Picture Books as an Impetus for Kindergartners' Mathematical Thinking

Abstract

Although there is evidence that the use of picture books affects young children's achievement scores in mathematics, little is known about the cognitive engagement and, in particular, the mathematical thinking that is evoked when young children are read a picture book. The focus of the case study reported in this article is on the cognitive engagement that is facilitated by the picture books themselves and not on how this engagement is prompted by a reader. The book under investigation, Vijfde zijn [Being Fifth], is a picture book of high literary quality that was not written for the purpose of teaching mathematics. The story is about a doctor's waiting room and touches on backwards counting and spatial orientation only tacitly as part of the narrative. Four 5 year olds were each read the book by one of the authors without any questioning or probing. The reading sessions took place in school, outside the classroom. A detailed coding framework was developed for analyzing the children's utterances that provided an in-depth picture of the children's spontaneous cognitive engagement. Surprisingly, almost half the utterances were mathematics-related. The findings of the study support the idea that reading children picture books without explicit instruction or prompting has large potential for mathematically engaging children.

Learning mathematics requires an environment that engages children in operating mathematically. Situations at home, in school, on the playground, and in shops, elicit, for example, counting and comparing magnitudes, exploring spatial relations, and recognizing patterns. This article addresses the way in which picture books may also provide children with such an environment. The case study described here was carried out in the Netherlands and is part of the Picture book Activated Learning of Mathematics (PALM) Project. ¹ The main goal of the project is to investigate whether and how picture books can elicit mathematics-related cognitive activity in kindergartners. To gather knowledge about this, children are observed and videotaped while being read a picture book.

In the present study, a picture storybook of high literary quality that is sold in bookstores and that is not written for the purpose of teaching mathematics was read to four 5-year-old children who were not yet able to read. The study focused on the nature of the cognitive activity that the story, text, and pictures elicited in the children in the absence of any prompting by the reader. Thus, the study was designed to investigate the power of the picture book itself. We developed a coding framework to understand and classify the abundant utterances produced in the four reading sessions. The results of this analysis were used to infer the children's cognitive activity elicited by the book.

PICTURE BOOKS AND THE LEARNING OF MATHEMATICS

Rationale for Using Picture Books to Support the Learning of Mathematics

Reading picture books to young children is considered of great significance for children's development—in particular, for learning language and literacy (Anderson, Anderson, & Shapiro, 2005). The majority of early studies on the use of picture books investigated their influence on this developmental aspect (Blok, 1999). However, in these studies, little attention was paid to mathematical development, which reflects a perception of mathematics as an intellectual abstract discipline that is outside the realm of a story (Griffiths & Clyne, 1991).

Since the early 1990s, the situation has changed. Linking mathematics instruction to children's literature has become increasingly popular (Haury, 2001). For example, it was recognized that children's literature can motivate students (Usnick & McCarthy, 1998), connect mathematics to emotions (Griffiths & Clyne, 1991), and provoke interest (Murphy, 2000).

Research has demonstrated that children's literature can provide children with a meaningful context for learning mathematics (Braddon, Hall, & Taylor, 1993; Lovitt & Clarke, 1992; Mooren, 2000; Murphy, 2000; Schiro, 1997; Welchman-Tischler, 1992). Complementary to this role, Griffiths and Clyne (1991) also mentioned the roles of children's literature to provide a model, illustrate a concept, pose a problem, and stimulate an investigation. An example of the latter is Harland's (1990) research which used Anno's story of the mysterious multiplying jar that contains water and becomes an ocean containing one island with two countries with three mountains each having four walled kingdoms and so on. In the end, there are over three-million jars in the first jar. The children in Harland's study used Anno's story to investigate patterns in increasing numbers.

Besides embodying particular mathematical concepts, picture books and stories also contribute to the development of children's mathematical attitude. They can demonstrate “the mathematical way of thinking: the triumph of ingenuity over cluelessness, of order over disorder” (Griffiths & Clyne, 1991, p. 42).

Picture books and stories and children's literature in general can thus supply children with an informal world of experiences that embodies mathematical objects and structures (Ginsburg & Seo, 1999). Children build up informal knowledge that serves as a foundation for developing a more formal and generalized understanding of mathematics as they meet the mathematical concepts in a way that makes sense and in which emotional engagement and cognitive engagement are wrapped together (Scribner & Cole, 1973).

Theoretical Perspectives

The aforementioned rationale for using picture books to support the learning of mathematics reflects three theoretical perspectives: a constructivist approach to learning, the importance of contextualized learning, and the role of learning by interaction. The latter is included in both of the first two positions.

Within the constructivist approach to learning, picture books are considered to offer an environment in which children actively construct mathematical knowledge (Phillips, 1995). The children resolve cognitive conflicts that become apparent through what happens in the story or through what is expressed in the text and the pictures. Children process the new information by connecting it to prior knowledge and by reflecting on it. Through this activity, they develop new ideas, structures, and schemas and achieve a higher level of understanding. One of the central tenets in this cognitive view of constructivism grounded in the work of Piaget and regarded crucial to learning is the role of novel information in creating cognitive disequilibrium in the mind (McLaughlin et al., 2005).

In addition to the above position, constructivism also involves a social perspective based on the sociocultural theory of learning of Vygotsky. This view emphasizes that young children come to know their world as a result of social interaction that offers opportunities to share knowledge and triggers reflection. As Vygotsky discovered, learners move beyond a certain level of understanding through the help of more knowledgeable others (McLaughlin et al., 2005). In mathematics education, this social view of constructivism means that learning mathematics is seen as a process of enculturation in which classroom interaction is a central element (Sfard, Nesher, Streefland, Cobb, & Mason, 1998). In this “social constructivist” theory of learning mathematics, learners are seen as “active constructors of knowledge in a social environment” (Romberg, 1993, p. 102; Cobb, 1994).

The position of contextualized learning encompasses the theory of situated cognition launched by Brown, Collins, and Duguid (1989) and the situated learning theory as introduced by Lave and Wenger (1991). Both theories emphasize that knowledge is situated and learning is a function of the activity, context, and culture in which it is developed and used. Similar to the social view of constructivism, a critical component of situated cognition and situated learning is that of social interaction in the community of learners and of practice. The difference with the constructivist approach is the crucial role assigned to the meaningful, authentic context in which the learning takes place. Situated learning is also usually unintentional rather than deliberate. Lave and Wenger (1991, p. 29) called this the process of “legitimate peripheral participation.”

Brown et al. (1989, p. 41) stressed that “[a] theory of situated cognition suggests that activity and perception are importantly and epistemologically prior—at a nonconceptual level—to conceptualization and that it is on them that more attention needs to be focused. An epistemology that begins with activity and perception, which are first and foremost embedded in the world, may simply bypass the classical problem of reference—of mediating conceptual representations.” In mathematics education, this recognition of the importance of preformal learning can, for example, also be found in the work of Donaldson (1979) and Hughes (1986) who showed that young children can understand mathematical concepts in context that they cannot understand at a formal level. As a consequence, in mathematics education, contexts and the intuitive and informal knowledge that is connected to them are exploited as a steppingstone for learning formal mathematics.

The three theoretical perspectives discussed above are also three important theoretical principles of Realistic Mathematics Education (RME); the Dutch approach to mathematics education (e.g., Van den Heuvel-Panhuizen, 2001) in which the picture book study is situated. RME sees children as active participants in the learning process, assigns great importance to giving children the opportunity to share and discuss ideas for solutions, and attaches high value to providing meaningful contexts from which context-based mathematical knowledge can emerge that serves as a basis for reaching more general and formal levels of understanding. In agreement with Griffiths and Clyne (1991), RME perceives mathematics as an integral part of human experience, which means that it can also be seen as an integral part of the stories that are told in picture books.

Using picture books to support the learning of mathematics fits quite well within RME. However, until now, the use of picture books for learning mathematics is a rather blank spot in Dutch mathematics education. The present study is a start in closing this knowledge gap.

