Highlights
Introduction
Children follow natural developmental progressions in learning and development. As a simple example, children first learn to crawl, which is followed by walking, running, skipping, and jumping with increased speed and dexterity. Similarly, they follow natural developmental progressions in learning math; they learn mathematical ideas and skills in their own way. When educators understand these developmental progressions, and sequence activities based on them, they can build mathematically enriched learning environments that are developmentally appropriate and effective. These developmental paths are a main component of a learning trajectory.
Key Research Questions
Learning trajectories help us answer several questions.
1. What objectives should we establish?
2. Where do we start?
3. How do we know where to go next?
4. How do we get there?
Development Progressions: The Paths of Learning
The second part of a learning trajectory consists of levels of thinking; each more sophisticated than the last, which lead to achieving the mathematical goal. That is, the developmental progression describes a typical path children follow in developing understanding and skill about that mathematical topic. Development of mathematics abilities begins when life begins. Young children have certain mathematical-like competencies in number, spatial sense, and patterns from birth.5,6
However, young children's ideas and their interpretations of situations are uniquely different from those of adults. For this reason, good early childhood teachers are careful not to assume that children “see” situations, problems, or solutions as adults do. Instead, good teachers interpret what the child is doing and thinking; they attempt to see the situation from the child’s point of view. Similarly, when these teachers interact with the child, they also consider the instructional tasks and their own actions from the child’s point of view. This makes early childhood teaching both demanding and rewarding. The learning trajectories we created as part of the Building Blocksa
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