MAE+4326

Chapter 3: Teaching Through Problem Solving

**__Technology Tools in Writing__**
//"Web-based tools can be used inside and outside of the classroom to allow students and teachers to collaboratively draft, read, and edit each other's mathematical ideas. Students who are reluctant to write by hand or in a word document could be motivated by the more interactive technologies, increasing the likelihood that they will produce quality written explanations and illustrations." (Van de Walle, 45)//


 * Text Editing (//real-time, collaborative tools//)**
 * Google Docs & Spreadsheets
 * Synchroedit
 * OpenEffort
 * Zoho Writer


 * Wikis (//free, asynchronous, collaborative website creation tools//)**
 * Wikispaces
 * Wiki-site
 * XWiki
 * Wikidot


 * Blogging Tools**
 * Blogger
 * WordPress

__**Metacognition**: //the conscious monitoring and regulation of your own thought process.//__
//**T**alk// about the problem. //**H**ow// can it be solved? //**I**dentify// a strategy to solve the problem. //**N**otice// how your strategy helped you solve the problem. //**K**eep// thinking about the problem. Does it make sense? Is there another way to solve it?
 * THINK Framework**- Improves problem solving.

**__Attitudinal Goals__**
A classroom environment built on high expectations for all students and respect for each student's thoughts will go a long way toward achieving attitudinal goals.
 * //Gaining confidence & belief in abilities//
 * //Being willing to take risks and to persevere//
 * //Enjoying doing mathematics//
 * //Build in success//
 * //Praise efforts and risk taking.//
 * //Listen to all students.//

**__A Three-Phase Lesson Format__**
****//Getting Ready//** **//**Students Work**// **//**Class Discussion**//
 * **Before**
 * Activate prior knowledge.
 * Be sure the problem is understood.
 * Establish clear expectations
 * **During**
 * **During**
 * Let go!
 * Listen actively.
 * Provide appropriate hints.
 * Provide worthwhile extensions.
 * **After**
 * **After**
 * Promote a mathematical community.
 * Listen actively without evaluation.
 * Summarize main ideas and identify future problems.

**__Online Resources__**

 * Annenberg/CPB
 * MathSolutions Lessons from the Classroom
 * ENC Online (Eisenhower National Clearinghourse)
 * Writing and Communications in Mathematics