PREVIOUS RESEARCH ON MATHEMATICS-RELATED EFFECTS OF PICTURE BOOKS

Picture Books' Impact on Children's Mathematics Achievements

Although there is a strong belief that children's literature can support the learning of mathematics, only a few studies have been carried out to investigate the impact of literature-based mathematics education on the achievements of children (Haury, 2001). A study that provided such evidence is the kindergarten experiment by Jennings, Jennings, Richey, and Dixon-Kraus (1992), in which for a period of five months, children's literature was incorporated into the mathematics curriculum. This instructional focus resulted not only in an improvement of mathematical achievement test scores but also in an increase in the children's interest in mathematics and the number of times that they used mathematical vocabulary during free play.

Hong (1996) investigated the influence of a program that included mathematics- related storybook reading and play with mathematics materials on the mathematical performance of kindergartners. She found that the experimental group provided with this program did better in classification, number combination, and shape tasks. In addition, more children in the experimental group liked the mathematics corner, chose mathematics tasks, and spent more time in the mathematics corner.

More recently, O'Neill, Pearce, and Pick (2004), while researching three- and four-year-old children over a period of two years, signaled a relationship between early narrative ability and later mathematical ability. In the same year, Young-Loveridge (2004) found increased numeracy levels and significantly greater gains in numeracy in a group of five year olds who followed an outside-the-classroom program using number books and games compared with a group of children not involved in the program.

A characteristic feature of the aforementioned studies (and this is especially true for Jennings et al., 1992 and Hong, 1996) is that in these studies picture books were used as the starting point of a mathematical activity. After a book was read, follow-up activities were conducted that highlighted the mathematical content of the book. Here, the follow-up activities rather than the book itself were seen as the treatment. With this approach, the reactions of the children that emerged during the reading session and that formed the starting point of the children's growth in mathematical understanding were not investigated.

To acquire knowledge on how picture books can support the learning of mathematics, knowledge about the children's in-the-moment cognitive engagement (McLaughlin et al., 2005) is very important. If we know what is triggered cognitively in the children when they are read picture books we will better understand how picture books may contribute to learning mathematics.

Children's Cognitive Engagement While Being Read a Picture Book

Although Lovitt and Clarke (1992) mentioned that picture books can offer a “cognitive framework” with “cognitive hooks” to explore mathematical concepts and skills, research into children's in-the-moment cognitive engagement while being read a picture book is a thinly researched area. The few studies we identified are those by Fletcher, Perez, Hooper, and Claussen (2005); Moschovaki and Meadows (2005a, 2005b); and the studies by Shapiro, Anderson, and Anderson (1997), Anderson (1997), and Anderson et al. (2005).

In Fletcher et al.'s (2005) study, the spontaneous responsiveness and the attention of toddlers (18 to 24 month olds) from an at-risk background were examined when they were read a picture book. The results of this study suggest that toddlers' spontaneous behaviors and attention during reading with an adult predict language development. In Moschovaki and Meadows' (2005a, 2005b) study, young children's spontaneous participation and cognitive engagement during teacher book reading was examined in Greek kindergarten classrooms. The focus of the researchers was on the differences in the cognitive demand of the classroom discussion between various types of books. The majority of children's spontaneous participation was related to the book illustrations and the children's personal experiences. Nonfiction books elicited more comments about personal experiences while fiction books elicited more predictions of what follows in the story, personal responses, chiming, recall, clarifying, and evaluation comments. Overall, most group discussion was of low cognitive demand and focused on text recall and labeling. Nonfiction books prompted higher cognitive demand discussion while fiction books prompted lower cognitive demand discussion. The authors did not report about mathematics-related talk.

Anderson (1997) investigated what mathematics occurred in parent-child interactions when different materials were used, including multilink blocks, blank paper, preschool worksheets, and a picture book. In the sessions with these materials the parents were expected to inject mathematics events such as counting, naming numbers, naming shapes, and comparing sizes.

Questioning the children's knowledge was the main way in which the parents elicited mathematics. Important, the study revealed that parents who are neither mathematics educators nor teachers can engage their children in mathematical talk and activity. Similar results were found in a later study (Anderson et al., 2005), with 39 parents from socioeconomically diverse backgrounds in which they read two books to their four-year-old children. This study revealed that during the shared book reading, the concepts of size (using descriptors of size like little or big, comparing the size of objects in illustrations, and using informal units to describe length) and number (using one as a descriptor or global descriptors such as lots and tons, and counting) arose most frequently, while utterances about shape occurred most infrequently. Other findings were that the amount and kind of mathematical talk differed between the two books and varied from family to family even for the same book and that most of the mathematical discourse was centered on the illustrations.

RESEARCH QUESTION

In the aforementioned studies, the focus was on cognitive engagement as prompted by the reader. In our research, we explored another avenue. The purpose of our study was to learn the kind of cognitive activity that is evoked by picture books themselves and the way in which the mathematics comes into play. In contrast to other research, our study was not meant to investigate how an adult who reads a book to children can prompt children's reactions. Instead, the focus was on the responses that a book can elicit by itself. Since we wanted to know how powerful a book on its own can be, we had to set up our study in a way that limited the assistance of the reader.

More precisely formulated, our research question was: What mathematics-related thinking does a picture book on its own evoke during the process of reading the book to young children?

At a more detailed level, our study intended to offer insight into the processes that are going on in a child's mind (perceiving, imagining, remembering, reasoning, anticipating, and so on) when the child sees the pictures of a picture book and hears the accompanying story. We investigated these invisible mental processes by observing the child's overt reactions that in one way or another showed engagement with mathematical phenomena that are in the book. Depending on the picture book involved, these reactions can be, for example, counting down when seeing a rocket, showing indignation when discovering that an amount is not shared fairly, predicting the growth of a flower, or recognizing that something is upside down. All these responses might be a sign that there is some mental processing. The assumption in our study was that the more that children are cognitively engaged in mathematical phenomena while being read a picture book the more the picture book can contribute to children's mathematical development.

Our definition of cognitive activity is connected to McLaughlin et al.'s (2005, p. 4) concept of student content engagement: “Content, in this formulation, includes all the stimuli faced by the student during a learning event … [and] engagement describes how the student and instructional content interact.” According to McLaughlin et al. (2005), student content engagement is a necessary condition for learning, and the more engagement there is the more learning takes place; however, both are not synonymous. In order for learning to take place, learning activities provide students with occasions for cognitive processing, which means that the brain receives, uses, stores, and retrieves information from the environment. However, as McLaughlin et al. (2005, p. 12) made clear, “processing is an internal, cognitive endeavor (i.e., the activation and strengthening of neural networks in the brain), its occurrence is largely unseen and its accurate and efficient measurement has not yet established. The student content engagement model therefore focuses on those behaviors that increase the likelihood of processing or the availability of processing occasions.”

It is interesting that McLaughlin et al. (2005) also mention some issues that could be particularly important for the use of picture books. For example, they emphasize the possibility of learning in “down” times, which means a reactivation of new associations that occur unintentionally during sleep or other times in which the students seems not to be actively involved. They bring up several other issues—the influence of the repeated exposure, the significant role of the students' personal experience with respect to new material and the emotional connections resulting in selective attention, and the motivation of the student to participate in the task of the moment that determines whether the student is engaged in the tasks. We think that the use of picture books can meet all these issues.

As a basis for identifying those utterances that might reflect cognitive engagement, we made use of the categories of mathematical thinking employed by Ginsburg, Lin, Ness and Seo (2003), the framework of thinking skills developed by Quellmalz (1985), and the categories of cognitive engagement used by Moschovaki and Meadows (2005a). We discuss these sources in the analysis section when we describe our coding framework.

METHOD

Subjects

The four 5-year-old children who participated in the study were in their second year of kindergarten (K2). ² This means that the children had no formal instruction in mathematics or reading. In Dutch kindergarten classes, the children are offered a play-focused environment. Reading instruction starts only in first grade. Consequently, most children in kindergarten cannot read. This was also the case for the four children involved in the study.

