Research shows that the work of a strong teacher is the most important school factor in student learning. But when it comes to teaching, there’s always something new to learn. Professional development sessions, such as in-service training, can help teachers keep up with the latest research on teaching and find ways to use it in their classrooms.
To help elementary math teachers, Paola Sztajn, associate dean for research and innovation for NC State’s College of Education, and P. Holt Wilson, associate professor of mathematics education at UNC Greensboro, have teamed up to edit a book on professional development.
Learning Trajectories for Teachers: Designing Effective Professional Development for Math Instruction uses experiences from four successful programs to show how to help teachers master strategies for teaching elementary math and use them with students. We asked Sztajn and Wilson to explain the challenges and rewards of this work – without using numbers.
The Abstract (TA): Can you explain the concept behind learning trajectories and give an example of how they work?
Sztajn/Wilson: Learning trajectories are frameworks that organize what we know about how learning can unfold. They are empirically developed maps describing how the learning of a particular mathematical concept progresses to become more sophisticated through instruction.
For example, a child learning to count starts by rote reciting the number names, then develops one-to-one correspondence, and then develops the concept of cardinality, which is the understanding that when counting a collection of objects, the number name associated with the last counted object represents the totality of the collection and not the name of that particular object. The child can then start producing quantities and also start counting backwards. Later, the child can count starting at any number and skip count. Such progression of thinking requires instruction and should also guide instruction.
TA: When you do in-service training on teaching mathematics, is there an “aha moment” when teachers see how learning trajectories can help them reach students?
Sztajn/Wilson: Of course learning always brings that “aha moment,” and for any teacher, these moments are what keep us going! In our work with teachers around learning trajectories, we always start by looking at students’ mathematical behaviors. Teachers, most of the time, have seen these behaviors in their classrooms. But once we start naming the behaviors and placing them in a trajectory that maps learning, it all comes together in that “aha moment.” Naming and recognizing these behaviors allow teachers to talk to each other about something that previously they perhaps were not sure was happening in all classrooms, with lots of students. Recognizing which of these behaviors represent more sophisticated mathematical ideas also helps teachers recognize what students know and appreciate their progress in learning a mathematical concept before mastering it.
TA: Your book focuses on the importance of sharing effective approaches to professional development about teaching math. What gets in the way of doing this?
Sztajn/Wilson: Our book is unique in the sense that, for each of the projects we include, instructional designers discuss what really happens in their professional development, and, just as importantly, how they got to that particular design. So we talk about the designers’ learning over time in programs they implemented and continued.
As a field, we know a lot about how to design professional development for teacher learning. Scaling up and sustaining these models of professional development are the challenges. Instructional improvement takes time as well as deliberate and continuous effort over many years within a supportive school environment – right there are some of the major barriers. Most school systems cannot afford to invest in teacher learning and in allowing learning to be an integral component of the teaching profession over time. We have not found a systemic way to include consistent time for teacher learning in our schools. Teachers spend a significant part of their time in the classroom with their students or attending to other demands within the school building.
TA: Who should take the lead in improving professional development in teaching math? Principals? Instructional designers? District leaders?
Sztajn/Wilson: Everyone! This needs to be a systemwide approach that has a consistent message all the way from the district leaders, to principals, to instructional leaders and then to teachers.
Several school systems now have great mathematics teacher leaders and coaches who can carry out professional development with teachers. These leaders are usually well aware of the research going on and of what represents high-quality mathematics instruction. These professionals play an important role in the school building, educating principals about what they should look for and, at the same time, working with teachers to improve instruction. They also connect to researchers and professional development designers, working with them to bring new knowledge and evidence-based instructional strategies into the schools. When this is happening in all buildings, then district-level leadership needs to maintain a consistent message about what counts in mathematics teaching and learning. Oftentimes, there are disconnected messages within the district and within schools about what high-quality instruction is – and that is a problem.
For example, it’s contradictory to say that communicating mathematical ideas is important and, at the same time, expect students in classrooms to be always quietly working on their individual worksheets. When the system lacks a coherent vision for high-quality mathematics instruction, together with a coherent message all the way through, it’s really hard to improve teaching through professional development. That’s why improving professional development and teaching is everyone’s job, from researchers to leaders at all levels of the educational system to teachers themselves.
TA: What lessons can we take from the four groups in your book that have been focusing on improving professional development with learning trajectories?
Sztajn/Wilson: Respecting teachers and their professional knowledge is one important message. Professional development has to offer actionable, useful ideas that matter to teachers in classrooms. When working with trajectories, it is important to attend to how teachers are making sense of the trajectories and what helps the teachers in their teaching. Also, a major issue for all projects is how instruction can position all students as competent to support each and every child in their mathematics learning. We learned that trajectories, when implemented with explicit goals of overcoming deficit perspectives on learning, can help teachers support the learning of all their students.