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The following list of tips for getting started with mathematical modeling are based on ideas presented during the Math Modeling 101 webinar. Feel free to download and share these tips as the Getting Started with Mathematical Modeling PDF.
Start small. You don’t have to start with a large-scale, open-ended project like, “What’s the relationship between speed and gas mileage?” Instead, start with a smaller activity, such as this one, adapted from Math TechbookTM, Grade 7:
One page of description lasts 10 seconds when converted to screen time, one page of dialogue lasts 1 minute, and one page of action lasts 90 seconds. Analyze a few pages of your favorite book, and predict how long the whole book would last if converted to a movie. If that’s too long, what parts would you cut from the movie?
Don’t reinvent the wheel! You don’t have to spend countless hours looking for new activities (though that can be rather fun). Try an activity from these excellent math modeling resources on the web:
- Robert Kaplinsky: http://www.robertkaplinsky.com/lessons
- Moody’s Challenge: http://m3challenge.siam.org/resources/sample-problems
- Catalog of 3-Act Tasks: http://tinyurl.com/Catalog3Acts
- COMAP: http://www.mathmodels.org/problems/
Use a variety of tasks. Some modeling problems have an open beginning, middle, and end. Others are closed in various parts. Use a variety, and choose based on whether the purpose is to prepare students for a new concept or to practice skills.
Help students be successful. Your first activity shouldn’t throw students into the deep end of the pool. Encourage success with these techniques:
- Scaffold the problem by suggesting the types of tools that they should use.
- Restrict the size of the problem by providing a limited set of information.
- Ask, “What are questions that someone might have?” (If you try the activity at http://tinyurl.com/tixprob, you may be amazed by your students’ questions.)
- Prepare students for variables by asking, “What would change? What would stay the same?”
- Identify alternative entry points for students who have trouble getting started.
Engage in math modeling often. Modeling is a skill that must be practiced, just like solving an equation or graphing a line. Modeling doesn’t need to happen every day, but students only get better by tackling authentic problems often. Make modeling a regular part of your instruction.
It’s worth it. Yes, modeling activities take longer than just teaching students how to implement an algorithm. But the rewards are greater, too. Students who engage in modeling develop greater conceptual understanding and procedural fluency.
Manage the conversation. The effectiveness of a modeling activity is directly proportional to the quality of classroom discussion. For guidance, read 5 Practices for Orchestrating Productive Mathematics Discussions.
Want to learn more? Watch the archives of Discovery Education’s series of three unique webinars developed around the topic of Mathematical Modeling. In this series of one-hour webinars, you will learn the what, why, and how of mathematical modeling in the secondary classroom.