Exploring the World of Mathematics: An Eight Week Curriculum

This semester my capstone math class started off with the question of, "Is mathematics discovered or invented?". As a class, we didn't spend a whole lot of time discussing this, but it stayed a common theme throughout the entire semester, and this is what sparked the idea for my final project.

Working together with Lauren Grimes, a friend of mine, we decided that this question was one that should be addressed in mathematics classrooms. This question could open up discussions and explorations into the world of mathematics and could even help students figure out how mathematics is applied to things in their personal lives. Therefore, with this in mind, we set out to create a curriculum that would form around this question.

The final curriculum we created resulted in an eight week unit of one day a week, for a time ranging from 30-60 minutes each day. This curriculum is made up of six different lessons that are focused on a variety of people, objects, ideas, and passions and create a way for students to see the ways that mathematics is used outside of the classroom. The curriculum is centered around these questions,

"Did we, as humans, create mathematical concepts to help us understand the universe around us? Or
is math the natural language of the universe itself, existing whether we find it or not?",

and the main goal is that students would form their own opinions and beliefs about mathematics based on mathematical history, facts, and discoveries that pertain to their interests and passions. After the six weeks of lessons, which include personal research and exploration for each student, the seventh and eighth weeks implement time to bring together all the things discussed, to determine an argument for whether mathematics was discovered or invented. To further show what I mean by this, here is what the general layout for a given lesson might be:

Welcome/Overview

Warm-Up

Introduction

Individual Activity

Group Activity

Discussion

Journal

 

The final two weeks, as mentioned previously, would be structured in a different way, allowing time for students to formulate solid opinions and beliefs during the seventh week, and allowing time for a full class debate during the eighth week.

After reading this description, it might seem as though this curriculum is tackling some big questions that involve a lot of work. However, while the theme of this curriculum is definitely a big topic, Lauren and I wrote this curriculum in such a way that we feel helps students to be excited about learning and discover meaning within mathematics. There are many different ways that this curriculum could be implemented, and there are several different topics that could be discussed within this curriculum. Our hope is simply that, if used in a classroom, this curriculum would produce an outcome that positively affects students in their mathematical knowledge, understanding, and appreciation, no matter where they fall on the 'discovered or invented' debate.

I know this post only provides a brief overview of what our complete curriculum entails, so I know there may be many unanswered questions. With that being said, I am more than willing to share a copy of our curriculum with anyone who desires to read and look through it, and we of course are open to comments and suggestions about how to make it better. I believe that if this curriculum eventually can be used alongside regular mathematics courses in schools, our students will develop a deeper understanding and appreciation for how mathematics is used in our world.