Monday, May 25, 2015

The Mathematics We Need

Here's a challenge:
• You are planning to make and sell ice cream cones at a school sports event.
• You expect to make and sell 300 cones.
• You buy ice cream in 1 liter tubs.
• Each tub costs $2. 
• You can fill ten cones from each tub. 
• Each empty cone costs 5¢.
• You plan to sell each filled cone for 80¢.
• Before buying the ice cream, you survey 60 people to find out what flavors they like. Here are the results of the survey:
    In this situation:
    1. Work out the quantities you need to buy and the costs
    2. What profit do you expect to make on the day?
    You know that if you try to work through the task above, you'll have to do more than remember what you learned in seventh grade.  Instead:
    • You'll have to figure out how the information fits together, and show some tenacity to work through to a solution.
    • There's a good chance that after you've been working on a problem like this for a couple of minutes, you'll erase something in order to change your strategy.  
    • When you've worked through the whole thing once, there's also also a good chance that you'll realize one of your steps wasn't done quite right, and for precision you need to do some of the work a second time.  
    • If you've been around this sort of block a few times, you know you want to make notes next to the calculations so someone else can look over your thinking and help you see if it's clear and sound.
    Most of all, you know you didn't learn the "one right way" to answer this task in school, and you know this kind of task above is the stuff of real life, relevant both for large scale capitalism and for local PTA leadership.

    To be ready for college and career, Kentucky's students need preparation for mathematics with these kinds of demands.

    That's what we're building by implementing Kentucky's academic standards.  Along with ability to do particular kinds of equations,  we're working to build eight mathematical practices, including four illustrated in my bullets above:
    • "Make sense of problems and persevere in solving them"
    • "Use appropriate tools strategically"
    • "Attend to precision"
    • "Construct viable arguments and critique the reasoning of others"
    This kind of readiness is also what we're building by participating in the work of the Mathematics Design Collaborative.  The task comes direct from a set of "summative tasks" developed for MDC that allow students to show and teachers to see how well student can put their mathematical learning to work.  It's a middle school task, confirming that we're aiming very high indeed for our high school graduates.

    Source note: No claim about standards should come without source specifics.  You can download a copy of the Kentucky Core Academic Standards for yourself, and check pages 56 and 57 to see the language quoted above.  You can see the same expectations without a download at the Common Core State Standards site by looking under Standards for Mathematical Practice.

    Geek note: The rubric for the task shows it as sound to round up on liters of strawberry and down on chocolate chip, based on assuming that the survey was accurate.  I myself would discount the survey substantially because it did not include chocolate and because I can't tell if the 65 people surveyed were a good sample of the kinds of people coming for the sports event.  Mind, I'd still end up with the same profit estimate, but I'd bring a different set of wares to the game.

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