Conclusiones y recomendaciones

The research focus for this study was on statistical reasoning within the Models and Modeling theoretical framework (Lesh & Doerr, 2003). From a Models and Modeling perspective, and therefore a task context perspective, the picture story book provided a realistic context used to authenticate and frame the modeling activity tasks, including the data modeling problem (Mousoulides, Sriraman, & Christou, 2007), and motivated and interested the children in expressing their statistical understanding (Doerr & English, 2003). In the modeling activities in this study, a picture story book acted to stimulate and contextualise the data modeling problem the children would engage with. The design of the data modeling problem embedded a need for the children to manage and make statistical sense of the problem, that is, the statistical idea to be worked, such as prediction or representing data, was integral to solving the problem (English, 2006). Knowledge needed for solving the problem included knowledge of the data context provided by the picture story book.

In addition to initiating and stimulating modeling, the picture story books used in this study fulfilled the role of providing the data context for the modeling problem to be solved. The data context in statistical problems is defined by

Pfannkuch (2011) as “the context of the real-world situation from which the problem arose (which is) inextricably linked to resolving the problem or learning more about the situation” (p. 28). The picture story book provided the real-world situation that gave rise to the data modeling problem. From a task context and data context perspective, the learning purpose for a picture story book in this study differed from a picture story book that might be chosen for specific instruction in mathematics, such as learning about shapes or number.

Examining characteristics of books that fulfill a statistical learning purpose was approached using existing classification frameworks for selecting books for mathematics instruction provide. Marston’s (2010) framework provides criteria for assessing mathematical content, including content that is incidental or unintentional, but still offers opportunities for ”mathematical problem solving and reasoning” (p. 387). On face value, the three commercially available picture story books, Michael

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Recycle (Bethel, 2008), Litterbug Doug (Bethel, 2009) and Charlie and Lola (Child,

2009) offer no discernible mathematical content. Any statistical content in the story is incidental or unintentional to the book’s primary purpose of entertaining. The three books provide a story plot that, given the children’s knowledge and experiences, encouraged them to make sense of a problem solving situation and moved them to recognise the need for a model to be developed to solve the problem (Lesh & Doerr, 2003). Classifying a story under Marston’s framework as affording problem solving and reasoning opportunities then is compatible with the Models and Modeling design intent, namely, the story initiate and stimulates a modeling problem for the children to work to a solution. The fourth picture story book, Baxter Brown’s Messy Room (English, 2009a) differed from the other three books in that it was written

specifically to initiate a data modeling problem. The statistical problem to be solved was embedded in the narrative content of the story. Using Marston’s (2010)

framework, Baxter Brown’s Messy Room can be classified as having content specific to the development of a mathematical concept, in this case, a statistical concept.

Although helpful, the unique role of picture story books in contextualising statistical problems is not accommodated by existing classification schemes. Finding support for determining picture story characteristics from comparable research is equally problematic for two reasons. First, with the exception of English (2009; 2010; 2011), children’s picture story books have not been used to initiate modeling activities for statistical problems solving with young children. Second, young children’s response to the characteristics of a picture story book that initiate and contextualise statistical problem solving has not been researched.

Capturing the children’s spontaneous and subsequent responses a picture story book in this study enabled characteristics of interest that support statistical reasoning to be explored. Prior studies on the role of picture story books in domain- specific mathematics learning, examined differences in categories of cognitive engagement of children’s spontaneous responses to fiction and non-fiction books (Moschovaki & Meadows, 2005) and child-initiated utterances as reactions to domain-specific mathematical phenomena in a book (Van den Heuvel-Panhuizen & van den Boogaard, 2008). This study proceeded on the same assumptions as the studies conducted by Moschovaki and Meadows (2005) and Van den Heuvel-

148 Panhuizen and van den Boogaard’s (2008). This study used similar methods to these studies to capture children’s spontaneous responses, and the picture story books were read without pre-empted questioning or probing by the teacher reading the story.

On the other hand, this study is distinguished in two ways from studies conducted by Moschovaki and Meadows (2005) and Van den Heuvel-Panhuizen and van den Boogaard’s (2008). First, the children’s responses were extended beyond their initial spontaneous comments or questions, to include questions or comments the children initiated immediately following the book reading. Second, this study sought to identify whether the characteristics that were of interest to the children were used as they subsequently engaged in statistical reasoning in the modeling activities (presented in Chapters 6 and 7). Discussion of the children’s responses to the picture story book is next.

5.7.3 Limited and Misdirected Interest

The children’s interest in the picture story book Michael Recycle (Bethel, 2008) was limited, and interest that was evident was misdirected from the story content that supported the modeling problem. These findings contrast with interest generated by the other three picture story books used in the study. Michael Recycle stimulated limited interest for the children in this study and the children’s only spontaneous response when Michael Recycle was read was to the rhyming in the book title. The children’s disinterested responses were demonstrated in their physical responses and lack of spontaneous comments as the book was read. The lack of spontaneous responses suggests that the story did not stimulate mental processing (Moschovaki & Meadows, 2005; Van den Heuvel-Panhuizen & Boogaard, 2008) or provide information that was interesting or personally meaningful to engage the children’s attention (De Young & Monroe, 1996). The story had a predictable story line and lacked mystery and it is possible that this failed to provide an authentic connection for the children (Nesmith & Cooper, 2010).

Misdirected interest in the story was revealed in the children’s comments and questions following the initial book reading. The book character Michael Recycle prompted animated debate about whether he was male or female due to the children’s perceived ambiguity observed in the book’s illustrations. Illustrations are part of the

149 whole picture book and can represent story-related components, so they have the potential to cognitively engage and interest children (Elia et al., 2010). In the book Michael Recycle, the children’s interest in the characters sex can be interpreted as a mystery to be solved or as tapping into core questions of gender identity for young children. The children’s responses highlight the importance of combining text and illustration of a similar content for books used to contextualise statistical problems. Ambiguity between text and illustration may be a useful tool for stimulating

discussion however, as a characteristic for stimulating interest in model development to solve a statistical problem this study found that ambiguity in the illustrations served to misdirect or distract the children’s attention away from other elements of the story, such the problem in the plot used to frame the modeling problem.

The picture story book Michael Recycle failed to generate any responses in the children to indicate enjoyment of the storyline, a liking for the character or interest in the problem in the story. The plot in the story reached a climax that was fully resolved by the characters within the story itself; Michael Recycle cleaned up the village successfully, and without fuss. The limited and misdirected interest by the children, particularly with respect to the plot may be explained by the findings of interest in the other three picture story books which are discussed next.