# Cowboys Count, Monkeys Measure ## Preface **Jane W.**: My children say I live in a different world—a mathematics world! **Jane K.**: My family says I live in a different world—a young child world! **Mary N.**: My friends say I live in a different world—a children’s book world! We have brought our three worlds together in response to the requests of teachers of young children. As we have listened to our teacher friends talk about their mathematics experiences, as children and as educators, we recognize ourselves. Many teachers resemble Jane W., who enjoys thinking about numbers and patterns; she plays with mathematical possibilities simply for the joy of engaging in the process. Many teachers tell us they resemble Jane K., who enjoys thinking with young children; she plays with the child perspectives simply for the joy of engaging in the process. Many teachers tell us they resemble Mary N., who enjoys thinking with storybook characters and contexts; she plays with literature responses simply for the joy of engaging in the process. The three of us bring similar but different mathematical lenses to our work with teachers and children. Jane K. wishes she had learned about meaningful mathematics when she was a child. Many decades ago, she learned mathematics was memorizing procedures to get the one right answer. Now, Jane K. knows that young children construct knowledge about mathematics all through their early lives. Jane W. wishes everyone could see and understand that mathematics is around us all of the time. Many decades ago, she learned mathematics was a way of contributing to the world as a means to solve problems, reason logically, and prove numeric and geometric relationships. Now, Jane W. knows young children with mathematical knowledge and problem-solving skills will learn to reason and apply critical thinking all through school and contribute solutions to world problems as adults. Mary N. wishes all children could enjoy the authentic mathematics that surround characters in storybooks. **What Is the Role of Storybooks in Mathematics?** Storybooks bring children into imaginative worlds where fascinating things happen. They appeal to children’s emotions and capture their interest through vivid illustrations, stimulating plots, and exciting characters. By linking mathematics within storybooks, teachers are able to contextualize mathematics by associating it with circumstances and things that occur in the storybook worlds and in children’s real worlds. Placing mathematics in a meaningful context helps children relate to mathematics and make sense of the mathematics. Thus, the mathematics becomes real. **What Is Authentic, Meaningful Mathematics for Young Children?** Mathematics is the “search for sense and meaning, patterns and relationships, order and predictability” (Copley, 2000, p. v.). Mathematics is not repetitively enacting a procedure to get a right answer to an irrelevant question. It involves actively engaging young learners in constructing new ideas and helping them reflect on what they are doing and why. Meaningful mathematics entails having young children use manipulatives and number charts to see how numbers and facts are related and help them discover patterns and rules. Mathematics should focus on having children talk about their thinking and have them experience opportunities where they apply reasoning and logic to solve problems. **When Do Children Begin to Think Mathematically?** Infants engage in the process of making sense of the world around them. In order to make sense and meaning, infants must deal with number, shape, size, and patterns. Toddlers know more from less, count, play with toys that provide them practice in evaluating sizes and shapes, and sort items based on classifications such as edible and non-edible. Preschoolers use mathematical thinking to work imagined and real-world problems by sharing, dividing equally, and figuring out pegboard patterns. Even more important, young children explore, examine, discover, alter, accommodate, adapt, and question constantly. As they do so, they are searching for meaning, patterns, and interrelationships. **What Can Teachers Do to Enhance Children’s Mathematical Thinking?** Children are very inquisitive and want to know about their world. One way teachers can stimulate children’s mathematical thinking is by posing open-ended questions that require children to explain or describe a process rather than just give an answer. Limiting the number of lower level questions posed in the classroom and focusing more on higher level questions helps to stimulate their higher order thinking skills. ## The Aim of the Book This book is written for prospective as well as experienced pre-K–3 teachers who are interested in stimulating children’s mathematical thinking by teaching mathematics in a way that encourages children to think about mathematical relationships and solve problems beyond those that emphasize routine procedures. We show how teachers can use storybooks as the context for mathematical problems and questions that are rich and meaningful to children and engage them enthusiastically in mathematical thinking. ## Structure of the Book The book is divided into two sections: 1) Mathematics and Storybooks and 2) Instructing with Storybooks. ## Kindergarten ### Kindergarten Curriculum Focal Points - **Numbers and Operations:** Representing, comparing, and ordering whole numbers and joining and separating sets - **Geometry:** Describing shapes and space - **Measurement:** Ordering objects by measurable attributes At the kindergarten level, the curriculum focuses on counting activities, creating and comparing sets, ordering numbers, and classifying objects into sets. Simple readiness activities for addition and subtraction and identifying and counting coins are emphasized as well. ### Lesson Plan: Kindergarten Example **Book**: Chen, C.-Y. (2004). Guji Guji. **Synopsis**: When a crocodile egg rolls into a duck nest, the emerging baby, Guji Guji, is raised by a mother duck and plays happily with brother and sister ducklings. One day some scary, snarling creatures inform Guji Guji that he is not a duck but a misplaced crocodile. Instead, Guji Guji thinks and thinks and figures out a way to save his duck family. **Materials**: Cutouts of rocks with numbers 1–12 on them **Numbers and Operations**: Representing, comparing, and ordering whole numbers and joining and separating sets - Guji Guji does not look like the other baby ducks. What does Guji Guji look like? Let’s see if we can all count to 12. - Guji Guji wants to know if we can help him figure something out. He counted three ducklings with spots and four ducklings with stripes, and he wants to know if there are more ducklings with stripes or spots? How could we find this out? **Geometry**: Describing shapes and space - The teacher can hold up different shapes from pattern blocks, die-cuts, or three-dimensional objects to pose the questions. **Measurement**: Ordering objects by measurable attributes - I wonder if Guji Guji ever wondered why he was so much bigger than his other family members. Do you think we could help Guji Guji find out if he is really a duck or really a crocodile?