The Use of Digital Imagery

in the

Mathematics Classroom

Three hours of instruction

Technical aspects for acquiring and using images digital imagery: cropping, resizing, posting

Improving pedagogical practices: exploration, linking concepts to real-world applications, theory building and testing

Hands-on activities designed to demonstrate the versatility of digital images and facilitate discussion about ‘best practices’

Digital Imagery in Secondary Math Methods Courses At UVA

In Today’s Class

Illustrate examples of a variety of uses for digital imagery in the teaching of mathematics

Conduct some hands-on activities

Discuss pedagogy

Background

This year digital cameras will out sell traditional cameras ($35/refurbished)

Many students already have experience using digital cameras

Digital images can easily be obtained from sources such as the Internet

But how can Digital Imagery be used in Math Class?

Dynamic Exploration

And

The Reversal of the Traditional Exercise

Golden Rectangles

1 unit

≈ 1.618 units

The ratio (length/width) in a Golden Rectangle is approximately 1.618

The actual ratio is (1+√5)/2

Parthenon Vitruvian Man

Exploring Concepts by Constructing Auxiliary Lines on Digital Images

Mapping 3-dimensional space into 2-dimensional space: A Matter of

Perspective

Ambrogio LorenzettiMadonna with Angels and Saints (1335)

Vanishing PointThe point at which parallel lines intersect

Leonardo da Vinci-The Last Supper (1498)

Last Supper Last Supper 2

Brian Sharp –On the Way to Class (2003)

UVA Columns

Manipulating the Image Itself

Rooftop

Collecting Data

Parabola

Fluff

vs

Content

Garrett was 48 inches tall in June. By Christmas, he had grown 2 ½ inches. How tall was Garrett at Christmas?

This picture of Garrett was taken last June. Approximate Garrett’s height when this picture was taken.

Garrett’s Height

A Four-step Framework to Consider

Acquire – Digital Cameras, Internet or Digital Media, Scanners

Analyze – Manipulation, Data Points, Auxiliary lines, Overlays

Create – Sketches, Student Reports, Teaching Modules

Communicate – Report Presentations, WebPages, Photo Journals

Homework

Take digital pictures of objects that can be used to support the learning of a mathematical concept

Golden Ratios and Crosses

Chains and Hyperbolic Cosines

Bug Out