What is a learning trajectory?

Children follow natural developmental progressions in learning. Curriculum research has revealed sequences of activities that are effective in guiding children through these levels of thinking. These developmental paths are the basis for the learning trajectories.

Why are learning trajectories important?

Research shows that when teachers understand how children develop mathematics understanding, they are more effective in questioning, analyzing, and providing activities that further children’s development than teachers who are unaware of the development process. Consequently, children have a much richer and more successful math experience in the primary grades.

Why use learning trajectories?

Learning trajectories allow teachers to build the mathematics of children – the thinking of children as it develops naturally. So, we know that all the goals and activities are within the developmental capacities of children. We know that each level provides a natural developmental building block to the next level. Finally, we know that the activities provide the mathematical building blocks for school success.

When are children “at” a level?

Children are at a certain level when most of their behaviors reflect the thinking – ideas and skills – of that level. Often, they show a few behaviors from the next (and previous) levels as they learn. Most levels are levels of thinking. However, some are merely “levels of attainment” and indicate a child has gained knowledge. For example, children must learn to name or write more numerals, but knowing more numerals does not require deeper or more complex thinking.

Can children work at more than one level at the same time?

Yes, although most children work mainly at one level or in transition between two levels (naturally, if they are tired or distracted, they may operate at a much lower level). Levels are not “absolute stages.” They are “benchmarks” of complex growth that represent distinct ways of thinking.

Can children "jump" ahead?

Yes, especially if there are separate “sub-topics.” For example, we have combined many counting competencies into one “Counting” sequence with sub-topics, such as verbal counting skills. Some children learn to count to 100 at age 6 after learning to count objects to 10 or more, some may learn that verbal skill earlier. The sub-topic of verbal counting skills would still be followed.

How do these developmental levels support teaching and learning?

The levels help teachers, as well as curriculum developers, assess, teach, and sequence activities. Through planned teaching and also encouraging informal, incidental mathematics, teachers help children learn at an appropriate and deep level.

Should I plan to help children develop just the levels that correspond to my children’s ages?

No! The ages in the table are typical ages children develop these ideas. But these are rough guides only-children differ widely. Furthermore, the ages below are lower bounds on what children achieve without instruction. So, these are “starting levels” not goals. We have found that children who are provided high-quality mathematics experiences are capable of developing to levels one or more years beyond their peers.