Making the Most of

Online Math Explorations

by Wendy Petti

What is a math jewel?

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 . . .

~ a multi-faceted resource with sparkling qualities ~

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.

.

~ 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

.

Activities may be harder to use online than off.

•Java pattern blocks

Games may be worksheets or flashcards with gimmicks.

•Funbrain’s math baseball

.

~ 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. .

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 probability and algebra explorations.

– 2-player factoring game involves strategy .

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

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~ 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

a treasure map to math jewels

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. .

getting the most out of math jewels

~ ask useful questions ~

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?

.

sample questions

~ after exploring

“What a Crowd” ~

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.

.

guided exploration with webquests

~ Create a page asking students to… ~

understanding comfort and competence curiosity and passion ability to analyze, synthesize, apply regular real-life connections lifelong learning empowerment .

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

Making Meaning

~ in English / language arts ~What do we hope for our students?

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? .

? ? ?

~ If we have the same goals ~and the same hopes…

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. .

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!)

8 Big Ideas Behind Constructionism

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 computersand 2 to 3 students sharing each

computer:– everyone can explore in rotations over 2

or 3 class periods. .

organizing the classroom

~ for productive computer activities ~

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 .

assessing understanding

“What you do with kids should have a reasonable chance of

leading to a new idea.”

~ Seymour Papert

Wendy Pettiwpetti@mathcats.com

mathcats.com/mathexplorations