Philip Kellman

An important expertise in mathematics is the rapid pick-up of task-relevant patterns and structures. Yet such skills are seldom taught explicitly. Instruction usually emphasizes declarative knowledge and procedures that can be enacted. Indeed, instruction is commonly understood to require verbal explanation and discussion-whether it takes the form of teacher led lectures, reading assignments, small group discussion, or self-explanation. Similarly, procedural learning in mathematics generally...

Two problems limit student learning in Algebra in most instructional settings. The first problem involves a lack of methods to advance students' ability to grasp patterns, process them fluently, and detect them in variable contexts and the second involves a lack of instructional formats that adapt to the individual learner. Recently developed perceptual learning and adaptive learning technology hold great promise for addressing these problems. This project team will develop perceptual and ad...

The objective of this project is to help students in Grades 3-8 develop an integrated mathematical knowledge base in which the domains of measurement and fractions are meaningfully connected to each other and to core concepts of multiplication, division, ratio, and proportion. This interrelated set of mathematical concepts has been selected because it is central to the mathematical standards identified for these grades (NCTM, 2000); it provides essential foundations for higher math learning...