Let's Talk About Math: The LittleCounters® Approach to Building Early Math Skills
reviewed by Gerunda B. Hughes - July 06, 2015
Title: Let's Talk About Math: The LittleCounters® Approach to Building Early Math Skills
Author(s): Donna Kotsopoulos & Joanne Lee
Publisher: Paul H. Brookes Publishing Company, Baltimore
ISBN: 1598575899, Pages: 152, Year: 2014
Search for book at Amazon.com
During my forty plus years in higher education in general, and mathematics education in particular, I have seen all types of educational reforms come and go. Each reform is proposed with the good intentions of improving both the educational experiences and outcomes of various constituencies. Most reforms, though not all, are grounded in sound research that provides compelling evidence to inform educational practices. Most often the focus of the educational reform is children or students defined by their age, grade, achievement level, race/ethnicity, or the socio-economic status of their family. Sometimes the focus of the reform is on teacherstheir preparation, particularly their knowledge, skills and dispositions, or their credentialing. Yet through it all I have always believed that no educational reform that involves children will ever be truly successful without the committed involvement of caring adults, especially parents or guardians.
Lets Talk About Math: The LittleCounters® Approach to Building Early Math Skills is not about educational reform. Rather, it is about informing parents or guardians about the ways in which they can interact with their children to build early mathematics skills. Other adults such as caregivers, grandparents, early childhood educators, and teachers are also part of the conversation, but Kotsopoulos and Lee make every effort to speak primarily to parents or guardians.
The impetus for writing Lets Talk About Math stems from the interdisciplinary research collaborations of Dr. Donna Kotsopoulos, whose expertise is in mathematics education and developmental psychology, and Dr. Joanne Lee, whose expertise is in early childhood cognitive development and psycholinguistics. Metaphorically speaking, the collaboration between Kotsopoulos and Lee is like a partnership made in early childhood mathematics education heaven. A primary aim of their research is to examine the ways in which adults can effectively use mathematical play and language to develop counting and other basic mathematics skills in children between birth and formal schooling. Little Counters®, the workshop series, as well as the book, are products of that research.
Chapter One outlines what the research from psychology, neuroscience, cognition, and mathematics learning tells us about early mathematical understanding, ability, and development. In fact, research shows that infants as young as one week old are able to differentiate among groups with one, two, and three objects (Antell & Keating, 1983). This result leads some scientists to believe that children have more innate mathematical ability than adults might think (Carey, 2009). The research also focuses on counting. Counting is the cornerstone of early numeracy competence (National Council of Teachers of Mathematics, 2000). It involves both knowledge of the meaning of numbers and knowledge of numbers and words. Hence, the ability to count objects, beyond detection of more or less, depends on a childs ability to communicate in a system that matches quantities to words and vice versa. Counting with meaning is a critical developmental milestone and sets the foundation for other mathematical understandings. Kotsopoulos and Lee refer to this type of counting as object counting because it links words with quantities in ways that allow children to answer the question how many? and helps in developing the concept of one-to-one correspondence (Clements & Sarama, 2009).
In Chapter Two, Kotsopoulos and Lee explore different types of play, and how play, as well as routine daily activities, can be organized in ways that maximize childrens mathematical learning. There are, however, important principles that must be respected by adults in the play environment in order for learning to occur: the play must be relevant and engaging to the child and must also be developmentally appropriate (NAEYC, 2009). Kotsopoulos and Lee introduce three types of play: free play, play-based learning, and purposeful play. Of the three types of play, purposeful is the most effective for developing childrens early mathematical learning, mathematical knowledge, and skills because it involves the intentional and spontaneous engagement of talk or actions by the adult with the child with the implicit intent of facilitating learning. And although purposeful play combines with free play and play-based learning, unlike the others, it also involves the assessment of learning during play in which an adult will: check for understanding; provide feedback; and advance learning within the childs zone of proximal development.
The workshop series, LittleCounters®, which Kotsopoulos and Lee introduced in 2009 is described in Chapter Three. LittleCounters® is a community-based workshop which consists of five 45 minute sessions and utilizes five key educational developmental approaches: (a) begin with developmentally appropriate countable sets; (b) start with forward counting first; (c) use fingers and gestures to count; (d) name it (say it), touch it (say it), move it (say it), say it!; and (e) count everything and anything. The workshops are interactive and the facilitators model and introduce early mathematical concepts through purposeful play using toys, games, songs, stories, and poems. Children can attend with the adults. The authors stress that Little Counters® is not a curriculum, nor does it advocate direct teaching during purposeful play.
In Chapter Four, Kotsopoulos and Lee show adults how to increase mathematically relevant talk in their everyday conversations with young infants, toddlers, and preschoolers. Mathematical talk is simply using numbers or quantity words to talk about everyday things. Additionally, in Chapter Five, Kotsopoulos and Lee expand the discussion of other kinds of mathematical thinking that can be introduced to children through play or talk at very early ages. These include visual representations or geometry, measurement, addition and subtraction, patterning and early algebra, estimation, proportional reasoning, and problem solving. Fundamentally, all of these forms of mathematical thinking require an understanding of counting and numbers and are connected to each other. The key is for adults to help children make those connections prior to entering formal schooling. In fact, Chapter Six contains a variety of informal, everyday activities that offer great opportunities for children to make connections and learn about numbers through talk. These everyday activities include meals, bedtime, chores, grooming, and organization, and time.
In Chapter Seven, Kotsopoulos and Lee acknowledge the role of professional organizations such as the National Council of Teachers of Mathematics (NCTM) and the National Association for the Education of Young Children (NAEYC) in providing guidance for both parents and teachers about developmentally appropriate mathematics education for young children. They also provide suggestions about how parents can remain actively engaged and involved in their childrens mathematics education as they transition to formal schooling. Teachers also have a role in keeping parents involved. Doing so will go a long way in dispelling common myths about who can and cannot learn mathematics.
Lets Talk About Math is an excellent resource for reviewing the research on the development of early mathematics skills in young children and for identifying gaps in the literature that are ripe for exploration. The appendices contain titles of books, as well as songs and poems that can be used to stimulate or support mathematics learning in young children. The authors even attempt to be culturally sensitive by suggesting materials that may appeal to adults and children from different cultures. I enjoyed reading and reviewing Lets Talk About Math. This experience reinforced my belief that all children can be raised as LittleCounters. I think you will reach the same conclusion!
Antell, S., & Keating, D. (1983). Perception of numerical invariance in neonates. Child Development, 54(3), 695701.
Carey, S. (2009). The origin of concepts. New York, NY: Oxford University Press.
Clements, D. H. & Samara, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston, VA: Author.