Research Pages

  1. Design Problem
  2. Literature Review
  3. Work Models
  4. Design Patterns
  5. Design Experiments
  6. Lessons
  7. Montessori Computes

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Patterns and Design

Montessori

Design Problem: Why Geometry?

Most of the arguments I see for teaching kids geometry are something like this one from the Improving Measurement and Geometry in Elementary Schools (IMAGES) Team (IMAGES, 2003):

Results from assessments such as TIMSS, NAEP, and PSSA, as well as anecdotal data from team members and the Pennsylvania Intermediate Unit curriculum coordinators, identified geometry and measurement as areas of student performance that continue to need improvement.

In other words, kids aren't performing up to some standard, or American kids are performing at a lower level than kids in other countries or other parts of the US.  This argument isn't terribly compelling from a Montessori point of view, since it is based on imposed standards rather than the needs of the child.

A somewhat better argument is presented by Kynigos (1992, p. 97):

Freudenthal has put forward the case for reconsidering the pedagogical importance of geometry, arguing that it has a characteristic not so common in education, namely, that it is a field within which both inductive and deductive learning can take place (Freudenthal 1973, p. 407)... Furthermore, it has been argued that understanding deduction is at least related to (if not dependent on) experience with inductive thinking (von Glasersfeld 1985, p. 484).

Montessori thought enough of geometry to devote one of seven parts to it in The Advanced Montessori Method (Montessori, 1965, Part IV), a book on her method applied to children aged seven to eleven.  The only other section of the book that deals with mathematics is Part III which deals with arithmetic (Ibid, Part III).  I don't know her reasons for giving such a prominent position to geometry.  I hope to find some argument of hers as I continue my literature review.

Leone Learning Systems, Inc. (LLS) is a North Shore company that provides online courses for kids anywhere and local teaching and tutoring services for students in Chicago and the Northern Suburbs of Chicagoland. LLS also provides a free geometry software package for children age 6 and up, and free resources for teachers and parents. This site includes information about classes taught, availability for tutoring, learning activities for kids, lesson plans, and an ongoing software and curriculum research and development effort.