Young Children and Mathematics: Specific characteristics of young children and mathematics

• Active engagement in acquiring basic concepts (Charlesworth, 1996).
• Young children are natural learners and approach new tasks with curiosity and a sense of experimentation (Copley, 2000).

Principles in Teaching Mathematics to Young Children (from Copley)


Curriculum Principles: Content; Process; Environment and Materials; Child-Centered

Instruction Principles: Planning Experiences; Interacting with Children; Orchestrating Classroom Activities; Facilitating Family-School Relations

Assessment Principles: Benefiting Children; Observing and Listening; Using Multiple Sources of Evidence; Assessing Learning and Development

Theoretical Frameworks

Piaget

• According to Piagetian Developmental Theory, most children age 2-7 are in the pre-operational developmental stage and most likely, by age 7, will be able to understand sets and classifying, comparing (objects/amounts), counting, parts and wholes, and the basic mathematical language to accompany the concepts.
• Children acquire knowledge by constructing it through their interactions with the environment. They do not wait to be instructed to do this; they are continually trying to make sense out of everything they encounter:
  • Physical knowledge-includes learning about objects in the environment and their characteristics
  • Logico-mathematical knowledge-includes relationships that each individual constructs in order to make sense of the world and to organize information (same/different; more/less)
  • Social (or conventional) knowledge is the type that is created by people (e.g., rules for behavior)
  • Constance Kamii (a student of Piaget) says that, according to Piaget, autonomy (independence) is the aim of education. The way to develop that is to create an atmosphere where children feel secure in their relationships with adults; where they have an opportunity to share their ideas with other children; where they are encouraged to be alert and curious; come up with interesting ideas, problems, and questions; use initiative in finding out the answers to problems; have confidence in their abilities to figure out things for themselves and speak their minds with confidence.

Vygotsky

• Vygotsky's Theory-also cognitive developmental; emphasis on developmental and environmental forces.
• After 2, the society of the child (the child's culture, social world) is necessary to expand thought
• More emphasis placed on the adult in the child's learning
• Vygotsky believed that speech was the most important sign system-speech enables the child to interact socially and facilitates thinking
• Vygotsky developed the concept of the zone of proximal development (ZPD), scaffolding, mediating etc.
• The teacher must identify each student's ZPD and provide developmentally appropriate activities

Both Piaget's and Vygotsky's views are used as a foundation for early childhood learning (Piagetian constructivists tend to be concerned about pressuring children and not allowing them freedom to construct knowledge independently. Vygotskian constructivists are concerned with children being challenged to reach their full potential). A combination of both views provides a framework such as the following-The Learning Cycle in Early Childhood:

• Awareness
• Exploration
• Inquiry
• Utilization

Other Early Childhood Mathematical Characteristics

• Children come to pre-K with knowledge and experience of the world as they know it; the knowledge they bring to the classroom is intuitive and informal mathematical knowledge.
• Young children have a wealth of informal knowledge of mathematics as a result of everyday experiences and strategies they create to deal with events in their lives (Copley, 2000) (e.g., counting buttons on shirt).
• Young children continually construct mathematical ideas based on their experiences with their environment, interactions with adults and other children, and from their daily observations (Copley, 2000).

Some basic pre-number math concepts that are usually addressed in the early years are:

• One-to-one correspondence (passing out snacks to each child; conservation)
• Counting objects (rote counting 1,2,3,…)
• Classifying (shapes/colours)
• Measuring (pouring sand from one container to another)
• Patterning (identifying a pattern unit; extending/duplicating the pattern; seeing patterns around them in their world).

Mathematical concepts learned in the early years are very important as a foundation for the more formal, abstract mathematics of the primary grades (adding; subtracting; multiplying; dividing).
Children are all learning at different rates and in different ways.

Young Children and Mathematics: The Teacher's Role

• As teachers we need to assess what our children know; this can best be done through meaningful activities.
• As teachers we need to listen to the children (Paley 1986), observe them as they work on activities, and we also need to interact with them (talk to them about what they are doing and ask appropriate questions).
• We need to structure a mathematical environment conducive to learning. What would this environment look like? What kinds of mathematical 'objects' would be in this environment? What kinds of mathematical tasks would children be doing? Take a few minutes at your table and generate some 'objects' and 'tasks.'

Structuring the Early Childhood Mathematics Classroom

Table Discussion


What would a mathematically-rich, developmentally-appropriate Early Childhood classroom look like?
What mathematical 'objects' would be in this classroom? (by 'objects' we mean concrete manipulatives; things from the world-real things)
What sorts of mathematical tasks or activities would be appropriate for young children to engage in?
What would the teacher be DOING in this classroom?

The following are some of the major pre-number concepts. List some activities that you can do in your classroom that would address these concepts:

1. classification

2. one-to-one correspondence; more than/less than/same as

3. ordering

4. patterning

5. counting objects

6. measuring