1999 Curriculum Abstracts

"Discrete mathematics and computer science,"

Incorporating Investigations into Two-Dimensional Geometry. The Area of Circles - Nina Todorov, Villa Intermediate

The purpose of this unit is to advance practical approaches of teaching geometrical concepts to the students of middle school. In this unit I will describe actual lessons taught to classes of sixth-and seventh-grade students along with presenting the details of the math activities. I will discuss how to incorporate the use of concrete materials and how to integrate writing into math instructions.

I truly believe that learning is not a process of passively absorbing information but that students should have, instead, opportunity to interpret mathematical theories and construct mathematical understanding for themselves, while participating in the investigation of different mathematical concepts. That is why in my classes I try to engage my students in problem-solving investigations that have thinking and reasoning as their primary emphasis. I intend to discuss the history of finding p through the ages to make students interested in this magic number as well as giving an opportunity to investigate it and understand from where it comes. This unit integrates geometry, measurements, and number, and presents one to two weeks of study about the area of circles.

Traditionally, students learn the standard formulas. They learn about derivation of the formulas, memorize them, apply them in many examples, and are tested on the use of them. I try to involve students in an exploration of various methods for understanding why a formula is making sense. I want students to think and reason instead of merely getting correct answers. For example, I try to promote understanding of the idea of the area of circles using different methods as well as finding the circumference and p. Along with explaining the math exploration, there is information about materials needed, and what assessments are done.

The unit can be presented to a class of sixth and seventh graders. They can work at their own pace in groups of four or in pairs. Students will make their own decisions about the sequence in which to do the tasks.

"Discrete mathematics and computer science,"

	Incorporating Investigations into Two-Dimensional Geometry. The Area of Circles - Nina Todorov, Villa Intermediate

	The purpose of this unit is to advance practical approaches of teaching geometrical concepts to the students of middle school. In this unit I will describe actual lessons taught to classes of sixth-and seventh-grade students along with presenting the details of the math activities. I will discuss how to incorporate the use of concrete materials and how to integrate writing into math instructions. I truly believe that learning is not a process of passively absorbing information but that students should have, instead, opportunity to interpret mathematical theories and construct mathematical understanding for themselves, while participating in the investigation of different mathematical concepts. That is why in my classes I try to engage my students in problem-solving investigations that have thinking and reasoning as their primary emphasis. I intend to discuss the history of finding p through the ages to make students interested in this magic number as well as giving an opportunity to investigate it and understand from where it comes. This unit integrates geometry, measurements, and number, and presents one to two weeks of study about the area of circles. Traditionally, students learn the standard formulas. They learn about derivation of the formulas, memorize them, apply them in many examples, and are tested on the use of them. I try to involve students in an exploration of various methods for understanding why a formula is making sense. I want students to think and reason instead of merely getting correct answers. For example, I try to promote understanding of the idea of the area of circles using different methods as well as finding the circumference and p. Along with explaining the math exploration, there is information about materials needed, and what assessments are done. The unit can be presented to a class of sixth and seventh graders. They can work at their own pace in groups of four or in pairs. Students will make their own decisions about the sequence in which to do the tasks.