Table 1 gives information about the four children involved in the study. The children are from different backgrounds. Two of them are autochthonous and two are from an immigrant background. The children are from two different schools. The first two attend a school that is located in a small town and is largely populated by autochthonous children from middle-class families. The other two children are from an inner-city school that has a large population of immigrant children with an at-risk background. For the two children that attend this school, Dutch is their second language.

TABLE 1. Information on the Reading Sessions and the K2 Girls Involved

Name∗	Age	First language	Location School	Reading session
				Date	Duration
Amber	5;8	Dutch	Small town	27 Jan 06	8 minutes
Sanne	5;3	Dutch	Small town	27 Jan 06	15 minutes
Banu	5;9	Turkish	Inner city	3 April 07	15 minutes
Ketifa	5;11	Berber	Inner city	3 April 07	21 minutes
∗Pseudonyms have been used throughout the article.

Their classroom teacher selected the children. We asked the teachers to choose children that scored about average compared with their classmates in both mathematics and language. To exclude gender-specific differences in the children's reactions to the picture book we decided to include children of the same sex. The choice for girls was an arbitrary one.

Both schools use picture books for stimulating language development and early literacy. The way in which the two schools deal with reading picture books in classroom is quite similar. The children are read aloud to regularly. At least one new book per week is introduced. During the reading sessions, interaction takes place and the teachers ask questions to check the children's understanding of the story. Moreover, the books are accessible for the children during free play. Besides these similarities in dealing with picture books, we also found some differences. The teacher at the inner-city school organizes reading sessions for small groups of about six to eight children at a time whereas the other teacher reads books to the whole group of about 25 children. The teachers are using different programs for selecting mathematical activities, but these programs are quite similar with respect to the kind of mathematical activities they offer. The teacher of the inner-city school was involved in the PICO-ma project, which means that she tried out some books with a small group of children. However, the two children that were involved in the present study did not participate in these PICO-ma reading sessions.

The Picture Book Used in the Study

In our study, we followed a broad definition of picture books: a book that contains pictures and that may contain text as well, but in which the illustrations play a significant role in telling the story. ³ To let the mathematics-related thinking emerge, there should in some way be mathematics in the book. However, in accordance with the idea that picture books can give children access to mathematics at an informal and meaningful story-connected level, the focus in our study was not on picture books that have been written for didactical purposes but on picture books of high literary quality—books in which the authors simply wanted to tell children a fascinating story. Most of these types of stories are in some way about life and the world in which we live. Therefore, it is very likely that mathematics will play a role in these stories but in a different way than in picture books that have been written on purpose for mathematics instruction. Literary picture books do not always take into consideration what is seen in teaching mathematics as an optimal didactic approach. In picture books, it is the story that counts. As a result, children may encounter mathematical concepts for which they are not yet ready, according to the regular program. Another consequence could be that concepts are treated in a fragmentary, incomplete, or even mathematically incorrect way (Schiro, 1997).

The book used for the study is Vijfde zijn [Being Fifth] (Jandl & Junge, 2000). ⁴ The book is written by Ernst Jandl and is illustrated by Norman Junge. It was first published in Germany by Beltz & Gelberg, Weinheim, in 1997. We selected the book with the help of Boekwijzer, an annotated database of children's books. ⁵ According to this database there is much to discover on the pictures of Vijfde zijn. Moreover, the number of awards ⁶ the book has won indicates that it is of high literary quality.

The story is about a doctor's waiting room in which five broken toys are waiting for their turn (see Figure 1). ⁷ The title page of the book intends to make clear that of the five toys, the wooden puppet is fifth (see Figure 2). The book has 16 full-page illustrations in total, with a white page that includes a text consisting of only a few words (see Figures 3 and 4) to the left of these pages. The front and back endpaper are similar and contain some ten, diagonally placed rows, each containing several groups of five chairs (see Figure 5). The complete text of the book is given in the Appendix.

FIGURE 1. Cover page [CF] of Vijfde zijn.

FIGURE 2. Title page [TP] of Vijfde zijn.

FIGURE 3. Page 3 of Vijfde zijn. English translation of the text: one in.

FIGURE 4. Page 4 of Vijfde zijn. English translation of the text: door closed, now only four.

FIGURE 5. Endpaper front [EF] and endpaper back [EB] of Vijfde zijn.

The toys go into the room behind the door in turn. When they come out of this room again they have been repaired and the next toy goes in. The last one to go in is the wooden puppet with the broken nose. Only then is it shown that the brightly lit room is a doctor's office.

Judging from what the reviews of the book said, it can be concluded that the book was not written with the intent to teach children mathematical concepts. For example, in the Netherlands, the Jury of Pluim van de maand (1999) mentioned the counting backward that is part of the story, but they did not recognize it as a key issue. Instead, the jury committee praised the simple way in which the book creates a certain amount of suspense. The repetitive character of the story is seen as being very important because it is considered to arouse expectations in the child and to give the child the feeling of being in the story, but the jury committee did not mention, for example, that the repetitions offer holds for learning mathematics. The cover text on the back of the Dutch version of the book says, “Vijfde zijn is more than a picture (counting backwards) book. It shows children that a doctor is not a gruesome person.”

Although the book was apparently not meant to teach children numbers, we judged the book as having the potential to evoke thinking about numbers. The story provides the children with a meaningful context in which numbers play a role. However, contrary to what the title suggests, the Dutch version of the text does not explicitly deal with ordinality and ordinal numbers. ⁸ Instead, the book focuses more on resultative counting (“Now only four”) and decreasing numbers. Notwithstanding this, the story also contains some interesting elements for obtaining a more profound understanding of ordinal numbers. The wooden puppet on the right is number five in line—it is fifth. This conclusion can also be reached by counting the number of toys. By following what happens in the waiting room, children might discover that an ordinal number can change when a situation changes. The wooden puppet is not fifth forever. None of the available reviews of the book mention the conflicting situation that may put children on the track of understanding the relative character of ordinal numbers.

In sum, we had enough reasons for choosing Vijfde zijn to answer the research question. The literary quality of the book is high and the book is not written with the purpose of teaching mathematics. Moreover, we expected the book to have the potential to evoke mathematics-related cognitive activity. Whether this conjecture could be verified in our study will be discussed in the results section.

Book-Reading Procedure and Data Collection

The same reader (one of the authors of this article) read the book to the children individually. Before the reading session started, we made sure that the book Vijfde zijn was new to the children. Table 1 shows when the reading sessions were held and the time they took. The children were told in advance that the reader would turn the pages and that the child had to tell what happens in the pictures.

The general rule of the reading session was to give the children many opportunities to react. Primarily, the book itself should evoke these reactions. To limit the influence of the reader as much as possible, reading guidelines were set up that proscribe unprompted assistance by the reader. In essence, the reader did not say anything about the book herself, nor did she go into the child's reactions. Instead of asking questions and giving comments, the reader just showed an inquiring expression as a result of her own cognitive involvement in the book. In order to standardize the book reading we put the general reading guidelines in writing. In addition, a reading scenario was developed that explained how each page should be presented. The reading sessions were done strictly according to the general guidelines and the reading scenario. Table 2 shows a part of this reading scenario. For the remaining pages of the book we also developed reading guidelines. All four reading sessions were videotaped in such a way that the child's mimicry and gestures as well as the interior of the book were visible.

TABLE 2. Part of the Book-Reading Scenario

Page	Instruction for book reading
CF (Cover Front)	Show the child the cover page of the book. The child may react to this page by spontaneously telling what is happening in the picture. If no spontaneous reaction comes up, ask what the child thinks the story is about.
3	Show the child page 3. Wait for a reaction. When the child gives no more reaction, read the line: “One in.” Wait some time to see whether the child reacts to this text.
4	Show the child page 4. Wait for a reaction. When the child gives no more reaction, read the lines: “Door closed. Now only four.” Wait some time to see whether the child reacts to this text.

