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Beyond Number Crunching
Transcript of Beyond Number Crunching
For Inquiry Doing mathematics is an act of sense-making. Mathematics teaching should focus on enduring understandings rather than just on acquiring facts. Open questions help students to develop their understanding and allow them an opportunity to think about their work and to verbalize their learning. Inquiry-based Learning: Designing and using activities whereby students learn new concepts by actively doing and reflecting on what they have done. Inquiry-based units are entry points into mathematics through which students will experience what it is like to think and act as mathematicians. Mathematics is a powerful tool for problem-solving and a way of understanding how the world works. As in all subjects, students construct meaning in mathematics by scaffolding their learning onto their previous experience. Allow students to wonder why things are, to inquire, to search for solutions and to resolve incongruities. Learn the basic facts
Learn the procedures
Learn the concepts once you have the tools. "Hey, I think I get it!"
"I can explain it like this." "I can use that to figure this out." Number
Crunching What calculations
will you do with paper and pencil this week? What will you figure out through estimation?
What will you figure out with a calculator ap? Yes, there's a place for learning facts.
Yes, there's a place for learning procedures.
But should it take the bulk of our time? How can we show this information the most clearly? How can I use a graph to prove my point? Different graph forms highlight different aspects of data more effeciently. Data can be summarized in a variety of ways - with or without bias or distortion Using technology during inquiry provides: Precision Manipulation Repetition Variation Shape
Space Can you construct an obtuse right triangle? What's the relationship between a circle's diameter and circumference? What shapes can tessellate? How can you figure out the sum of the angles if you know the number of sides? Using the technology:
Really cool websites! Regular and irregular polygons have properties that define them. Ratios can be used to enlarge and reduce shapes. And don't forget the 'Wow!' that helps everybody want to learn. Students can appreciate the intrinsic fascination of mathematics and explore the world through its unique perspective Number Pattern
and Function The base 10 place value system extends infinitely in two directions. Fractions, decimals and percentages are ways of representing whole-part relationships Using the technology:
Construct your own How much bigger is a 6.3 earthquake than a 6.5? How can you make a fair tournament with an odd number of teams? How long would it take to count to a million? When you win the lottery, when is it better to take the lump sum and when is it better to take payments? How do pattens help me graph and handle data? How do patterns show up in similar polygons? What patterns can I find in prime and composite numbers? Patterns are central to the understanding of all concepts in mathematics. Functions make it possible to make predictions in math problems. How do I describe the patterns I see so others can understand? Using the technology:
Graphical Analysis Using the technology:
Websites Saves time from "A Mathematician's Lament" by Paul Lockhart A Lament