The Path To Early Math

What Preschool Teachers Need to Know

Ingrid Crowther

• Publisher: Gryphon House Inc.
• Year: 2021
• Print ISBN: 9780876599204
• eBook ISBN: 9780876599211
• Topic: Education
• Subtopic: Early Childhood Education

Whether you are a teacher looking for ways to strengthen the math learning in your early childhood classroom, an educator in a community of practice who wants to learn more about teaching math in developmentally appropriate ways, or a teacher-educator who wants to offer students an easy-to-use reference and guide for helping young children develop their math competencies and skills, this text will help you make math learning a fun and worthwhile activity in your setting.

Filled with photographs of children engaged in real experiences that demonstrate specific math concepts, chapters follow a developmental order.

• One-to-one correspondence
• Forming sets
• Object counting
• Patterning
• Measurement
• Two- and three-dimensional geometric shapes
• Parts and wholes
• Computation

CHAPTER 1:
Understanding Developing Math Concepts

“Mathematical thinking is cognitively foundational, and children’s early knowledge of math strongly predicts their later success in math.”

—Clements and Sarama, “Math in the Early Years: A Strong Predictor for Later School Success”

Across the world, parents, citizens, departments of education, and governments are concerned about the poor math competence of children in the educational systems. “[T]he current situation of more than 20 percent of young Europeans not reaching a minimum level of basic skills in mathematics and science is alarming” (European Commission Directorate-General for Education and Culture, 2013).

In North America, concern has mounted that children’s math abilities are decreasing. Many school boards and politicians are looking at ways to improve math instruction in the educational systems. “Math has become a flashpoint in many parts of the country as falling test scores have ignited debate about how the subject is being taught in schools” (Alphonso, 2018). “Over the past decade, there has been no progress in either mathematics or reading performance, and the lowest-performing students are doing worse” (Carr, as quoted in Camera, 2019). Debates have arisen on how to improve math skills, especially for young children.

Math: A Predictor of Future Academic Success

Much research has focused on developing literacy in reading as a predictor of later school success. Research is now beginning to show, however, that early math development is one of the most consistent predictors of later academic performance. A study conducted by Greg J. Duncan and colleagues (2007) found that children’s understanding of early math concepts such as knowledge of numbers and ordinality—first, second, third, and so on—are the most powerful predictors of later learning. Similarly, in a report for the Education Commission of the States, researchers Douglas Clements and Julie Sarama (2013) conclude that preschool math also predicts later reading achievement and oral language abilities, including vocabulary competence, making inferences, independent reading activities, and using grammatical complexities. “Given the importance of mathematics to academic success in all subjects, all children need a robust knowledge of mathematics in their earliest years.”

Math is a consistent predictor of future success. Many of the core math skills are also foundational to other learning competencies. Math skills encourage active problem solving.

When engaged in appropriate math experiences, children learn to think both convergently and divergently. Convergent thinking involves problem solving to arrive at one correct response. Divergent thinking, on the other hand, involves using multiple strategies to solve a problem, which may result in a variety of correct responses.

• Math enhances language development.
• Math reinforces expectations for writing and documentation.
• Math supports the development of spatial awareness.
• Math supports the development of matching and sorting skills.
• Math supports the development of patterning skills.

Core math skills transfer to other curricular areas. For example, one-to-one correspondence is the concept that numbers have only one possible correct placement. The number 2 will always belong between 1 and 3. This leads to the ability to count objects by:

• matching each object counted to a corresponding verbal number,
• matching a number of objects to a printed or concrete number, and
• recognizing that each number represents a specific quantity.

So, when counting a group of items, each item must be counted only once. Similarly, in reading and writing, each letter in a given word must be in a specific location. For example, in the word cat, the letter a must be in the middle of the word to spell cat. In science, when measuring length, only one number will indicate the appropriate length. In music, only one key on the piano represents middle C. In geography, only one place on the map designates a certain lake.

A pattern is a continuous sequence of repeating elements. Poetry, rhymes, and song lyrics are often written with patterns of repeating elements. In science, it is easy to find patterns in nature. For example, plants sprout leaves or petals in repeating arrangements. Seasons come and go in a pattern: winter, spring, summer, and autumn. Plants and animals grow in cycles of repeating stages. Music is usually made up of patterns of notes and rhythms. Art can use patterns of shapes, colors, and lines. In geography, a map can show patterns of streets and other city features.

The math concepts of matching and sorting are also found in other curriculum areas. Matching involves finding two items that are the same, such as two red cars. Sorting involves grouping more than two items that have the same characteristic, such as red toys or items with wheels. Children can learn to match and sort numbers, letters, and words. They can match two words that end in the same rime (run and bun) or sort words that begin with the same onset (run, rock, and rose). In science, they can match and sort by color, temperature, texture, and so on. In music, children can match and sort by note pattern or rhythm. Children can match and sort by type of art (painting, sculpture, drawing, and so on) or subject (animals, buildings, flowers, and so on). Geography, too, involves matching and sorting. For example, parks can be located in cities or in rural areas. Cities can be located in different countries, but they are still cities. Two cities can be called by the same name: Springfield, Illinois, and Springfield, Arkansas.

How Children’s Thinking Affects Developing
Math Concepts

Just as in any other area of human development, acquiring math competencies is a natural progression of learning key concepts and skills that build upon one another. Although core child development in math is universal, children will develop understandings and skills at their own rate, depending on the background experiences of the child. The teacher’s knowledge of child development is critical and will help the teacher make decisions about what activities to encourage the children to engage in, what materials to provide, how to organize the environment, and what types of tools to use to document learning. Consider the following aspects of child development.

Concepts and skills develop in a logical sequence; for example, one-to-
one correspondence precedes the ability to count objects. Thinking
skills develop slowly over time and relate to how children approach tasks and how they solve problems. Since thinking skills are not directly observable, children’s interactions with each other and the materials and resources in their learning environments will give clues to what and how they are thinking.

Egocentric Thinking

Egocentric thinking is the first type of thinking that emerges in all children. Children relate everything that happens around them to themselves. At this stage, the child is not yet able to understand a different point of view. What a child sees, hears, tastes, touches, or smells relates to her background experiences and will reflect how she reacts to new situations.

Melanie, a two-year-old, is very excited to talk to her grandmother on the phone. At one point she exclaims, “Wait a minute!” She runs to her room to get a picture she h...

Table of contents

• Copyright
• Introduction
• CHAPTER 1:Understanding Developing Math Concepts
• CHAPTER 2:The Role of the Facilitator: Supportive Environments, Interaction, and Documentation
• CHAPTER 3:One-to-One Correspondence
• CHAPTER 4:Forming Sets
• CHAPTER 5:Object Counting
• Resources to Support Counting Songs
• CHAPTER 6:Pattering
• CHAPTER 7:Measurement
• CHAPTER 8:Two-and-Three Dimensional Geometric Shapes
• CHAPTER 9:Parts and Wholes: Beginning Understanding of Fractions
• CHAPTER 10: Computation: Addition and Subtraction
• References and Recommended Reading