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Identifying mathematics in children's literature: year 7 students' results

Pamela Perger
Pamela Perger is a lecturer in mathematics education at the University of Auckland


This article is adapted from the author's paper of the same title, published as part of the MERGA 2011 conference proceedings. Permission to republish gratefully acknowledged.


Children's literature is now recognised as a means to assist the teaching and learning of mathematics, although the responsibility to maintain the integrity of both curriculum areas is a challenge for many teachers (Perger, 2004). Over time, a range of resources have been produced to support teachers in using literature in their mathematics programs.

However, there are debates on how best to use children's literature for this purpose. One key debate concerns the level of support required by children to recognise mathematical concepts within the literature, and the sort of adaptations to text and/or illustrations needed for this to occur. At one end of the argument, Schiro (1997) states mathematical information needs to be presented explicitly to the reader, in digit and/or equation format, in both text and illustrations. At the other end of the scale, Van den Heuvel-Panhuizen and Van den Boogaard (2008) believe that young children are able to identify mathematical ideas without a teacher's prompting. 

This article presents the results of a study to identify the extent year 7 students could identify the mathematics in children's literature. The article is adapted from the paper of the same title, published as part of the MERGA 2011 conference proceedings.


The study

This study focused on two questions:

  1. Could students identify the mathematics in a storybook without being given any indication that mathematical concepts/opportunities were present?
  2. What mathematics do students identify in a story, when there is no indication of mathematical content, but when they are told mathematics is present?

To answer these questions, a group of year 7 students (11-year-olds) were given two tasks that examined their ability to identify mathematical learning opportunities within children's books. The students were of mixed ability in both mathematics and reading. They were approaching the end of their first year at intermediate school, and the tasks were completed as part of their normal class program.

The students had been exposed to children's books throughout the year, although never in their mathematics program. The 30 books used in this study (listed in the original paper, Appendix A) all included some mathematical concepts. They varied in the mathematical topics covered, in the complexity of these topics, in the visibility of the mathematical content, and also in the degree of reading difficulty they posed.

Book review (Task 1)

The first task was to select and review one of the books. As part of the review, students were asked to identify how a teacher might use the book in their classroom program, but students were not given any indication which areas of the curriculum or age level the books could be used for. This task involved 16 students.

The majority of students were able to identify the mathematics even when not alerted to its presence: 13 recognised mathematical learning possibilities for a teacher within the book they had reviewed. These students identified learning opportunities related to number, measurement (size) and geometry (shape). Here are some extracts from their reviews:

If I were a teacher the children in my class would learn how to divide in half. 
(The Great Divide, Dodds, 2000)

If I were a teacher children will learn how to multiply, add and learn more about maths.
(Anno’s Mysterious Multiplying Jar, Anno & Anno, 1982)

If I were a teacher the children would learn how to find the area of a circle and how to measure.
(Sir Cumference and the Dragon of Pi, Neuschwander, 1999)

Two students elaborated further on the mathematics children could learn if a teacher used the book they had reviewed. One wrote:

Children could learn how zeros make a number even bigger and numbers never end. They could also learn how to count from one to a googol; which has 100 zeros! You can also learn the names of other huge numbers.
(Can You Count to a Googol? Wells, 2000)

Another student included detail of a task he would set the class:

If I were a teacher I would get my students to find out how many humpback whales and dogs would fit in the classroom and how many peas would fit in a bowl. The students would learn about measurements like metres, centimetres, and weight.
(Counting on Frank, Clement, 1990)

When identifying mathematical possibilities for a teacher, four students were confident enough to recommend an age group for the book they reviewed, on the basis of the curriculum areas or interests it covered. All the age levels they suggested were suitable for the story and for the level of mathematical challenge it posed.

The students perceived that books with a strong mathematical content could also enrich learning in other curriculum areas, such as reading, language (narrative text), and science, supporting claims made in this regard by Whitin and Whitin (2004) and Griffths and Clyne (1991).

Five students identified opportunities for learning in other areas of their lives, on themes such as 'love and romance' and 'wisdom'. These are the sort of connections that Griffths and Clyne, as well as Whitin and Whitin, had suggested to be the responsibility of teachers.