Data Analysis

We applied Glaser and Strauss's (1967) grounded theory to analyze the collected data and to produce knowledge about picture books as an impetus for kindergartners' mathematics-related thinking. In particular, we made use of the general idea of the “constant comparative method” (Strauss & Corbin, 1998), which generated in a constantly progressing coding framework. This included starting with open coding—“memoing” everything that could be important and eventually, through a process of iteration and adaptation, arriving at coding categories that identify key utterances that reflect the children's mathematical thinking that is prompted by the picture book. From the very first moment of our data collection we tried to identify elements in the utterances of the children that entailed cognitive engagement whether or not it related to mathematics. Then, through repeatedly reexamining the data and the theoretical notions that emerged from this process, we eventually came to the final coding framework that we used for analyzing the utterances of the children. This iterative process brought us to the results described later.

The analyses were done both on the video clips and on the transcripts that were made of these clips. We considered the video clip of a reading session and the transcript of it as one data set. In agreement with our research question that focused on the power of the book, only those utterances were included in the analysis that were prompted just by looking at the pictures or listening to the text. Utterances that came up after (unintended) remarks or questions from the reader were left out of the analysis. In general, we considered the smallest possible meaningful grammatical part of a response as the unit of analysis. These parts mostly contain a finite verb or a verb phrase, but sometimes only contain a subject or an object, or even merely a sigh or an exclamation. Furthermore, an utterance was coded according to its most dominant characteristic.

The final coding framework is shown in Table 3. The framework has a two-dimensional nature by distinguishing a general qualification of utterances and a domain-specific one. The general qualification includes categories such as description, assumption, and explanation, and the domain-specific qualification covers number-related and spatial orientation-related utterances. All utterances were given a general qualification and some also received a domain-specific qualification. In Table 3, the coding categories are circumscribed and illustrated by one or more examples from the transcripts in square brackets. The framework came into being in several successive rounds, as described in the following.

TABLE 3. Framework for Coding Children's Utterances Made During Picture Book Reading

General Qualification of Utterances

01. Description Static:

Child describes a static aspect of the picture that is shown [S-15∗: And the door is open.]

02. Description Static Comparison:

Child describes a static aspect of the picture that is shown and makes an explicit or implicit comparison between pages [B-EB: Again hundred chairs!]

03. Description dynamic stationary:

Child describes a dynamic but stationary activity in the picture; e.g., an object moves (turns its head, moves the eyes, swings) but stays in its place; this category also applies to the stationary movement of looking at something or in a direction [S-06: Then this lamp goes that way… .] [B-11: The bear is dancing… .] [K-02: He looked at the lamp.]

04. Description dynamic stationary comparison:

Child describes a dynamic but stationary activity in the picture and makes an explicit or implicit comparison between pages [K-12: And this one looked there again.]

05. Description dynamic relocation:

Child describes a movement of the toys to another place [A-12: Now the frog goes in.]

06. Description dynamic relocation Comparison:

Child describes a movement of the toys to another place and makes an explicit or implicit comparison between pages [B-11: He comes back again.]

07. Posing question:

Child asks a question [A-12: Why does he have a sticking plaster?]

08. Assumption story line:

Child makes an assumption about how the story will continue [B-04: Four will be leaving.]

09. Assumption other:

Child makes an assumption about things other than the story line [K-01: Maybe they are waiting.]

10. Explanation Own Utterance:

Child gives an explanation concerning her own utterance [S-13: (After S said that the puppet cries:) … because he is alone.]

11. Explanation other:

Child gives an explanation concerning things other than her own utterance [A-16: (After the reader read the text “Hello doctor”:) That is the waiting … the waiting … at the doctor's… .]

12. Giving opinion:

Child tells what she thinks of the book [A-07: Nice book!]

13. Commenting text:

Child comments on the read-aloud text [B-05: (After the reader read the text “Door open. One out”:) Out is go outside.]

14. Commenting picture:

Child comments on a picture [S-16: (While pointing to the “noses” on the shelf in the doctor's office:) … and this doesn't actually belong at the doctor's.]

15. Repeating text:

Child repeats the read-aloud text [A-09: (After the reader read the text “One in”:) One in.]

16. Correction:

Child corrects her own utterance [B-14: (After B said that “this one will come”:) … no, this one will go out.]

17. Self-reflection own utterance:

Child reflects on her own utterance [A-11: (After A said that the toys are eating in the other room:) … that is what I think.]

18. Self-reflection other:

Child reflects on things other than her own utterance [S-02: (While trying to describe how the bear is looking:) I cannot see it very well.]

19. Contemplation:

Child ponders on something [S-04: (When wondering whether the duck has a little string or a little stick:) Hm… .]

20. External reference other story:

Child makes an external reference to another book or story [A-TP: It looks like Pinocchio, …]

21. External reference other:

Child makes an external reference that has nothing to do with the book or story [A-09: My little sister is outside now.]

22. Unclear utterance:

For example, child says something that is (partly) inaudible or that does not make sense to the researchers [S-04: And (inaudible) looks that way again.]

Domain-Specific Qualification of Utterances—Number Related

N1. Resultative counting:

Child makes a statement about the numerosity of a collection, with or without precisely counting, including subitizing and estimation [K-07: (While pointing to the chairs:) Three people are sitting here. (13)∗∗]

N2. Using all/everyone:

Child makes a reference to the undefined quantifiers all or everyone [B-13: … because everyone is gone. (10)]

N3. Using none/nobody:

Child makes a reference to quantifier none or nobody [K-04: Maybe, when this one is gone … then nobody is there. (08)]

N4. Using some:

Child makes a reference to the undefined quantifier some [S-CF: And some are sitting … (01)]

N5. Using ordinal numbers:

Child uses ordinal numbers [A-TP: Fifth? (07)]

Domain-Specific Qualification of Utterances—Spatial Orientation-Related

S1. Waiting room perspective

Child takes the waiting room perspective: this means, for example, saying “going out,” “leaving,” etc. when a toy goes into the doctor's office, and “going in, “coming,” “is back etc. when a toy goes into the waiting room [S-02: (In the picture a ladybird is coming into the waiting room:) … and a ladybird is coming. (05)]

S2. Waiting room perspective + adjunct:

Child takes the waiting room perspective using an adjunct of place like “here” and “there” [K-03: (While pointing to the penguin and the doctor's office:) And then this one wants to go there. (13)]

S3. Doctor's office perspective:

Child takes the doctor's office perspective; for example, saying “going in” when a toy goes into the doctor's office, and “going out” when a toy goes into the waiting room [B-02: (After the reader read the text “Door open. One out,” while pointing to the ladybird:) This one is out. (13)]

S4. Doctor's office perspective + adjunct:

Child takes the doctor's office perspective using an adjunct of place like “here” and “there” [A-05: (After the reader read the text “Door open. One out,” while pointing to the doctor's office:) At that, one out. (13)]

S5. Describing direction:

Child describes a direction [K-13: And the lamp is almost upwards. (01)]

∗The first letter refers to the child (A = Amber; S = Sanne; B = Banu; K = Ketifa) and the code refers to the page of the book.

∗∗The general utterance is placed between parentheses. Note that a general utterance can be number-related and spatial orientation-related.

After the first two reading sessions with Amber and Sanne, we jointly watched the videos and discussed them. When we found something that stood out, we made a memo. We then made full transcripts of the entire reading sessions, supplemented with our observations, interpretations, and remarks. In this way, we arrived at annotated transcripts. In the next step in the analysis we made a narrative summary of the reading sessions. This summing up focused our attention on differences and similarities in the children's utterances. By reexamining them with the “cognitive activity lens” and repeatedly going back to the annotated transcripts and the videos, we came to a large collection of utterances that might be an indication of cognitive activity elicited by the picture book. To capture the key aspects of the cognitive engagement, we identified several types of utterances.

