EMAT 4650/6450 Mathematics in Context

CONTEXT?   What might this mean?

Some of the ideas for evolving this course can be traced by to a UGA project funded by the USDOE  for  Contextual Teaching and Learning (CTL). The fundamental thrust was that CTL would examine teaching and learning that was tied to the workplace, to cultural activties, or to daily life.    Some examples might be

Mathematics in Architecture
The golden ratio in art and nature
The Golden Ratio in Art and Architecture
The mathematics in irrigation systems design
Mathematics in music
Mathematics in small building design and construction
An Intro to Building Construction
Building a ramp for handicap access
Building a deck
Recreational mathematics
Mathematics in Science
Penrose Tilings
Quality Control
Gears - Math in Context
Measure, Precision, and Accuracy
Building Code Inspections
The Mathematics of Global Positioning Systems
CTL: Use and Application of the Parabola

Global Positioning Systems
Voronoi diagrams:  An application of computational geometry
Mathematics of Epidemiology
Kid's Corner: Math Quilts, Poem, and Songs
For the Love of Quilting
Genomics
Sinusodial Modeling
Public Key Cryptography
Surface Area and Volume of A Pond
The Birthday Problem
The Fibonacci Sequence and the Golden Ratio in Stock Market Theories
Quilt Web Site

ETC.

Let Us Teach Guessing  --  A demonstration lesson of George Polya examining the question of the maximum number of parts for dividing space by 5 planes.  Warning:   This is a 60 minutes video but worth every minute of it.

Class Members

Deleted

Syllabus                                                  COURSE EVALUATION (to be made active near the end of the semester)

Schedule

Course Format

Still tentative.     Park of our work will be in examining the concept of "context" for mathematics.

There will be a major project for each class participant to examine some context in depth, sharing your developing work with the class while you are working on it, and preparing some "product."

The "product" is not to be something I will define.      It is to be YOUR project and the rest of us may be making suggestions but our role is to facilitate meaningful exploration rather than evaluate what you are doing.   The product could be a monograph on a particular topic and discussion of the mathematics imbedded in it.    On the other hand, the goal might be to develop instructional materials you could use with your students.    The goal might be to explore and present a significant mathematics exploration that arises from your investigation of the context.

Resources

1. The web site, https://pumas.gsfc.nasa.gov, is a site for "practical uses for mathematics and sciences."   The site is suggested as a resource for this class.
2. The Encyclopedia of Mathematics and Society is a three-volume encyclopedia that William has kindly made available for us to use in class. An extensive list of topics is available here.
3. Combining Rates
4. Combining Percentages
5. Bridge Expansion Problem
6. Kite

Context Topics In Previous Semester

Michael Ferra --

For my topic I thought of doing an activity that explores different probabilities in context. My thought was to begin with a Casino/Probability Fair in order to get students engaged and interested in the topic. This fair would explore calculating the different chances of winning among popular casino games such as blackjack, roulette, craps, poker, etc. This idea of exploring different probabilities in context would then continue by observing how probability can be used in different areas of interest such as in business, medicine, sports, etc.

Probabilities Project (Final 7/28/13)      Excel File for Project Rubric

Colleen Foy --

For my projcet I want to focus on building instructional materials for a lesson/project dealing with the golden ratio. Specifically I want to focus on the golden ratio in architecture and art. The students will hopefully be able to take pictures and find the golden ratio in them. I could possibly extend it to having them draw/build their own art using the golden ratio. I will also touch on other components of the ratio as well.

Golden Ratio (7/29/13)

Mary Ellen Graves --

I will be creating three lesson plans that involve geometry and architecture/nature. I would like to create lessons that require students to find mathematics outside of the classroom. I want them to physically see how mathematics is used and found in life. The lessons will most likely consist of a project/report of findings. More to come!

Finding Volume and Area Outside the Classroom (Draft 7/24/13)

David Hornbeck --

"My project is going to center around the mathematics that go into guitar making. I will focus on some subset of guitar bracing, frequency formulas, basic music theory, and the geometry and measurement involved in building a guitar body."

It's still pretty broad because I don't know exactly how I want to tie these together, but it's a start.

