Douglas H. Clements is Professor, Kennedy Endowed Chair in Early Childhood Learning, and Executive Director, of the Kennedy Institute for Educational Success and the Marsico Institute for Early Learning and Literacy, at the University of Denver, USA. Dr. Clements received his PhD from the University at Buffalo, State University of New York. Previously a preschool and kindergarten teacher, he has conducted funded research and published over 500 articles and books in the areas of the learning and teaching of early mathematics and computer applications in mathematics education. Dr. Clements was a member of President Bush’s National Math Advisory Panel, the National Research Council’s Committee on Early Mathematics the Common Core State Standards committee and a coauthor of their reports. His research interests include creating, using and evaluating research-based curricula, taking successful curricula to scale using technologies, and learning trajectories in standards, assessment, curriculum and professional development. Dr. Clements recently visited Sultan Qaboos University, Oman, and delivered a keynote address at the “International Conference on Trends in Innovative Mathematics Curricula: Highlights on Early Mathematics Education” organized by the Oman Mathematics Committee. In this interview, Dr. Clements, speaks about the strategies for early mathematics education, based on his extensive research experience in this area.
Why Is Teaching Mathematics So Different From Teaching Other Subjects?
Dr. Clements: Early mathematics is surprisingly important. We ignore the early years at our peril. That is, we know that children’s early knowledge of math strongly predicts their later success in math. More surprising is that preschool mathematics knowledge predicts achievement even into high school. Most surprising is that it also predicts later reading achievement, as well as early reading skills. One reason teaching mathematics is different than teaching other subjects is that in most subjects, children have to learn skills first, such as word recognition. But in early mathematics, they can be immediately engaged at the “cutting edge” of their intellect. For these and other reasons, mathematical thinking is cognitively foundational. Given the importance of mathematics to academic success in all subjects, all children need a robust knowledge of mathematics in their earliest years.
Why do many students avoid Mathematics despite the much value placed on this subject of study?
Dr. Clements: Even though mathematical processes are cognitive, they are influenced by emotions and beliefs. For example, if people are anxious about mathematics, they may perform poorly, not necessarily because they have limited ability or skills, but because nervous thoughts “push” themselves into their minds, limiting the amount of working memory available to work on mathematics. In many cultures, such as the U.S., many people have unfortunate, negative emotions and beliefs about mathematics.
One deeply embedded belief is that achievement in mathematics depends mostly on aptitude or ability. In contrast, people from some countries believe that achievement comes from effort. The belief in aptitude—you’re either a “math person” or you’re not—hurts many children and, further, it is just not true. Children who believe—or are helped to understand—that they can learn if they try, work on tasks longer and achieve better throughout their school careers than children who believe you either “have it” or you do not. This view often leads to failure and learned helplessness. On the other hand, those who have mastery-oriented goals—who try to learn and see the point of school to develop knowledge and skills, achieve more than children whose goals are directed toward high grades or outperforming others. They even see failure as an opportunity to learn.
Could you explain the concept “Teaching Early Mathematics for Understanding with Trajectories and Technologies”, the topic of your talk at SQU?
Dr. Clements: Teachers who learn to use curricula based on learning trajectories are not only better teachers of mathematics, they continue to use that curriculum for years after its introduction and their teaching improves each year. Teachers need help to do this. However, we have the tools to provide that help. We know a lot about how children think about and learn math. And we know a lot about how to use learning trajectories to synthesize this knowledge into effective interventions for children. Our books detail the learning trajectories that can help underlie scientific approaches to standards, assessment, curricula, and professional development. Our new web site, learningtrajectories.org, provides similar information with videos that make the learning trajectories come alive. Our research on our Building Blocks curriculum and TRIAD scale up model show effect sizes that are large and signification. High-quality instruction has meaningful effects on children’s mathematics knowledge. All children can learn mathematical thinking.
How would you summarize your years-long research on early childhood learning?
Dr. Clements: Young children can learn amazingly broad, complex, and sophisticated mathematics. For example, preschoolers can learn to invent solutions to solve simple arithmetic problems. Also, almost all preschoolers engage in substantial amounts of pre-mathematical activity in their free play. They explore patterns, shapes, and spatial relations; compare magnitudes; and count objects. Importantly, this is true regardless of the children’s income level or gender. They simply need opportunities to engage in interesting mathematics. Teachers can and should provide rich environments, questions, and interactions to engage children in such experiences.