As a basis for identifying utterances that involve cognitive engagement, we made use of the categories of mathematical thinking used by Ginsburg et al. (2003). Their framework of categories of mathematical thinking has been developed for children's everyday mathematical activities during free play and contains the following categories: classification (systematic arrangements of groups of objects), magnitude (“There's a lot here”; “This tower is more higher”), enumeration (“three” blocks), dynamics (exploration of the process of change: “Now I got two. Now I got one. Now I got none”), pattern and shape (recognizing “square”), and spatial relations (one block is “under” another).

Another source for developing our coding system was the framework of thinking skills developed by Quellmalz (1985), which contains general thinking activities such as recall, analysis, comparison, inference, and evaluation. Finally, we were inspired by the categories of cognitive engagement as used by Moschovaki and Meadows (2005a), including predictions, analysis, reasoning, clarification of comments, vocabulary analysis, personal experiences, and evaluating, book-focused comments, chiming (standing for rhyming, singing, and playing with the language), labeling, recall, personal responses to text, and dramatization.

When we included the transcripts of the reading sessions with Banu and Ketifa in the analysis, we experienced that more fine-grained categories and a rearrangement of the categories were required to bring the cognitive activities prompted by the book more clearly to the fore. The revised coding framework was used to code the four transcripts again. Like in the other coding rounds, we worked together on coding the children's responses. This means that we first coded the four transcripts individually and then compared and discussed our coding until we reached agreement.

After we finished our new coding of the four transcripts we asked a colleague who is familiar with coding protocols to code one of our transcripts. Before she did this, we gave her a training based on two of the other transcripts. Comparing her coding with ours showed an agreement on the domain-specific qualification categories but some remarkable differences in some of the general qualification categories such as static or dynamic descriptions and making assumptions. A discussion about these differences in which we also included other colleagues led to a rearrangement and a more precise description of the categories and resulted in the final coding framework as shown in Table 3. This framework was used to generate the data set of classified utterances that we used to answer the research question. As in the earlier coding rounds, we did the coding based on mutual agreement. Our final coding was checked by another colleague. Of every transcript, she took a random sample of 15 to 20 utterances—70 utterances in total. When comparing her coding with ours, only one utterance was coded differently, producing an interrater reliability of 99%.

RESULTS

First, we describe the children's utterances that can be considered as evidence for cognitive activity in general. Second, we zoom in on domain-specific utterances. Third, we focus on the book and depict the power of the different book pages to prompt cognitive activity in the children. Fourth, we address the differences in utterances we found between the four children.

Found Evidences for Cognitive Activity in General

Table 4 shows the children's utterances that can be considered expressions of their cognitive activity that came up during the reading sessions with Vijfde zijn. In total, we identified 22 types of general utterances. Only 3% of the utterances could not be classified.

TABLE 4. Number and Percentage of Found Utterances During the Reading Sessions

	Reading Session								Total
	Amber		Sanne		Banu		Ketifa
	N	(%)	N	(%)	N	(%)	N	(%)	N	(%)
General qualification of all utterances
01. Description Static	14	(24)	49	(38)	18	(21)	54	(34)	135	(31)
02. Description Static Comparison	8	(14)	22	(17)	4	(5)	17	(11)	51	(12)
03. Description Dynamic Stationary	2	(3)	15	(12)	20	(24)	16	(10)	53	(12)
04. Description Dynamic Stationary Comparison							2	(1)	2	(0)
05. Description Dynamic Relocation	2	(3)	3	(2)	4	(5)	9	(6)	18	(4)
06. Description Dynamic Relocation Comparison	6	(10)	6	(5)	2	(2)			14	(3)
07. Posing Question	5	(8)					3	(2)	8	(2)
08. Assumption Story Line	4	(7)			2	(2)	6	(4)	12	(3)
09. Assumption Other	1	(2)	4	(3)	18	(21)	28	(18)	51	(12)
10. Explanation Own Utterance	2	(3)	4	(3)	4	(5)	6	(4)	16	(4)
11. Explanation Other	2	(3)	3	(2)					5	(1)
12. Giving Opinion	1	(2)							1	(0)
13. Commenting Text	3	(5)	1	(1)	8	(10)	6	(4)	18	(4)
14. Commenting Picture			1	(1)			1	(1)	2	(0)
15. Repeating Text	2	(3)							2	(0)
16. Correction	1	(2)	4	(3)	3	(4)	2	(1)	10	(2)
17. Self Reflection Own Utterance	4	(7)	1	(1)	1	(1)	4	(3)	10	(2)
18. Self Reflection Other			1	(1)					1	(0)
19. Contemplation			7	(5)			1	(1)	8	(2)
20. External Reference Other Story	1	(2)					1	(1)	2	(0)
21. External Reference Other	1	(2)							1	(0)
22. Unclear Utterance			8	(6)			4	(3)	12	(3)
Total Utterances	59	(14)∗	129	(30)∗	84	(19)∗	160	(37)∗	432	(100)
Domain-specific qualification of utterances
Number-related
N1. Resultative Counting	11	(19)∗∗	6	(5)∗∗	15	(18)∗∗	3	(2)∗∗	35	(8)∗
N2. Using All/Everyone	2	(3)∗∗	6	(5)∗∗	7	(8)∗∗	7	(4)∗∗	22	(5)∗
N3. Using None/Nobody							1	(1)∗∗	1	(0)∗
N4. Using Some			1	(1)∗∗					1	(0)∗
N5. Using Ordinal Numbers	1	(2)∗∗			1	(1)∗∗			2	(0)∗
Total	14	(24)∗∗	13	(10)∗∗	23	(27)∗∗	11	(7)∗∗	61	(14)∗
Spatial Orientation-related
S1. Waiting Room Perspective	8	(14)∗∗	8	(6)∗∗	14	(17)∗∗	21	(13)∗∗	51	(12)∗
S2. Waiting Room Perspective + Adjunct			1	(1)∗∗			4	(3)∗∗	5	(1)∗
S3. Doctor's Office Perspective	2	(3)∗∗			1	(1)∗∗	1	(1)∗∗	4	(1)∗
S4. Doctor's Office Perspective + Adjunct	3	(5)∗∗					1	(1)∗∗	4	(1)∗
S5. Describing Direction			34	(26)∗∗	25	(30)∗∗	9	(6)∗∗	68	(16)∗
Total	13	(22)∗∗	43	(33)∗∗	40	(48)∗∗	36	(23)∗∗	132	(31)∗
∗Percentage of the total number of utterances (432).
∗∗Percentage of the total number of utterances of the child.

The static descriptions were the kind of utterances with the highest frequency; 43% of the utterances belonged to that category. In 19% of the utterances, children gave a dynamic description of what they saw on the picture. In 12% of the utterances, the dynamic description referred to a stationary movement, and in 7% of the utterances, the dynamic description referred to a movement to another place. Making assumptions was the third highest category; 15% of the utterances fit into this classification.

Of the 22 types of general utterances, nine were found in the responses of all four children. All children spontaneously made static descriptions with and without comparisons, dynamic descriptions including stationary movements and relocation, assumptions, and explanations of their own utterances. In addition, all four children commented on the text, on occasion corrected their own utterances, and reflected on their own utterances.

Five categories of utterances were only found in the responses of one child. Three of them were found in Amber's reactions. These concern the categories giving opinion, repeating text, and external reference other. Ketifa was the only child who scored an utterance in the category description dynamic stationary comparison, and Sanne in the category self-reflection other.

A closer look at the description utterances revealed that of the 186 static descriptions, 27% contained a comparison. Of the 87 dynamic descriptions, this was 18%. Within this category, however, we found a large difference between the categories description dynamic stationary and description dynamic relocationt. In the last category, 44% of the utterances contained a comparison while this was only the case in 4% of the utterances in the first category.

Found Evidences for Domain-Specific Cognitive Activity

In total, 45% of the utterances contained a domain-specific reference. Table 4 shows that 14% of all utterances was number-related and 31% was spatial orientation-related.

