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Ms. McKenney teaches an elective class on probability and statistics, with an emphasis on data analysis. As part of the data analysis unit, she has used graphing calculators equipped with motion detectors. Her students have been assigned a problem similar to the one you just worked on. In the following video segment, you can watch her students as they actively work to develop equations related to graphs that are modeled on the graphing calculator screen, produced through the use of Calculator-Based Laboratory (CBL) technology.
As you watch, listen to the students' ideas about the problem and think about how your own students would tackle this task. Are Ms. McKenney's students making use of connections?
Now watch an extended video segment at left (duration 2:20) of the
"Calculator-Based Laboratory" video.
Think about the video you just watched and reflect on the following questions. Once you've formulated an answer to each question, select "Show Answer" to see our response.
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Question: What concepts and skills beyond their current probability and statistics course do students connect to this data analysis task?
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Our Answer:
Students consider what they know about gravity situations and quadratic and exponential functions. They interpret points and distances on their graphical displays. They work with specific points to develop and propose an exponential function related to the curve. They work from past experience to develop possible equations for their graphs.
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Question: How does the sequence of this lesson motivate and challenge students?
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Our Answer:
Before this lesson, students learned some foundational ideas, such as equations for falling bodies and how to develop an equation for a parabolic function based on known points. Students then started with an active experience requiring group cooperation, and they worked in groups so that they could pool their ideas regarding related equations.
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Question: How does working with data of this kind help students make connections?
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Our Answer:
The use of real data means that students must assess their data collection methods and their data set, rather than relying on data from the textbook or another source. They understand that their mathematical results are connected to their data gathering, and that such issues as rounding, how to label axes, what part of the window to zoom in on, and how to account for the "messiness" of experimental data all have mathematical connections and implications.
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