# Mathematics

## The Broughton Archipeligo Monitoring Program

This talk was one of the IGTC Student Presentations.

## Modeling Spotting in Wildland Fire

This talk was one of the IGTC Student Presentations.

## Life History Variations and the Dynamics of Structured Populations

This talk was one of the IGTC Student Presentations.

## The Mathematics of Doodling

Doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, there is often some sophisticated and fun mathematics buried inside common doodles. I'll begin by doodling, and see where it takes us. It looks like play, but it reflects what mathematics is really about: finding patterns in nature, explaining them, and extending them. By the end, we'll have seen some important notions in geometry, topology, physics, and elsewhere; some fundamental ideas guiding the development of mathematics over the course of the last century; and ongoing work continuing today.

- Read more about The Mathematics of Doodling
- 3302 reads

## Memory Induced Animal Movement Patterns

This talk was one of the IGTC Student Presentations.

## Min Protein Patter Formation

This talk was one of the IGTC Student Presentations.

- Read more about Min Protein Patter Formation
- 3985 reads

## Multi Variable Operator Theory with Relations

TBA

## Raising the Floor and Lifting the Ceiling: Math For All

"Math. The bane of my existence for as many years as I can count. I cannot relate it to my life or become interested in what I'm learning. I find it boring and cannot find any way to apply myself to

it since I rarely understand it." (high school student)

Today, mathematics education faces two major challenges: raising the floor by expanding achievement for all, and lifting the ceiling of achievement to better prepare future leaders in mathematics, as well as in science, engineering, and technology. At first glance, these appear to be mutually exclusive: But are they? Is it possible to design learning that engages the vast majority of students in higher mathematics learning? In this presentation, I will present the findings and discuss the implications from a research study that explored the ways to teach mathematics that both raised the floor and lifted the ceiling.

## Changing the Culture of Homework

Who do your students think their homework is for? Does attaching credit to homework promote student understanding, or encourage students to find answers by whatever means necessary? Are they focused on calculating the answer, or seeing the big picture? Is their homework grade a true reflection of their own understanding of the material, or does it better reflect the understanding of their "support network"?

In this workshop we will describe our efforts to improve student feedback and to promote good study skills in first and second year mathematics classes.

## As Geometry is Lost - What Connections are Lost? What Reasoning is Lost? What Students are Lost? Does it Matter?

In a North American curriculum preoccupied with getting to calculus, we witness an erosion of geometric content and practice in high school. What remains is often detached from "making sense of the world", and from reasoning (beyond axiomatic work in University). We see the essential role of geometry in science, engineering, computer graphics and in solving core problems in applications put aside when revising math curriculum. A second feature is that most graduates with mathematics degrees are not aware of these rich connections for geometry.

We will present some samples of: what we know about early childhood geometry.; and then of the critical role of geometry and geometric reasoning in work in multiple fields outside of mathematics. With a perspective from "modern geometry", we note the critical role of transformations, symmetries and invariance in many fields, including mathematics beyond geometry.

With these bookends of school mathematics in mind, we consider some key issues in schools, such as which students are lost when the bridge of geometry is not there to carry them through (caught in endless algebra) and possible connections other subjects. We also consider the loss within these other disciplines. We will present some sample investigations and reasoning which can be supported by a broader more inclusive set of practices and which pays attention to geometric features and reasoning in various contexts. In particular, we illustrate the use of dynamic geometry investigations, hands on investigations and reflections, and making connections to deeper parts of the rest of mathematics and science.