Julie Sarama is Kennedy Endowed Chair in Innovative Learning Technologies and Professor at the University of Denver. Her research interests include developing and evaluating research-based educational software and other technologies, using learning trajectories in standards, assessment, educational technology, curriculum and professional development, developing and evaluating research-based curricula, and asking successful curricula to scale using technologies.
Douglas H. Clements is Kennedy Endowed Chair in Early Childhood Learning and Professor at the University of Denver. Previously a kindergarten teacher and preschool teacher, he has conducted research and published widely in the areas of the learning and teaching of early mathematics and computer applications in mathematics education. His most recent interests are in creating, using, and evaluating a research-based curriculum and in taking successful curricula to scale using technologies and learning trajectories.
Doug and Julie have collaborated over the past 20 years on research and implementation projects focused on improving early math development in young children.
ED: How did you begin your career in early learning and early math?
Doug: I was always interested in math and was planning on being an engineer but after I graduated, I decided to go into early education. My first job out of college was teaching kindergarten. As a teacher, math was the shining star for me. I was so interested in young kids’ thinking around math. When I went back to school to get my doctoral degree, I focused my dissertation on preschoolers’ thinking about early math. How do young kids learn math ideas and skills? How do they think about early math? What are the best ways to teach early math?
Julie’s background was in teaching high school and middle school math. In the 1990’s we became involved in a National Science Foundation (NSF)-funded project on developing a kindergarten-through-fifth-grade math curriculum. We had developed some of the technology for the kindergarten piece of the curriculum, but weren’t able to complete it since the project ran out money. Thankfully, NSF soon came out with a call for a focus on early math, and then we had the opportunity to really start our work on early math and began developing what we call our Building Blocks project.
Julie: Previous efforts around early math focused on activities or developing ideas that sounded cool but weren’t based on research. Alternatively, we focused on identifying (from the research base) the specific features that help young children in early math. In the first year of Building Blocks, we worked on identifying the early math learning trajectories for young children. Doug reads everything from everyone; he looked at studies from a variety of related fields (developmental science, cognitive science, mathematics education, early childhood education, etc.). We pulled from all of those areas to help us develop these learning trajectories. What do kids learn, when do they learn it, and what can we do to help them progress? In the end, we developed an assessment and curriculum to help teachers understand learning trajectories. Later we were very lucky to receive funding from NSF and the U.S. Department of Education’s Institute for Education Sciences for our TRIAD project. This allowed us to develop the needed professional development materials and scale-up approaches for our work. Through TRIAD we were able to help early childhood teachers across multiple sites (e.g., Boston, Buffalo, and Nashville) understand the learning trajectories and how to implement the assessment and curriculum. This was especially important given many early childhood teachers often report they went into early childhood so they wouldn’t have to teach math!
ED: How has your research improved the quality of early learning and influenced approaches to teaching early math?
Doug: Everyone can write more cute activities that might touch on basic math concepts, but with the growing consensus on the ways young children learn to understand mathematical concepts and engage in mathematical thinking, we believe that understanding the early math learning trajectories is critical for early childhood educators to teach early math.
Julie: Learning trajectories have three parts:
- a learning goal (i.e., target, benchmark, expectation);
- a developmental path along which children develop to reach that goal; and
- a set of activities matched to each of the levels of thinking in that path that help children develop the next higher level of thinking.
The idea behind a learning trajectory is that these are the stepping stones to get you to your goals. Each of these stepping stones represents a significant change in the way kids think; they are the developmental progressions or descriptions of kids’ behavior that give us a hint of where a kid is developmentally. The activities that follow are critical to help move children from one stepping stone to the next.
Through our TRIAD project we taught early childhood teachers to understand how young children think about math; how to identify where kids are with their mathematical thinking; and then to provide instruction or activities that take the kids to the next level of mathematical thinking. We found that teachers when given this framework and the learning trajectories became excited about teaching math. When they saw their students’ growth along the learning trajectories, it was transformative. Teachers often tell us “I had no idea young children could learn this or think like this.”
ED: What are some of the challenges you have experienced in this work and what strategies have you tried to overcome them?
Doug: The biggest challenge is the perception that math doesn’t belong in early childhood and that we don’t need to teach it yet. Another challenge is the false dichotomies that our field creates such as academics versus non-cognitive skills, or teaching math versus teaching literacy. We know we can teach math and literacy and social-emotional skills in early childhood. We know that early math skills are fundamental to children’s overall learning. Along with one of our post-doctoral researchers, Alissa Lange, we found improvements in oral language in classrooms that implemented Building Blocks. The learning is connected.
Julie: An effective strategy for overcoming the negative perception about math in early childhood is getting out there and talking about it. You really need a Doug! He travels a lot, spreading the word and accepting speaking engagements to all different kinds of groups about the work we are doing. Writing research articles isn’t enough. You also need your champions. The teachers we trained in our TRIAD project continue to implement Building Blocks without any coaching or support. We went back two years later and were shocked and delighted that they had all increased their fidelity of implementation, meaning they were implementing Building Blocks the way it was intended. Six years later, the teachers who were still teaching continued to implement Building Blocks. It is important to share their experiences.
[Check out this video report on the successful implementation of Building Blocks in Boston]
ED: What suggestions do you have for others interested in supporting early math development in young children?
Julie: When you focus on math, either alone or as part of a STEM (Science, Technology, Engineering, and Math) initiative, be sure to focus on the learning trajectories, not just math activities or projects, and embed math growth.
Doug: Professional development (PD) is critical and you need to start-off thinking about the PD as lasting for at least year. We know that a math day or a math workshop won’t change classroom practices, yet this is what we continue to offer to teachers. We need to be honest and start planning alternatives. Through foundation funding we developed a website with resources that support teachers to better understand learning trajectories. The website is called Learning and Teaching with Learning Trajectories (LT2), and is a great free resource for programs wanting to get started in thinking differently about early math.
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