What counts in number books? A content-domain specific typology to evaluate children’s books for mathematics

Abstract

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as counting books. These counting books were complex with regard to portrayal of counting sequences, explicitness of counting, and degree of rationality. The analysis yielded the multi-dimensional Counting Book Typology, which revealed nuanced ways counting books accurately portray numerical ideas as well as ways books could mislead young readers. The typology could aid researchers investigating how children learn with books to focus study design decisions on particular mathematics content features, which would clarify and strengthen resulting implications. Furthermore, this study revealed the need for more such conceptual tools to advance theorizing about learning math with children's books, which has been missing in research and practice.

“Books I Used as a Child were Mathematically Incorrect”: Reasons to Use Children’s Shape-Related Books as a Resource to Improve Mathematical Knowledge for Teaching

“…Although children's books are increasingly promoted for mathematics learning, there is little rigorous research evidence that such instruction is effective (Flevares & Schiff, 2014). Moreover, when researchers intend to determine the efficacy of using children's books to improve mathematics learning, they should rigorously critique the books' mathematics content prior to use, which so far has been uncommon (Flevares & Schiff, 2014;Nurnberger-Haag, 2017, 2018Nurnberger-Haag et al, 2019;Nurnberger-Haag, Alexander & Powell, 2021). In a content analysis of the mathematical quality of 69 children's books about shapes, about half conflated 2D and 3D shapes, and 76% showed or stated an inaccuracy about 2D shapes (Nurnberger-Haag, 2017).…”

A Field Guide to Whole Number Representations in Children’s Books

“…Another study that focused only on those books that presented numbers in sequence, which Nurnberger-Haag et al, (2020) defined as counting books, categorized these books by how explicitly the pictures of objects represented sequences. They defined three categories on the rationality dimension of the Counting Book Typology: sequences of numbers without images (Rote Counting Books), sequences of numbers with corresponding pictures to represent each term of the sequence without grouping (Rational Term Counting Books), and those books that consistently grouped images of each term (Rational Scalar Counting Books; Nurnberger-Haag, et al, 2021). In other words, Rational Term Counting Books simply provided children the opportunity to learn the cardinality of each number that happened to be in a sequence, whereas Rational Scalar Counting Books provided visuals that represented the change in quantity from term to term (e.g., if a book provided written symbols of numerals of even numbers in sequence, the number four was pictorially represented as two groups of two, six as three groups of two, eight as four groups of two and so forth so that the change or addition of 2 from term to term was visually accentuated; Nurnberger-Haag, et al, 2020).…”

“…Reference books such as math dictionaries, encyclopedias or workbooks were excluded. Following the definition of number-related books as books with at least two instances of numerals or number words (Nurnberger-Haag, et al, 2021), the mathematical criteria for selection in this study were two instances of whole numbers (i.e., not fractions, decimals, percents, nor measurement) on at least two separate pages represented as numerals or number words. Books were retained for analysis if the intended meaning of the pictures could be determined in relation to one or more written symbols.…”

“…Second, this field guide with 103 traits, inspires the field to recognize the extent of diversity of number representations that are possible. For although the numbers used in children's books have been shown to be overly simplistic, often focusing within 10 (Powell & Nurnberger-Haag, 2015;Ward et al, 2017), recent research on a specific kind of number-related book, counting books revealed that the ways sequences are portrayed in children's books are quite varied with eight counting sequence types (Nurnberger-Haag et al, 2021). In other words, children's number books are more varied and should be more varied than adults would expect for a topic they might view as "simple" (Lee & Ginsburg, 2009;Nurnberger-Haag, et al, 2021).…”

“…For although the numbers used in children's books have been shown to be overly simplistic, often focusing within 10 (Powell & Nurnberger-Haag, 2015;Ward et al, 2017), recent research on a specific kind of number-related book, counting books revealed that the ways sequences are portrayed in children's books are quite varied with eight counting sequence types (Nurnberger-Haag et al, 2021). In other words, children's number books are more varied and should be more varied than adults would expect for a topic they might view as "simple" (Lee & Ginsburg, 2009;Nurnberger-Haag, et al, 2021). The Field Guide to Whole Number Representations in Children's Books contributes evidence on a wider range of books than counting books to describe the complexity of representations in whole number-related books.…”