Teachers’ uses of a learning trajectory in student-centered instructional practices

Wilson, P.H., Sztajn, P., Edgington, C., & Myers, M. (2015). Teachers’ uses of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66(33), 227-244.


The concept of a learning trajectory is currently important in mathematics education. A learning trajectory basically has three components: 1) an instructional goal, 2) a progressive set of “levels” of understanding that we can expect learners to pass through as they build increasingly more complex understandings of the content and skills needed to achieve the goal, and 3) the instructional tasks and activities that are implemented at each level to help learners achieve the goal and progress to more complex levels.

The authors here make the case that teachers who understand learning trajectories and can use them to plan mathematics instruction will teach in student-centered ways that help learners progress in their mathematics knowledge and skills. They support this claim by presenting a qualitative study of 19 elementary teachers who experienced intensive professional development focused on mathematics learning trajectories. The results were convincing, overall. The teachers showed evidence that they did learn the content of the professional development, and in many cases, what they learned was seen in observations of math lessons in their classrooms. As could be expected, some teachers implemented some aspects of the learning trajectory better than others did. That is, though all participants seemed to incorporate the knowledge and skills learned in professional development when they taught mathematics in the classroom, there were individual differences across different teachers, and as a teacher educator, I see that as something to be expected. Individual differences in learning will always be present, no matter how good the professional development may be. Still, the authors here have made and supported a case for professional development on learning trajectories.

The concept of learning trajectories at first seemed new to me, but a little research helped me see that it is new terminology but not necessarily new ideas. Learning trajectories as defined in this article fit with current trends to make mathematics instruction more student-centered and more developmentally appropriate. As a literacy educator, I have long used various systems of developmental levels that seem very like what I am reading about in this article. Such developmental levels are not written in stone, and learners do not always progress through them in linear ways, but these levels do give us helpful notions about what to expect from learners and a helpful sequence for approaching increasingly complex knowledge and skills in our instruction. I teach these kinds of things in literacy education, and am glad to see mathematics instruction approached in similar ways.

The current impetus for learning trajectories in mathematics seems to come from the Common Core State Standards (CCSS), which reportedly were developed with research on learning trajectories as an influence. When one looks at the CCSS, one can indeed see the way each anchor standard develops progressively as a learner moves through the grades. That “spiral” or “stairstep” organization of gradually more complex thinking and skill development is for me one of the most useful aspects of the CCSS. It’s a general and sometimes vague document (as with all standards documents), and educators can (and do!) argue about whether everything at all levels is really developmentally appropriate. Still, the CCSS document clearly shows us learning trajectories for many important instructional goals in English Language Arts and mathematics.

For those not really familiar with learning trajectories, I recommend some Internet research, perhaps before reading this article. Most of the information out there now relates to mathematics, so web sites directed toward mathematics education would be the best place to start. However, there is exciting potential for researchers to develop learning trajectories, or perhaps revise existing developmental levels, in all other subject areas. This article suggests that such research could benefit teachers, and in turn, benefit students.