Running head: MATHEMATICS & PRESCHOOLERS 1. Mathematics & Preschoolers: Helping Teachers Incorporate. Meaningful Learning into Everyday Activities

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1 Running head: MATHEMATICS & PRESCHOOLERS 1 Mathematics & Preschoolers: Helping Teachers Incorporate Meaningful Learning into Everyday Activities Tom Chiaromonte, Ph.D. 1, Jenn Kinkel, M.A. 2, Mark Whitney, Ph.D Department of Child Development & Educational Studies, Fullerton College; 321 E. Chapman Avenue, Fullerton, CA Department of Early Childhood Education, Huntington Beach City School District; Beach Blvd. Suite 560, Huntington Beach, California Department of Child Development, Mira Costa College; 1 Barnard Drive, Oceanside, CA Note: The authors would like to thank the children, families, staff, and teachers of the Child Development & Educational Studies Laboratory School at Fullerton College for their help and participation with this paper.

2 MATHEMATICS & PRESCHOOLERS 2 Abstract Mathematics is a natural part of the preschool environment. Young children actively construct mathematical knowledge through everyday interactions with their environment, whether inside or outside (California Preschool Curriculum Framework Vol. 1, 2010). While this statement reflects the sentiment of many early childhood professionals, there are still a great deal of teachers of young children who resort to didactic methods of instruction when teaching mathematics, utilizing packaged materials including worksheets and other activities with limited child participation. This paper will examine applied methods of teaching mathematics to young children utilizing a constructivist pedagogy. All of the images presented were taken at a laboratory school in a large suburban community college in southern California. This paper was presented at the 32 nd annual conference of the Association for Constructivist Teaching, Union, New Jersey, October, Keywords: Mathematics education, constructivist pedagogy, inquiry based learning, didactic instruction

3 MATHEMATICS & PRESCHOOLERS 3 Teaching mathematics to young children: A practice based in anxiety While some teachers of young children embrace every opportunity to teach mathematics, or really any STEM based curricula, many others find it to be a difficult concept to teach appropriately. This could possibly be due to the teacher s lack of knowledge as to what preschoolers are capable of understanding or what activities are best suited or developmentally appropriate for young children. It might be due to the teacher s own math anxiety, something described as a feeling of tension, apprehension, or fear (Ashcraft, 2002). Or it could also be possible that some educators might feel that preschool-aged children, specifically those transitioning to kindergarten, should be plied with worksheets and other forms of didactic instruction. This may be due to a misunderstanding that these forms of instruction will better prepare children for the push down curriculum found in many elementary school classrooms. The challenge then, especially for those who work with preservice teachers, is how to build within the educator an understanding of what a young child s mathematical needs are and how to create rich environments for these children that will naturally build upon the preschooler s very real need for discovery, inquiry, and social cognition. This paper will present ideas on how to build upon these aspects of the child and create learning environments that will invite, challenge, and enlighten the child s natural mathematical abilities. The mathematical child Children from a very early age seem to have a keen awareness of and budding interest in the rudimentary concepts of mathematics that only builds as the child gets older. A toddler certainly understand the concept of addition as he asks for more crackers, while the preschooler

4 MATHEMATICS & PRESCHOOLERS 4 deals with one-to-one correspondence as she navigates the snack table with a bowl of five apple slices and four hungry friends. So what is it exactly that young children need to become proficient mathematicians within their classrooms and beyond? First of all, the child s working memory is needed for short term storage and retrieval of information. This usually begins in the second half of the first year of life and later becomes a tool for learning such mathematical tasks as counting, addition, subtraction, classification, and patterns as the child gets older. The child also needs to have the Piagetian concept of symbolic function, or the mental representation of objects, images, and number. As the child thinks about these items, they can drawn upon mentally and added to, taken away from, sorted and compared infinitely. There is also a needed basic understanding of number. During the preoperational period children will gain the concepts of counting, number knowledge (understanding of the value/quantity of numbers), number transformation (addition & subtraction first in the hand then in the mind), estimation, and number patterns (extending number patterns, and discerning numerical relationships). With these newly developing skill sets, children are even more ready to explore the mathematical world that surrounds them. Now for the bigger task at hand, helping teachers understand how to create an environment that provides for meaningful learning. Creating the environments, providing the time, supporting the learning In order for children to be engaged in mathematics or any learning for that matter, environments, materials, and teachers must be engaging. In their position statement Early childhood mathematics: Promoting good beginnings, (Author, 2010) the National Association for the Education of Young Children, and the National Council of Teachers of Mathematics, listed

