I was glad to stumble upon this research,
Learning and Teaching Early Math: The Learning Trajectories Approach
By Douglas H. Clements, Julie Sarama
This research talks about the three parts of the learning trajectories; The mathematical goal which is the Big Ideas of Mathematics basing on concepts and skills consistent with children's thinking; The path of learning by developmental progression which consist of level of thinking which lead to mathematical goals and the path of teaching using instructional task to match the level of thinking in development progression. And how it helps teachers like us to deliver mathematics effectively.
Children follow natural developmental progression in learning, even in Mathematics. Hence, as a teacher, we need to know these progression in order to develop their Mathematical goals for the the children and create task, activities and environment that are effective and developmental appropriate to help them reach these developmental goals.
Hence, I believe the learning trajectories approach serves as a very good guide for teachers to set goals and activities that are within developmental capacities of the children which in turn provide an environment that caters each level with natural developmental progression to the next.
Do take time to read this research. It will be of great help to all.
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