Of the 61 number-related utterances, 35 belonged to the category resultative counting. That means that these utterances involved statements about “how many there are.” The resultative counting category was found in the responses of all four children. The other large category within the number-related utterances is using all/everyone. This category was also found in the responses of all four children. Of the 61 number-related utterances, 22 were of this type. The other categories of number-related utterances in which children used quantifiers, including using none/nobody and some, appeared only in negligible numbers. Despite the title of the book, this was also the case for using ordinal numbers.

A closer look at all the utterances that reflect resultative counting revealed that in two cases the children were structuring numbers. On page 9, where the bear is going into the doctor's office and two toys are still in the waiting room, Ketifa said, while pointing to the doctor's office, “Just one is there and these two… .” Banu described the picture on page 2, in which the five toys are sitting in the waiting room, as follows, “two are looking at the ceiling, and three are watching television.”

Of the 193 domain-specific utterances, two thirds were spatial orientation-related, including taking a particular spatial perspective and describing a direction. In contrast to the doctor's office perspective that is taken by the author, all four children spontaneously took the waiting room perspective. This means that the text was not in agreement with the children's utterances. For example, the children say “one out” (meaning out of the waiting room) while the book's text says “one in” (meaning into the doctor's office). In total, 56 utterances (that means 13% of the total number of utterances) expressed the waiting room perspective. Only a few utterances (8 in total) reflected that the children took over the doctor's office perspective from the author. Half these utterances included an adjunct of place (words like “here” or “there”) to clarify a perspective that seemed strange to the children. The use of an adjunct of place might be seen as an indicator of the children's awareness that different ways of saying are possible. In 68 of the utterances (16% of the total number of utterances), children described a direction.

Found Evidences for Cognitive Activity per Book Page

To get a better understanding of the power of the book in prompting cognitive activity in children, we constructed a page profile by adding up the number of utterances per book page. Table 5 shows that the utterances were about equally distributed over the 22 pages of the book. In pages 1 to 8 ⁹ the scores were a little bit higher than in the second half of the book. The highest percentages of utterances (8%) were found on pages 2 and 11. On page 2 the door of the doctor's office opens for the first time and the ladybug comes out. On page 11 the bear is going out of the doctor's office. Of the introduction pages CF to TP, the cover page had the highest percentage of utterances. No utterances were found on page FF. This so-called French page only contains the title. Moreover, the reading scenario did not provide the children with an opportunity to react to this page.

TABLE 5. Number and Percentage of Found Utterances per Page

Book Page
	N	%	CF	EF	FF	TP	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	EB	CB
All Utterances
Amber	59	14	2	1		3	2	8	1	2	4	2	2	2	5	2	5	3	2	3	2	6	2
Sanne	129	30	10	2		2	7	9	5	11	6	6	6	6	7	5	11	6	7	7	4	10	2
Banu	84	19	1	2		4	3	7	7	6	6	5	4	5	5	3	6	4	5	6	3	1	1
Ketifa	160	37	13	3		3	11	12	12	8	10	11	6	11	10	6	11	5	8	6	5	5	1	3
N Total	432	100	26	8		12	23	36	25	27	26	24	18	24	27	16	33	18	22	22	14	22	6	3
%			6	2		3	5	8	6	6	6	6	4	6	6	4	8	4	5	5	3	5	1	1
Number-related
Amber	14	24∗∗		1		1			1		2	2	1	1	1	1		1			1		1
Sanne	13	10∗∗	1	1			1	5									2				1	1	1
Banu	23	27∗∗		2		1		3	3	2	1	3					2	1	3		1		1
Ketifa	11	7∗∗		1			1	1	1	1			1		3								1	1
N Total	61	14∗	1	5		2	2	9	5	3	3	5	2	1	4	1	4	2	3		3	1	4	1
%			2	8		3	3	15	8	5	5	8	3	2	7	2	7	3	5		5	2	7	2
Spatial orientation-related
Amber	13	22∗∗						1			3	1		1	2		2	1		1	1
Sanne	43	33∗∗				1		5	3	1	2	4	3	4	4	2	3	3	1	3	2	2
Banu	40	48∗∗				1	1	4	5	1	4	3	2	3	4	1	3	1	2	3	2
Ketifa	36	23∗∗						3	2	6	3	2		3	3	1	2	2	2	2	2	1		2
N Total	132	31∗				2	1	13	10	8	12	10	5	11	13	4	10	7	5	9	7	3		2
%						2	1	10	8	6	9	8	4	8	10	3	8	5	4	7	5	2		2
CF = front cover, EF = endpaper front, FF = French page front, TP = title page, 1 through 16 = page 1 to 16, EB = endpaper back, CB = back cover.
∗Percentage of the total number of utterances (431).
∗∗Percentage of the total number of utterances of the child.

When we look at the domain-specific utterances, the largest proportion of number-related utterances was also found on page 2. Pages 3 and 6—the pages on which the penguin and the duck go into the doctor's office, respectively—scored rather high as well. Remarkably high scores were also found on the endpapers at the front and the back of the book. These pages are only covered with diagonally placed rows of five chairs and are not part of the story. Despite this, these were the only pages to which all children reacted with number-related utterances.

The relatively highest scores in spatial orientation-related utterances were discovered on page 2 and pages 5 and 9. These latter pages are the pages on which the penguin is coming out of the doctor's office and the bear is going into the doctor's office, respectively.

Differences in Found Evidences for Cognitive Activity between the Children

Although the book Vijfde zijn was read to all the children in the same way, following the reading scenario strictly, the utterances that were prompted by the book were not the same in all children. As stated earlier, Amber was the only child who came up with an opinion, who repeated text, and who referred to a situation beyond the scope of the book. Banu showed remarkably fewer categories of utterances than the other girls, and Amber and Ketifa showed the most. The children also showed a large difference with respect to the total number of utterances. Ketifa had the largest number of utterances while Amber had the least. The difference in the number of utterances results, in particular, from the differences that were found in the category description static.

Some of the categories showed a broad range in number of utterances. The scores on description dynamic stationary were between 3% and 24% of the child's total number of utterances, the scores for assumption other were between 2% and 21%, and those for describing directions were between 0% and 30%. The totals in the domain-specific utterances showed a range of 7%–27% for the number-related utterances, and a range of 22%–48% for the spatial orientation-related utterances. Remarkably, the children with the lowest number of utterances (Amber and Banu) had the highest number of number-related utterances. For the spatial orientation-related utterances, we did not find this pattern.

As noted earlier, one of the most surprising findings was that the children spontaneously took the waiting room perspective instead of the doctor's office perspective that the author of the book takes, resulting into a discrepancy between the children's utterances and the text. However, the children reacted differently to this discrepancy. Sanne did not get out of balance by the deviating text. She kept the waiting room perspective (9 utterances) throughout the book. Only once did she use an adjunct of place to make clear what she meant. Amber, on the contrary, started with the waiting room perspective but shifted to the doctor's office perspective after she had heard the text. The next time, she took the doctor's office perspective without the prompt of the text. However, on the next page she moved back to the waiting room perspective. Further on in the book this change of perspective happened a second time. In the total, she showed 13 utterances related to perspective, of which 5 reflected the doctor's office perspective. In the case of Banu this was 1 of 15, and for Ketifa it was 2 of 27.

When we grouped the four children according to their ethnic background it was revealed (Table 6) that the total utterances of the two children whose parents are not born in the Netherlands was higher than the number of utterances of the children with Dutch parents. Both groups had the same proportion of mathematics-related utterances but differed largely with respect to making assumptions. For the two children with Dutch parents, only 5% of the utterances was of this type, while the rate was 22% for the two children with non-Dutch parents. We also found some differences for the utterances that contained a description. The proportion of utterances that expressed a static description was higher for the autochthonous children (50%) than for the immigrant children (39%), while the latter made slightly more dynamic descriptions (18% versus 21%).

