Making the Most of Online Math Explorations

1. Making the Most of Online Math Explorations by Wendy Petti

2. What is a math jewel? ~ a multi-faceted resource with sparkling qualities ~ • I can explore and “learn by doing” in open-ended ways. • I am in control. • I’m having fun without games. • I would enjoy this activity even if I were older or younger. • . It’s a math jewel if . . .

3. I can explore this activity better on the computer than off. • I can read and understand the text. • I can be creative. • I see real-world connections. • I can share ideas or data with classmates or students in other places. • I understand. • .

4.  ~ some sad sites ~  • Google’s top ten math sites • Flaws: • Pages may contain distracting ads. math.com • Text may be dense, unclear, or misleading. • AAAMath.com – place value, subtracting money, circumference • .

5. Activities may be harder to use online than off. • Java pattern blocks • Games may be worksheets or flashcards with gimmicks. • Funbrain’s math baseball • .

6.  ~ sad hidden messages ~  • Math is mostly about finding right answers. • Math is not fun, so it needs to be sugarcoated. • Math is an isolated activity. • .

7. open-ended math explorations • National Library of Virtual Manipulatives* • finding distances with a 3D globe • finding area and perimeter with a geoboard • solving fill and pour problems • exploring place value & different bases. • NCTM’s Illuminations* • 95 activities including probabilityandalgebra explorations. • 2-player factoring game involves strategy .

8. Project Interactivate* • adjustable spinner • directable fire simulation • Math Cats* • What a Crowd! • Math Playground • Algebra Activities and Function Machine • Thinking Blocks for guided exploration of word problems • .

9. a treasure map to math jewels ~ Click on the map for links and descriptions of great sites for open-ended math exploration: • Online manipulatives and applets • Sites for creating with math • Logic puzzles • Math games with that “extra something” • Sites targeting specific concepts • Sites with real-life connections • Math tools and resources • Sites with data for kids to share and use • Software for exploring with math

10. getting the most out of math jewels ~ ask useful questions ~ • 2 or 3 questions that are: probing and open-ended, providing some direction and some flexibility • Ask questions before, during, or after the website visit. • Responses may be written, discussed in small groups, or discussed as a class. • .

11. sample questions ~ after exploring “What a Crowd” ~ • What strategies did you use to make your estimates? • Did you find it easier to estimate crowds of a certain size range? If so, what range? Why was it easier to estimate crowds of this size? • .

12. guided exploration with webquests ~ Create a page asking students to… ~ • collect or analyze specific information • try one or more specific or open-ended tasks • develop a computer project to apply or synthesize some aspect of the site visit. • .

13. Making Meaning ~ What is our purpose? ~ What do we hope for our students? • understanding • comfort and competence • curiosity and passion • ability to analyze, synthesize, apply • regular real-life connections • lifelong learning • empowerment • .

14. Making Meaning ~ in English / language arts ~ What do we hope for our students? • understanding • comfort and competence • curiosity and passion • ability to analyze, synthesize, apply • regular real-life connections • lifelong learning • empowerment

15. ? ? ? ~ If we have the same goals ~ and the same hopes… • Why do we immerse our students in a world of good books but don’t immerse our students in Mathland? • As our students learn math… can we help them live math? • .

16. 8 Big Ideas Behind Constructionism • Learn by doing ~ Use what we learn to make something we really want. • Technology is a building material. • Learning by doing is hard fun. • Learn to learn. Take charge of your own learning. • Take enough time to do the job. • .

17. 8 Big Ideas Behind Constructionism • You can’t get it right without getting it wrong (at first). Look carefully at what went wrong. Push against the resistance of reality. • Do unto ourselves what we do to our students. Be active learners. • It’s the digital age ~ use technology now. • (Thanks to Seymour Papert for these big ideas!)

18. organizing the classroom ~ for productive computer activities ~ • With one computer and a projector: • a whole class can explore cooperatively • a teacher can demonstrate before students explore independently • With 5 + computers: • everyone can explore in groups • With 2 or 3 computers and 2 to 3 students sharing each computer: • everyone can explore in rotations over 2 or 3 class periods. • .

19. assessing understanding • teacher’s informal observations • students’ responses to questions • assessment rubrics * • teach a friend • learning journal: reporting, reflecting, connecting • digital or print portfolio • improvement on standard measures • extension activities • .

20. “What you do with kids should have a reasonable chance of leading to a new idea.”~ Seymour Papert

21. Wendy Petti wpetti@mathcats.com mathcats.com/mathexplorations