5 MATHEMATICS & PRESCHOOLERS 5 ten demands absolutely needed for children to engage in the principles of high quality mathematics learning. This paper will elaborate on three of the ten demands and will provide an example for each. For a complete list, the reader is encouraged to obtain a complete copy of the NAEYC/NCTM position statement. The curricula that is listed here all took place in a laboratory school at a large, suburban community college in southern California. 1. Enhance children s natural interest in mathematics and their disposition to use it to make sense of their physical and social worlds: The Pumpkin Project Fall in southern California is not as cool as it is in many other parts of the country. However, just like in many other parts of the country, pumpkins and other varieties of gourds are plentiful at this time of the year and are always of interest regardless of address. The laboratory school children began showing interest in this late season squash like so many children do. Teachers started the dialogue with children and brought out literary materials, creative art materials, and manipulatives and asked parents to provide the classrooms with pumpkins. The response was overwhelming and teachers got to work developing an inquiry based project that would enhance the children s knowledge of pumpkins utilizing mathematics and other aspects of social cognition. First the pumpkins were sorted by shape, size, color and variety. This information was documented utilizing many mediums including measuring, charting, drawing, painting, and even making clay representations. The children were interested in growing their own pumpkins, so a few pumpkins were cut open, the seeds explored, sorted, counted, dried, some were eaten, and some were planted into cups to produce seedlings. These seedlings were eventually transplanted and the

6 MATHEMATICS & PRESCHOOLERS 6 growth process will continue to be charted. Of course planting seedlings in the late fall is not recommended in colder climes. As the fall season continued the children began discussing the possibility of cooking and eating the pumpkins themselves. Working with the laboratory school chef and parents, the teachers and children began to look at recipes that included pumpkins. Two were of most interest, a pumpkin soup using Thai flavors introduced by one of our families, and a traditional pumpkin pie. As any chef and mathematician knows, recipes are full of numbers, quantities, sorting, and other mathematical concepts. Measuring, adding of ingredients, mixing, timed cooking, ladling out of the soup and cutting the pie were all aspects of mathematics learning as well as aspects of the children s physical and social world. This project took several weeks to move through and will actually continue as the seedlings begin to further their growth. It brought together mathematical concepts with aspects of the child s physical and social worlds, creating an inquiry based project utilizing a constructivist pedagogy. A child uses a measuring tape to figure out the circumference of a pumpkin.

7 MATHEMATICS & PRESCHOOLERS 7 2. Integrate mathematics with other activities and other activities with mathematics: Roly Poly Investigation Every garden in every yard contains the ubiquitous sow bug. This roly poly quietly lives amongst the dead and dying debris, is able to defend itself by tucking its many legs into its plated shell, and of course is loved by children everywhere. But just how many legs does a roly poly have to tuck in? While there are a few ways to correctly arrive at the answer, thorough investigation, utilizing an array of activities allows the child to not only come up with the definitive answer, but also leave behind documented proof of their findings. This was the question posed by a few of the children at the laboratory school. Books were read, and although there were ample drawings and photos contained in the pages, the roly poly s legs were difficult to completely count when one is really just looking at a two-dimensional bug on a page. Children and teachers discussed this dilemma as well as possible ways to find the answer, all agreed that it was best to investigate the bugs both in their natural environment as well as collecting a few for closer observation. Magnifying glasses, bug cages, clipboards and pencils were gathered, along with the referenced texts and the investigation began. It was determined that a large number of the bugs lived in close proximity to an outdoor dramatic play area, and while it was a bit difficult to get an accurate count as the bugs moved in and out of the dead leaves, it wasn t difficult to collect some lively specimens. These were brought back to the classroom and placed on large sheets of white butcher paper for easier observations. With the

