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Explorations in Mathematics

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Cacey Wells

on 4 May 2010

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Transcript of Explorations in Mathematics

Explorations in Mathematics Rationale: Goals: Reasoning Areas of Exploration: Number Theory
Non-Euclidian Geometry Art in Mathematics History (NOVA Fractal Video
Explore a line that is continuous everywhere, but nowhere differentiable
Construct Koch Snowflake
Explore similar examples like Cantor Set
Explore Fractal Landscapes
Mandelbrot Set
Julia Set
Fractal Art
Explore connections between Fractals and Chaos

The purpose of this course is to get away from the notion that says you can’t learn the “good stuff” in mathematics until you have the basics down. To explore meaningful mathematical topics within different areas of math without necessarily having all the basics down.

To provide a concise course of different topics of interest in mathematics to promote interest in math and to see how mathematics can relate to the community.
Dewey emphasizes the importance of integrating school and life.

The reason for having a community-oriented project is to find a mathematical outlet that matters to both students and their community.

Doll emphasizes the 4 R’s—Richness, recursion, relation, and rigor

Richness: Curriculum needs to reflect the community both in and out of school. This course has potential to affect outside community as well as build community within the classroom.

Recursion: No disconnected units. Create a flow within the course that engages reflection. This course is structured in a way that units overlap and allows time for reflection within subtopics.

Relation: Be thinking about the relations between the parts--Units and
Students. Hopefully students will be able to see the relations between the different units.

Rigor: Constantly question actions and the results of actions—it is a changing change.

Attractors: Areas of mathematics being explored. The design of this course was build the major units as attractors with sub-topics designed to encourage a swirling around those topics that include reflection, discussion, and hands-on activities.
Whitehead emphasizes a romance with mathematics.
One aim of this curriculum is to take students’ curiosity to the next level by creating an environment conducive to budding a sort of romance with mathematics.
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