TABLE 6. Number and Percentage of Found Utterances of Autochthonous Children and Immigrant Children

	Autochthonous Children		Immigrant Children		Total
	N	(%)	N	(%)	N	(%)
General qualification of all utterances
01. Description Static	63	(34)	72	(30)	135	(31)
02. Description Static Comparison	30	(16)	21	(9)	51	(12)
03. Description Dynamic Stationary	17	(9)	36	(14)	53	(12)
04. Description Dynamic Stationary Comparison			2	(1)	2	(0)
05. Description Dynamic Relocation	5	(3)	13	(5)	18	(4)
06. Description Dynamic Relocation Comparison	12	(6)	2	(1)	14	(3)
07. Posing Question	5	(3)	3	(1)	8	(2)
08. Assumption Story Line	4	(2)	8	(3)	12	(3)
09. Assumption Other	5	(3)	46	(19)	51	(12)
10. Explanation Own Utterance	6	(3)	10	(4)	16	(4)
11. Explanation Other	5	(3)			5	(1)
12. Giving Opinion	1	(1)			1	(0)
13. Commenting Text	4	(2)	14	(6)	18	(4)
14. Commenting Picture	1	(1)	1	(0)	2	(0)
15. Repeating Text	2	(1)			2	(0)
16. Correction	5	(3)	5	(2)	10	(2)
17. Self Reflection Own Utterance	5	(3)	5	(2)	10	(2)
18. Self Reflection Other	1	(1)			1	(0)
19. Contemplation	7	(4)	1	(0)	8	(2)
20. External Reference Other Story	1	(1)	1	(0)	2	(0)
21. External Reference Other	1	(1)			1	(0)
22. Unclear Utterance	8	(4)	4	(2)	12	(3)
Total Utterances	188	(44)∗	244	(56)∗	432	(100)
Domain-specific qualification of utterances
Number-related
N1. Resultative Counting	17	(9)∗∗	18	(7)∗∗	35	(8)∗
N2. Using All/Everyone	8	(4)∗∗	14	(6)∗∗	22	(5)∗
N3. Using None/Nobody			1	(0)∗∗	1	(0)∗
N4. Using Some	1	(1)∗∗			1	(0)∗
N5. Using Ordinal Numbers	1	(1)∗∗	1	(0)∗∗	2	(0)∗
Total	27	(14)∗∗	34	(14)∗∗	61	(14)∗
Spatial orientation-related
S1. Waiting Room Perspective	16	(9)∗∗	35	(14)∗∗	51	(12)∗
S2. Waiting Room Perspective + Adjunct	1	(1)∗∗	4	(2)∗∗	5	(1)∗
S3. Doctor's Office Perspective	2	(1)∗∗	2	(1)∗∗	4	(1)∗
S4. Doctor's Office Perspective + Adjunct	3	(2)∗∗	1	(0)∗∗	4	(1)∗
S5. Describing Direction	34	(18)∗∗	34	(14)∗∗	68	(16)∗
Total	56	(30)∗∗	76	(31)∗∗	132	(31)∗
∗Percentage of the total number of utterances (431).
∗∗Percentage of the total number of utterances of the two children.

CONCLUSIONS

Our special interest in this study was whether mathematics-related thinking would evolve when young children were read a picture book that was not written with the intention of teaching mathematics. The results described in the previous section revealed that Vijfde zijn has the power to elicit this thinking. The number and type of utterances that reflect children's cognitive engagement clearly indicate that the book has the potential to make children think. Moreover, the results seem to lend evidence for the strength of the book. All four children showed cognitive engagement when they were read this picture book, resulting in general utterances and in domain-specific mathematics-related utterances that accounted for as much as almost half the utterances. These utterances were child-initiated and came up spontaneously without probing by the reader.

Within the domain-specific utterances, the spatial orientation-related utterances exceeded the number-related utterances. Of this latter type, most utterances had to do with telling “how many there are.” The children did not actually mention ordinal numbers. Within the spatial orientation-related utterances, three of four children referred to directions and all children spontaneously chose the waiting room perspective. Three of the children adapted this perspective and changed it one or more times into the doctor's office perspective that is taken by the author. In half the cases, this adaptation was accompanied by the use of an adjunct of place. As indicated by Scherer, Van den Heuvel-Panhuizen, and Van den Boogaard (2007) teachers have to take into account that children can interpret pictures in different ways. Steinbring (1994) made clear that instead of avoiding this ambiguity, teachers should take advantage of it. On top of this, we experienced that children are even able to handle ambiguous situations by themselves.

The domain-specific utterances were about equally distributed over the pages of the book, so the book as a whole has the potential to elicit mathematical thinking. On most pages, three or all four children showed spatial orientation-related utterances whereas more than half the children showed number-related utterances on fewer pages. We found that all four children showed number-related utterances on the endpapers in the front and the back of the book, so the pictures of diagonally placed rows of five chairs seem to give children food for thought about number. The endpapers are often ignored in reading sessions because they are not considered to be part of the story. Our findings give reason to take the endpapers of a picture book into account.

Finally, we found some differences among the four children and, in particular, between children with an autochthonous and an immigrant background. The latter group showed more utterances and especially made more assumptions during the reading session. However, in terms of percentage, both groups of children showed the same amount of number-related and spatial orientation-related utterances. This finding might indicate that immigrant children profit as much from picture books as do autochthonous children—which is a promising result. Normally, immigrant children often seem to gain less from education because of their arrears in language development.

In sum, the mathematics-related thinking that could be identified in the children's utterances gave support to the idea that children can be mathematically engaged by being read a picture book. This is true even when the reading session does not have an instructional purpose and the book at hand has not been written with the intention of teaching mathematics and does not explicitly display mathematics, for example, by means of number and number symbols and shapes.

DISCUSSION

Although our findings confirmed what we already know from previous research about children's mathematical utterances when they are read a picture book, our study also provided us with some new insights. Analogous to studies like those by Ginsburg (Ginsburg & Seo, 1999; Ginsburg et al., 2003), our results made it clear that when children are in an inspiring environment with elements that can be mathematized, they inevitably come up with mathematics-related thinking. This was also shown earlier by Shapiro et al. (1997), who observed mathematical talk in shared book reading of parents and children without mathematics being the focus in the research. Our reading sessions also revealed some new knowledge. In contrast to, for example, the research conducted by Anderson (1997), Shapiro et al. (1997), and Anderson et al. (2005), who did not find child-initiated mathematics, we found that without any prompting by the reader, half the utterances were mathematics-related and that all the four children in our study contributed to this result.

In a certain sense, this discerned power of the picture book sheds a new light on the theoretical positions that support the use of picture books to learn mathematics. The study clearly evidenced the constructivist and the contextualized positions to learning by showing that the book Vijfde zijn provided the children with an environment in which they could actively construct mathematical knowledge about number and spatial orientation (contextualized in the book in a meaningful way). However, evidence was not directly available for the role of social interaction that is intrinsic to both positions. In our study, the role of the reader was minimized. The lack of what is usually considered to be a crucial element of the learning process—namely that children can come to a certain level of understanding by means of interaction with knowledgeable others—is put in a different perspective here. The other is present here but not the verbal interaction that is mostly connected to those others. In our study, the knowledgeable other who is reading the book to the children is just somebody who only shows interest in the book and who is evidently cognitively active. In addition to this, our study made a reasonable case for extending the concept of the knowledgeable other by including the knowledgeable material, which a picture book can be.

This finding also has practical implications for how to read picture books to children in classrooms. Anderson et al. (2005) advocated the parents' way of book reading based on their observation that parents in contrast to teachers integrate mathematical talk almost seamlessly into the book reading. Our findings can be understood as an encouragement to teachers to exercise restraint and not to overload children with questions and explanations but instead to make use of the power of a book.

However, no matter how revealing our study was in several respects we have to emphasize that further research is necessary before we can draw firm conclusions. First, the study included only one picture book. If we want to have more evidence for picture books as an impetus for young children's mathematics-related thinking, we need to investigate how it works with other books. According to Anderson et al. (2005), different books can generate different amounts of mathematical talk and different kinds of mathematics.