Only three students failed to identify any opportunities for mathematical learning in their books. Two of these students had chosen books where the mathematics was relatively hard to identify.

Identifying the mathematics (Task 2)

After a 20-minute break, students undertook a second, more mathematics-focused task: to list possible mathematical learning opportunities in one of the 30 books. For this task students were alerted to the fact that the books had been purchased for use in mathematical programs, but they were given no information about what particular mathematical concepts each book contained. This task involved three additional students, once again of mixed mathematics and reading ability. The students who had been involved in the first task were asked to choose a different book for task two.

All 19 students were able to identify appropriate mathematical learning possibilities. Students identified mathematical concepts associated with number (11 books), measurement (seven books) and geometry (three books).

The mathematics identified in this second task was more detailed than in the first. An example is students' differing treatment of the book The Dot and the Line (Juster, 1963) between tasks one and two. In the first task, when no indication of mathematical content was given, a student described the book as including 'some mathematics shapes'. In the second task, when students were alerted to the mathematical content, more specific mathematical learning was identified, with one student stating: 'children could learn shapes – squares, triangles, hexagons, parallelograms, rhomboids, polyhedrons, trapezoids, decagons, tetragrams as well as angles'.

Some students once again made links to other kinds of learning opportunities, relating, for example, to riddles and rhymes, history, reading and science. One student also made links to more general aspects of mathematics such as problem solving ('being able to answer mathematics problems').

Another student linked mathematics to everyday life. In reference to the book Maths Curse (Scieszka, 1995) she concluded her list of possible mathematical learning with the sentence, 'Children can learn that maths is all around us and mathematics has real life applications and is very important'. 


Conclusion

The year 7 students in this study showed that they could identify opportunities for mathematical learning present within samples of selected children's literature. In many cases they noted that these mathematical ideas could be linked to a wider field of knowledge – both other curriculum areas and life skills.

They made these links without the books having had text or illustrations adapted to highlight this mathematical content, as recommended by some authors. In fact, it is possible that if such adaptations had been evident in the text or illustrations of these books, the mathematical opportunities may have been limited to those of the authors, and students may not have made the wider links they did to other curriculum areas or to general life skills.

When alerted to the presence of mathematical content, the students' descriptions of mathematical possibilities were even more detailed. This would indicate that although students can independently identify the mathematics in children's literature, the input of a teacher could further enhance learning opportunities. With a student's ability to recognise the mathematics and a teacher's careful selection and introduction of books, the use of children's literature could be a powerful tool in both motivating and consolidating mathematical knowledge.


References

Anno, M., & Anno, M. (1982). Anno's Mysterious Multiplying Jar. New York: Penguin.

Clement, R. (1990). Counting on Frank. Sydney: Collins.

Dodds, D. A. (2000). The great divide. London: Walker Books. 

Juster, N. (1963). The dot and the line. New York: Random House.

Moore, I. (1990). Six dinner Sid. London: MacDonald Young Books.

Neuschwander, C. (1999). Sir Cumference and the Dragon of Pi. USA: Charlesbridge.

Perger, P. (2004). Using literature to launch mathematical investigations. In B. Tobias, C. Brew, B. Beatty & P. Sullivan (Eds.), Proceedings of the 41st Annual Conference of the Mathematical Association of Victoria: Towards Excellence in Mathematics (pp. 377–385). Melbourne, Australia.

Schiro, M. (1997). Integrating Children's Literature and Mathematics in the Classroom: Children as Meaning Makers, Problem Solvers, and Literary Critics. New York, NY: Teachers College, Cumbria University.

Scieszka, J. (1995). Math Curse. London: Penguin.

Thraikill, C. (1994). Math and literature: a perfect match. Teaching K–8, 24(4), 64–65. 

Van den Heuvel-Panhuizen, M., & Van den Boogaard, S. (2008). Picture books as an impetus for kindergartners' mathematical thinking. Mathematical Thinking and Learning 10, 341–373.

Wells, R. (2000). Can You Count to a Googol? Chicago, IL: Albert Whitman.

Whitin, D. J., & Whitin, P. (2004). New Visions for Linking Literature and Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Key Learning Areas

Mathematics

Subject Headings

Children's literature
Mathematics teaching