Math, Music, and Guitar -- (7/24/13)

Sarah Major --

For my project, I will basically be presenting a potential lesson on the mathematical aspects and uses of ROI (return on investment). First, I will present the basic definition of ROI and a simple form of the formula. Students will then be given simple problems to calculate. After this concept is mastered, students will calculate ROI over time for different basic scenarios and them be prompted to find the best scenario based on their calculations. Students will then graph their answer so that they can physically view which is the best scenario and then approximate the equation of the line produced by the points. I will then show different factors that may affect the calculation of ROI through increases/decreases in net revenue or net cost that may cause the growth to not be linear. Students will then go through the process of calculating and graphing points to see how the type of growth has changed and be prompted to figure out what type of growth it is (exponential, etc.) and approximate the equation of the function. Students will then be asked to find their own scenarios for calculating ROI (examples include business investments, buying a car, paying for college, etc.), research the ways their calculations can be affected by different factors, and then produce their own calculations, graphs, and approximations of the best investment.

Elizabeth Nelli --

I want to design a house plan and figure out how much flooring/wallpaper/paint I would need and how much it would cost to build this house. I would have students choose houses from different cultures and design houses in a fashion that those cultures are accustomed to.

Mathematics in House Design (7/31/13)

Kristin Ottofy --

I will do my course project on the mathematics in networking. I have mostly studied the network of the Internet, so I would like to focus on that. Some of these topics I could explore are Dijksta’s algorithm and the idea of finding the path of least resistance, converting IPV4 into IPV6, which requires base conversions, or speeds of transmissions (how long does it take to transmit a packet of a given length and distance).

Mathematics and Computer Science (07/24/13)

William Plummer --

My project will look at the application of the conic sections in the field of optics. I will consider how these geometric shapes and their properties are utilized to project small objects as larger images in the use of telescopes and microscopes.

Optics Project  (7/29/13)           Optics GSP file

Sydney Roberts --

For my project I plan on using mathematics to predict whether or not a person will be a good swimmer. I plan on taking a random sample of the swimmers on my team and gathering different body measurements such as height, wingspan, and lengths of different body parts (feet, palms, forearm, legs, etc). Using these measurements I will try and analyze the data to see if there is any association between these measurements and their speed.

Linear Regression Report (7/30/13)

Benjamin Roper --

My project will be on the mathematics used in designing roller coasters. After researching the process, I hope to create instructional tools that will enable students to use various polynomials and trigonometric functions to create the most thrilling ride for an amusement park.

Roller Coaster Design (7/30/13)

Nicolina Scarpelli --

Mathematics in Sports

I specifically want to focus on the sport of baseball. The mathematics that I will be focusing on are as follows:

1) Finding the distances around the baseball field
2) Pythagorean Theorem (ex: how far does a catcher have to throw the ball to get from home plate to second base?)
3) Projectile Motion and Trajectories of baseballs (calculate the height of the arch created by the ball's path)

Possible Extension: baseball statistics (batting average, earned run average, etc.)

In addition, I might make a cross - curricular connection with physics and highlight the property of force (how much force does one need to hit a ball a certain distance?)

Mathematics in Sports (Update 7/23/13)                 Activities for MiS (Update 7/23/13)

Kip Tanner --

I would like to discuss learning opportunities inspired by a stroll through town. This is something I do with my soon-to-be first grader on a very basic level. I think there will be some more sophisticated or interesting mathematics to discuss as well.. An example would be using a yard sale to introduce Egyptian Mathematics: a type of binary multiplication - explorations can lead to some interesting algebra. Also this can be culturally interesting as it is still used in markets (the segue) in southern Egypt and Sudan (as well as computers). There are many opportunities like this example. Another example would be two ways to estimate the height of an oak tree using geometry. I plan on perhaps blending in a little real estate math (my original idea) as well.

Stroll (7/30/13)

Melissa Wilson --

My project will focus on volume of products and their packaging with the goal of producing a set of instructional materials for the classroom. The purpose is to investigate the wasted space in containers (such as the air left over in a tennis ball canister). The volume of certain solids relates to the Common Core Standards for Georgia (MCC9‐12.G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems). Students will then use this concept of "wasted space" to determine what impact it may have on shipping costs.

Volumes Project (Final 7/30/13)

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