8 MATHEMATICS & PRESCHOOLERS 8 magnifying glasses and clipboards at the ready, the children began counting as the roly polies made their way across the paper. To get the most accurate count, some of the bugs needed to be corralled, unit blocks were brought in for this purpose. After close investigation, the children concluded that all roly polies have seven pairs of legs, fourteen in total and they also have a pair of antenna. The children took this information to the easels and documented their discovery. All too often adults, including teachers of young children, are quick to give answers to the many questions children ask. By providing children with opportunities to read, investigate, and document, using an array of materials, children gain a deeper understanding of the mathematical world that surrounds them. A few representations of roly polies complete with an accurate count of seven pairs of legs. Note the slightly curved line at the far left, this represents the roly poly s antenna.

9 MATHEMATICS & PRESCHOOLERS 9 3. Provide ample time, materials, and teacher support for children to engage in play, a context in which they explore and manipulate mathematical ideas with keen interest: The Builders Group The campus where the laboratory school is located has a collection of rich, old, Spanish style buildings. Teachers and children make their way across campus for many outings, sometimes just to admire the architecture. After one such adventure, the teachers and children began to discuss replicating the campus environment at the laboratory school. The group went back to campus, now equipped with clipboards, paper, markers, pencils, and cameras. As the children sketched the buildings, the teachers took photographs. Arriving back at the laboratory school a discussion was had about the use of buildings, the straight lines and geometric shapes contained in the architecture, and how they were going to recreate the campus buildings with the materials they had. The laboratory school has specialized classrooms or studios, just for the exploration of these types of ideas. One of these is the construction studio where children can create with unit blocks, ramps, loose parts, recycled materials and other design elements. The children got busy taking their sketches and replicating them with the unit blocks, other wooden geometric shapes, transparencies, and clay. Some children were designing specific aspects of the buildings like archways and doors, while other children were designing the entire building. Each representation was photographed, talked about, and placed in the Builders Group notebook. As children wanted to continue their designs they would refer back to the notebook and then add to the building. This process literally went on for months as the representations were designed and redesigned. Children began to see relationships

10 MATHEMATICS & PRESCHOOLERS 10 between lines and geometric shapes, and not only discovered the mathematical principles used in construction, they began to see the relationships of these lines and shapes in numbers and letters. The Builders Group became a multifaceted project as children began to write using the lines and curves to make letters and words, evolving into a literacy project. Helping children understand the mathematical world that surrounds them takes ample amounts of time. By continuing a project over days, weeks, or even months not only helps to solidify mathematical concepts, it can also bring about ideas not originally thought of in the original concept. Archways are just one of the many interesting shapes on campus

11 MATHEMATICS & PRESCHOOLERS 11 An elaborate representation of campus complete with buildings, archways and bridges Two more representations of campus with clay and drawing

12 MATHEMATICS & PRESCHOOLERS 12 An enlarged photograph of a block building with added inked details Conclusion It certainly seems as if children are born mathematicians, and even if this is not necessarily true, we do know that they live in a world rich with mathematics. Helping children uncover this world comes not through the numerous skill and drill didactic worksheets that are unfortunately the staple of so many early childhood classrooms, but rather through everyday activities. These can be intentionally set up or can be found capriciously throughout the classrooms and yards in

13 MATHEMATICS & PRESCHOOLERS 13 every early childhood setting. Teachers can embrace and expand upon the child s mathematical knowledge by having a keen eye, a perceptive imagination, an open mind and above all a willingness to observe and listen to children as they embark on this wonder mathematical journey. References Ashcraft, M.H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Directions in Psychological Science, 11, California Department of Education (2010). California preschool curriculum framework: Volume 1. Sacramento, CA: Author. National Association for the Education of Young Children (2010). Early childhood beginnings: Promoting good beginnings. Washington, DC. Author.