) declared no potential conflicts of interest with respect 1. “Family day care—comprises services providing small group to the research, authorship, and/or publication of this article. care for children in the home environment of a registered carer. Cohrssen et al. 13 Care is primarily aimed at children aged 0-5 years, but pri- Curby, T. W., LoCasale-Crouch, J., Konold, T. R., Pianta, R., mary school children may also receive care before and after Howes, C., Burchinal, M., . . . Barbarin, O. (2009). The rela- school, and during school holidays. Educators work in part- tions of observed pre-K classroom quality profiles to children’s nership with scheme management and coordination unit staff” achievement and social competence. Early Education and (Steering Committee for the Review of Government Service Development, 20, 346-372. Provision, 2012). Department of Education Employment and Workplace Relations. 2. Although attendance patterns vary, children attending stand- (2009). Belonging, Being and Becoming: The Early Years alone sessional kindergarten (“Kinder”) programs typically Learning Framework for Australia (EYLF). Canberra: Council attend for several hours per day, 2 or 3 days per week. of Australian Governments. 3. Colored cards are included with the resources for the “What’s Drake, C., & Sherin, M. G. (2009). Developing curriculum vision your favorite color?” activity. and trust: Changes in teachers’ curriculum strategies. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. 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Classroom assess- 36(2), 4-12. ment scoring system (CLASS) manual, pre-K. Baltimore, MD: Zvoch, K. (2009). Treatment fidelity in multisite evaluation: A mul- Paul H. Brookes. tilevel longitudinal examination of provider adherence status Sheffield, L. J., Cavanagh, M., Dacey, L., Findell, C. R., Greenes, and change. American Journal of Evaluation, 30, 44-51. C., & Small, M. (2002). Navigating through data analysis and probability in prekindergarten—Grade 2. Reston, VA: Author Biographies National Council of Teachers of Mathematics. Caroline Cohrssen is a senior lecturer in the Melbourne Graduate Shulman, L. S. (1986). Those who understand: Knowledge growth School of Education at The University of Melbourne. Her research in teaching. Educational Researcher, 15(2), 4-14. investigates children’s diverse demonstrations of mathematical think- Snider, V. E. (2004). A comparison of spiral versus strand curricu- ing and how this informs effective early childhood pedagogical strate- lum. Journal of Direct Instruction, 4, 29-39. gies during the years prior to school. Her current research explores Spillane, J. P. (2000). Cognition and policy implementation: opportunities to support children’s spatial thinking in the context of District policymakers and the reform of mathematics educa- playful preschool curricula. Besides teaching pre-service teacher can- tion. Cognition and Instruction, 18, 141-179. didates, her work is also directed towards supporting the ongoing post- Spillane, J. P., & Zeuli, J. S. (1999). Reform and teaching: Exploring qualification professional learning of early childhood practitioners. patterns of practice in the context of national and state math- ematics reforms. Educational Evaluation and Policy Analysis, Amelia Church is a lecturer in the Melbourne Graduate School of 21, 1-27. Education at The University of Melbourne, where she teaches Steering Committee for the Review of Government Service courses in reesarch methods in early childhood education, applied Provision. (2012). Report on Government Services 2012. conversation analysis and qualitative research methods. Her current Canberra, Australia: Productivity Commission. research involves children’s talk, classroom interactions, and how Stigler, J. W., & Herbert, J. (1998, Winter). Teaching is a cultural misunderstanding is resolved in talk-in-interaction. activity. American Educator, 1-10. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyver, V. Collette Tayler holds the Chair in Early Childhood Education and L. (2001). Teachers’ beliefs and practices related to math- Care in the Melbourne Graduate School of Education at The ematics instruction. Teaching and Teacher Education, 17, University of Melbourne and co-authored the OECD Report 213-226. “Starting Strong II”, an international analysis of ECEC policy and Tayler, C., Ishimine, K., Cleveland, G., Cloney, D., & Thorpe, K. provision. Her work addresses program access and engagement; (2013). The quality of early childhood education and care ser- program standards and quality, the curriculum and pedagogy vices in Australia. Australasian Journal of Early Childhood, applied in different services, leadership and staff development, 38(2), 13-21. child and family involvement, and program outcomes.

Journal

SAGE OpenSAGE

Published: May 31, 2016

Keywords: early childhood; mathematics; teacher attitudes; teacher beliefs; curriculum; maths talk; play-based mathematics

References