Teaching and Learning Mathematics: A Philosophical Statement Mathematics is the study of patterns. The patterns may be found in numbers or spatial relationships. Mathematics is a complicated landscape of ideas and strategies to articulate these patterns and relate them to each other. It spans the realms of counting, arithmetic, algebra, geometry, probability and statistics, topology, computer science, analysis and beyond. Today’s scholars of mathematics have such highly developed vocabularies and specialized areas of study that they may have only a few peers who can understand the original work they are doing. The learner is new to this landscape. The learner has access to mathematical ideas through experimenting, model building, sketching, listening, reading and talking to others. Ultimately the learner constructs his or her own understanding of the ideas. This understanding is empowering, yet may include only partial understanding or misunderstandings. The learner perceives a very limited view of the field. Enlarging his or her vision of mathematics requires broad experience that tests the boundaries of the learner’s comfort zone. The teacher is familiar with at least parts of the landscape. It is the teacher’s role to create an environment that provides learners with opportunities to experiment, build models, sketch, listen, read and talk to others about the ideas they are constructing. Much can be learned through direct hands-on experience with objects and numbers. The teacher knows important features of the concepts to be studied and provides experiences that will lead to efficient mastery of the ideas. The teacher acts more like a coach. It is not the teacher’s role to provide tightly structured lectures that attempt to organize all of the ideas for the learner. The learner must take a more active role than that of passive receiver of information. The teacher will model different strategies for learning. The teacher understands that the student has the central role in constructing the understanding of the mathematics so that the learners in a classroom will be in many different places at the same time as the class strives for understanding of a new topic. The teacher will try to find ways for each learner to document his or her developing understanding through providing writing tasks, problem solving challenges, projects, tests and other assessment activities. The teacher will also try to help students identify the boundaries of their understanding and correct misunderstandings. The teacher optimistically hopes that some of the students will grow beyond the teacher’s own level of mastery.
Class Information
 
 
Fall 2007 Courses: Click on course name for more information
    Structure of Math III:Number Patterns Math 305
    Curriculum and Technology in Secondary Math I Math 327
    Structure of Math IV: Development of Geometry Math 306
    Research in Mathematics Education Math 598
    
Archived course information from previous semesters