A second issue of discussion is the number of children involved. To find more robust evidence for the power of picture books to prompt mathematics-related thinking and to generate knowledge about the nature of this thinking, more children, and children from different backgrounds, should be involved in data collection. Nevertheless, when we looked at the results from the two autochthonous children and the two immigrant children whose parents were not born in the Netherlands, we saw an unexpected difference that we do not want to leave unmentioned. The two immigrant children showed a larger number of utterances, including more utterances that reflected the making of assumptions, than the two children with Dutch parents. These positive findings give reason to investigate on a larger scale whether picture books offer immigrant children a good environment to prompt mathematics-related thinking and whether picture books can stimulate their learning of mathematics in this way.

A third shortcoming of our study is that we did not collect information about the children's mathematical knowledge at the time they were read the picture book. It is now widely understood that children acquire mathematical knowledge before starting formal schooling. As reported by Leder (1992), many children are able to count meaningfully, can use appropriate terms like more and less, and have understanding of addition and subtraction of small numbers. In our study, the children showed to be capable of counting, using quantifiers like all and everyone, taking a certain perspective, and describing directions. However, we do not know what part of this understanding was already there and what was really brought in by the picture book experience. A quasi-experimental pretest-posttest design can illuminate this.

A fourth issue that needs further deliberation is how to measure children's cognitive activity. In our study, we focused on what was observable of this assumed cognitive activity. The children's deep inner thinking was outside our scope. Perhaps in future studies techniques from neuroscience may help to get a better grip on the cognitive activity that picture books induce in children's minds.

Finally, a fifth point that needs attention is connected to the specific research question of the present study. The focus was on what the book prompted on its own. Consequently, the reader had to hold back. Probing was not allowed, and if the reader could not restrain herself and asked additional questions, the children's responses to this probing were left out of the analysis. In this way, it became clear what the book itself could bring about. However, research on the effect of picture books should not be limited to this. The role of the adult reader is equally or may be even more important. We experienced this at yet another reading session with the same book (Van den Heuvel-Panhuizen, Van den Boogaard, & Scherer, 2007) that included probing. By asking questions it was revealed that although spatial orientation and ordinal numbers belong to two different domains of mathematics, they also have something in common. In both domains, relativity plays a key role. How we perceive space depends on the perspective we take. The same is true for ordinal numbers. In the case of space, the perspective you take determines whether you go into or out of a room. In the case of ordinal numbers, the place in a row depends on where you start counting and it changes over time. If we go by the findings of this experience, young children might know how to handle relativity quite well. While textbooks often try to avoid this kind of confusing situation, picture books do not. Picture book authors have more freedom. They just like to tell a compelling story, and by doing so, they unintentionally provide children with a rich context for mathematical thinking.

Despite the limitations of our study, our findings were strong enough to continue our explorations of the potential of picture books for evoking kindergartners' mathematical-related thinking. Knowing about the power of picture books means that we will be better prepared to develop guidelines on how to deal with picture books in kindergarten classrooms so that they become an impetus for the learning of mathematics. In addition to this practical benefit, recognizing how children cope with mathematics in an environment that is not focused on mathematics learning widened our scope on learning processes in mathematics. Reading picture books to children and just observing what it brings about in their thinking showed us an environment of learning mathematics that often does not reflect the “paved” optimal didactic approach that we have in mind when we are teaching particular mathematical content. Picture books with high literary quality create their own priorities separate from possible didactical intentions. This makes them an interesting research area and a source for new understanding of the learning of mathematics.

The writing of this article was partly supported by the Netherlands Organization for Scientific Research (NWO). The authors are grateful to the children and their teachers for cooperating in this study. Furthermore, they would like to thank Iris Verbruggen, their colleague at the Freudenthal Institute for Science and Mathematics Education, for testing the coding. Very special thanks go to Petra Scherer, Bielefeld University, Germany, for the enlightening discussions about how to understand the children's utterances and for checking the final coding. The authors also are obliged to Lyn English and the anonymous reviewers of this article. Their critique to two earlier versions of it stimulated the improvement and report of the study considerably. The finishing touch came from Anne Teppo, who helped non-native speakers of English with making the authors' plain writings more sophisticated.

Notes

1. The PALM project group consists of: Marja van den Heuvel-Panhuizen (Freudenthal Institute, Utrecht University, the Netherlands and IQB, Humboldt University, Berlin, Germany), Sylvia van den Boogaard (Freudenthal Institute, Utrecht University, the Netherlands), Shuk-kwan Susan Leung (National Sun Yat-sen University, Taiwan), Yu-Liang Chang (Aldy) (Mingdao University, Taiwan), Petra Scherer (Department of Mathematics, Bielefeld University, Germany), and Hans Röthlisberger (Fachhochschule Nordwestschweiz, Pädagogische Hochschule, Liestal, Switzerland). The PALM project was launched in 2005 as a small-scale satellite project of the Dutch PICO-ma project (PIcture books and COncept development MAthematics), which is part of the multidisciplinary and multimethod four-year PICO study funded by the Netherlands Organisation for Scientific Research (NWO) into the use of picture books as a support to kindergartners' literary, social-emotional and mathematical development.

2. In the Netherlands, education is compulsory from the age of five, but most children go to school at age four when they start kindergarten. There are two kindergarten classes (K1 and K2), which form a part of primary school.

3. Sometimes such books are also called “picture storybooks” (Reeder, 1997). Mitchell (1994) used the term “imagetext” and described it as “composite synthetic works (or concepts) that combine image and text” (p. 89); and Lewis (2001) emphasized the ecology of the picture book, in which pictures and words “interact ecologically, [so] that the book acts as a miniature ecosystem” (p. 48).

4. The original German title is Fünfter sein. The Dutch title is Vijfde zijn and is published by Uitgeverij Ploegsma Amsterdam. In the United Kingdom and the United States the book is called Next Please.

5. Boekwijzer is developed by the University of Tilburg, Biblion Uitgeverij, Malmberg Uitgeverij, and KPC Group (see Ghonem-Woets & Mooren, 2001).

6. The book Vijfde zijn was given an award at an international children's books fair in Bologna, was nominated for an important German award, and won an award in the Netherlands. In November 1999, it was awarded with the “Pluim van de maand.” This is a monthly award founded by some children's magazines in the Netherlands (Bobo, Ouders van Nu, and Leesgoed) and the Utrechtse Kinderboekwinkel. The award is meant for books for children between three and eight years. The pictures by Norman Junge were also singled out for an award. In 2000, the book got an award from the “Penseeljury” in the Netherlands.

7. The codes refer to the page of the book (CF = front cover, EF = endpaper front, FF = French page front, TP = title page, 1 through 16 = page 1 to 16, EB = endpaper back, CB = back cover).

8. While preparing the international continuation in the PALM project, Petra Scherer discovered that the (original) German version has the ordinal number approach; for example, where the Dutch text reads “Now only four,” the German text reads “Being fourth.” Later on we found more remarkable differences between the different versions of the book, and even the English translation differs in the editions for the United Kingdom and the United States. Of course, differences like these can influence the effects of the picture book and need further research.

9. See Note 7.

Appendix

The Complete Dutch Text of the Book Vijfde zijn and its Translation into English

Table

Page	Dutch text∗	Translation in English
2	Deur open. Een eruit.	Door open. One out.
3	Een erin.	One in.
4	Deur dicht. Nu nog vier.	Door closed. Now only four.
5	Deur open. Een eruit.	Door open. One out.
6	Een erin.	One in.
7	Deur dicht. Nu nog drie.	Door closed. Now only three.
8	Deur open. Een eruit.	Door open. One out.
9	Een erin.	One in.
10	Deur dicht. Nu nog twee.	Door closed. Now only two.
11	Deur open. Een eruit.	Door open. One out.
12	Een erin.	One in.
13	Nu nog een. Dan ben ik.	Now only one. Then it is my turn.
14	Deur open. Een eruit.	Door open. One out.
15	Ik erin.	Me in.
16	Dag dokter.	Hello doctor.
∗We completed the text with punctuation marks and capitals.