The Development of Mathematical Thinking Curriculum
The content and methodology of the VITAL: Early Childhood Mathematics Education resource are based on a series of mathematics education courses taught by Prof. Herbert Ginsburg (Co-PI) at Teachers College, Columbia University, and by Prof. Rochelle Kaplan (Investigator) at William Paterson University. These courses employ learning activities using brief video clips (or "cases") to help students (prospective and practicing teachers) in undergraduate and graduate courses analyze the development of young children's mathematical thinking and learning, and critically examine early mathematics instruction.
The "Development of Mathematical Thinking" CurriculumProf. Herbert Ginsburg's course at Teachers College covers topics ranging from children's informal understanding of basic mathematical concepts to the implications of developmental psychology for formal pedagogy and curriculum. The course is based on the premise that teachers can be more effective if they understand and can build upon the mathematics that children have already learned from an early age, with or without limited instruction. Students in the course are expected to learn theories of developmental psychology as they pertain to mathematics, and specific techniques adapted from psychology research.
Approach and TopicsStudents spend the first part of the course examining the developmental features of children's mathematical knowledge in the context of a series of discrete video-based "cases." Later, students focus on how certain aspects of mathematics instruction, including pedagogical theory and curriculum design, can and should be informed by an understanding of children's mathematical thinking and learning. Topics include the following:
Course StructureEach week students prepare for class by completing readings, watching videos, and completing assignments all within the VITAL environment. Completing assignments in VITAL in advance of class not only prepares students to engage more deeply in the lecture, it helps Prof. Ginsburg anticipate their questions. By highlighting comments selected from the week's assignments, he can connect his lecture more closely with students' concerns and also motivate them with the knowledge that their interpretations may be recognized publicly in class.
During class, Professor Ginsburg uses video clips of children solving mathematical problems to illustrate important concepts. Both in and out of class, he encourages students to think critically about their observations and hypotheses and to use evidence from the videos and readings to support their ideas.
Course AssignmentsStudents complete three types of assignments during the semester: multimedia essays, video lessons, and a final project for which they create and try out a mathematical activity and an interview, and reflect on the outcome in an extended multimedia essay.