how real are real-world contexts in mathematics

The grande iced coffee in the lobby costs $3.57.

Just one block away you could get the same for $2.91.

Did You Know…?Imagine the extra cost of the specialty drinks!!

$0.66 23% more

How Real Are Real-World Contexts

in Mathematics?Professor AJ Stachelek

Hostos Community CollegeBronx, New York CityTHE

Who Are You?For starters…• Name, College, City, State• Favorite class and/or level to teach• Something unique that you are willing to share

about yourselfWrite down some real-world contexts you use in the classroom

One response per sticky note pleaseSort the answers from your group

Group Work• What does ‘real-world context’ mean and how do

we find them?

• Should ‘real-world contexts’ be used in math classes? What are some benefits? What are some dangers?

What does ‘real-world context’ even mean and how does one find them?

Group Responses:

What is a ‘real-world context’?Definition anyone?• Research on real-world contexts often skip defining this

phrase (because we all know what it means, right?)Dictionary Definitions:Real: “Existing or occurring as fact; actual rather than imaginary, ideal, or fictitious.”World: “The earth or globe, considered as a planetContext: “The set of circumstances or facts that surround a particular event, situation, etc.”

What is a ‘real-world context’?Building on the dictionary definitions...• Exists outside the mathematics classroom• Simplifying assumptions do not depart from reality• Involves actual values (or rounded actual values)• Relates to students’ experiences, not mine or

others

How do I find them?It’s essential to get to know and understand my students’ lives:• Exploring the community• The area around the college is where my students

spend a lot of time, so I start there• I also try to travel further out and explore other

areas of the Bronx • Showing interest in my students lives• Start the class with a brief survey about their

interests, hobbies, extra curricular, jobs (current and desired), etc.• Follow through!

Should ‘real-world contexts’ be used in math classes? What are some benefits? What are some dangers?

Group Responses

What are the benefits?Motivation• Gain student interest

Prior Knowledge• Access student knowledge to aid in learning

Learning Transfer• Concepts extended outside the classroom

What are the dangers?Insert here an intricate problem that explores the hazards of texting while driving. You spent hours finding the actual formula in physics that will allow the students to calculate the braking time based on different speeds one may travel on highways…

You have in mind...

Then a students asks….“What’s miles per hour?”

Motivation Prior KnowledgeTransfer

I’m in New York City, which means…My Students Don’t Drive!

Motivation

Prior Knowledge

Transfer

Addressing Context Pitfalls • Cultural differences are important and are how

individuals understand, misunderstand, or do not understand the context• Miles per hour means what exactly?

• School context differs from realistic contexts in unrealistic ways• No you may not share the Metro Card with your

family

• Here is another story about me, but my life is not theirs• As much as I love my son, my students don’t even

know him

How Real Are Real-World Contexts

in Mathematics?(To My Students)

The Beginning of Metro-MathI Quant NY SEPTEMBER 5, 2014How Memorizing “$19.05” Can Help You Outsmart the MTA

We’ve all been there. The train is coming into the station, and you grab your MetroCard and quickly try and swipe it at a turnstile.  “Please Swipe Again”. "Please Swipe Again". "Insufficient Fare”.

The last two words are killer. You think to yourself “I swear I had a balance on this card”.  You go and check the card out and you see you have “$2.45”. Yes, you need $2.50 to ride the subway, and you have $2.45 on your MetroCard. Sure enough you miss that train all because of that nickel. How did you end up in that situation any way?   It turns out the MTA has designed it that way.

Just a Little Math…

• Quick press buttons: $9.00, $19.00, and $39.00

• 5% bonus added to your card• $2.50 per ride• What amount is left over on the card when

you’ve used up all your possible trips?

Snapshots of Other Lessons

The Bronx and NYC are My Sources of Inspiration

Systems of Linear Equations

• An unlimited 30-day Metro Card costs $112, a 7-day Metro Card costs $30, while a pay-per-ride costs $2.50 per ride.

• Can you use linear equations to model these three options over the course of 30 days?

NYC Population Density

Borough Population(as of July 2011)

Land Area (square miles)

Manhattan 1,601,948 23Bronx 1,392,002 42Brooklyn 2,532,645 71Queens 2,247,848 109Staten Island 470,467 58

NYC Population Density

Borough Population(as of July 2011)

Land Area (square miles)

Population Density(people / 1 sq. mile)

Manhattan 1,601,948 23 69,650Bronx 1,392,002 42 33,143Brooklyn 2,532,645 71 35,671Queens 2,247,848 109 20,623Staten Island

470,467 58 8,112

1 square mile = 20 by 20 blocks in the Manhattan

During this past weekend, my friend watched in horror as I poured 4 full sugar packets into my 16-ounce ice coffee. He didn’t say anything, but I saw the look on his face. Later on, I was drinking a tall glass of my favorite beverage – Kool Aid (water by itself is so boring) and he finally got up the nerve to lecture me on the impact sugar has on health. Meanwhile, he was drinking a can of Coca-Cola, which I thought made him a hypocrite. Why would I think that?Can you help me explain to my friend why he is misguided?To help you, here are some facts: 1 tablespoon of Kool-Aid makes an 8 ounce drink that contains 16 grams of sugar 1 packet of sugar has 4 grams of sugar and recall I used 4 of these in my ice coffee 1 can of Coca-Cola is 12 ounces and contains 39 grams of sugar (according to label)

Group Activity: Sugar

Tools for Others to Use

You can do this in your own class

Finding Contexts Online

Type in words in a search engine online

I combine the following words and phrases with the right location:• Quantitative Facts• Facts and Statistics• Historical Information• Industries and/or Economics

Other Sources:• Find inspiration in conversations with your students• Sugar activity

• Find inspiration in the surrounding communications• Geography impacts the experiences of students

Anyone Else Notice a Lot

of Seafood Around Here?

4.833 billion pounds of seafood consumed per year (U.S.)

40% of which came from Louisiana’s fishing industry

The U.S. had a population of 308,745,538 people

Sources: National Oceanic & Atmospheric Administration (NOAA)

New Orleans Tourism and Marketing CorporationUnited States Census 2010