ED6639 Technology and the teaching and learning of mathematics.

Winter 2008 with Margo Kondratieva.

Meeting 2. on January 22.

Goals and outcomes of extra mathematical activities:

• public awareness;
• recreation and fun;
• identification of mathematical abilities;
• enrichment of mathematical knowledge;
• nurture high achievers with challenging problems

How do those goals can be achieved with the help of technological tools?

Mathematical activity	Technological assistance
Math publications for general public and professionals(lectures, TV-programs, books, magazines, etc)	1. presentation in the electronic forms: hypertext, multimedia. 2. provide users with information. 3. provide immediate feedback(discussion forums, blogs, wikis etc)
Mathematical events (conferences, fairs, competitions, etc)	1.support by virtual resources (CD-ROMs, Internet); 2. allow register on line. 3. allow to communicate with other participant
General, math specific and interdisciplinary activities (puzzles, games, clubs, circles, correspondence schools, etc)	1. all the above 2. on-line and CD-ROM based interactive resources (in the form of applets) 3. interactive tools such as smartboards
Web based resources in mathematics (encyclopedias, dictionaries, discussion forums, learning scenarios, lessons, etc)	all kinds of resources including those that can not be used without help of technology: programming; multimedia design; modeling; investigations.

Types of educational software found on web:

1. learning activities,

for example Millie’s Math House http://www.kidsclick.com/descrip/millies_math.htm

or http://www.adibou.com or http://www.learningcompany.com

2. living stories that allow children to explore an animated story and discover mathematical knowledge.

3. creativity software that allows children to build their own world by using mathematical structures such as models, shapes, and transformations, artist’s software KidPix.

4. electronic mind boosting games.

http://www.superkids.com/

http://www.superkids.com/aweb/tools/math/ Math activities (worksheets)

http://www.superkids.com/aweb/tools/logic/ttt/ Classic tic-tac-toe game

5. … and humor

http://www.superkids.com/aweb/pages/humor/120300.sht

For math investigations which depend on math software and calculators search for:

1. TI graphing calculator, e.g.

http://www.tialgebra.com/ Some algebra activities with TI83.

2. Geometer’s sketchpad.

3. http://www.cabri.com/ Cabri. (watch the video)

4. Maple or Mathematica.

5.Microsoft Ecxel.

15 minutes video The Number Sense and discussion about the article 1

Video:

1. Mental arithmetic needs to be exercised more compare to written algorithmic ways to handle number operations.
2. Students should be encouraged to make more sense of addition /subtraction problems rather than follow a given instruction.
3. Someone who perfectly apply the method and obtain correct result not necessarily understands what (s)he is doing and thus his/her action may not be optimal. (Episode in the bookstore 2.50:2+2:50:2=1.25+1.25=2.50).
4. On the other hand, someone who achieves the result by making sense on numbers validates his/her own procedure even if s(he) fails to follow the given method (algorithm).
5. We as math teachers shall respect students’ way of doing arithmetic as long as they assign the correct meaning to their operations.

Article: Bottino, R. M. et al Advanced technology and learning environments: their relationships with the arithmetic problem-solving domain.

There is a (huge) gap between concrete question involving quantities which students can handle and the abstract mathematical sentence which often is requires from the student as a result of mathematical activity.

The article makes an attempt to show how the transition across this gap could be made in a meaningful for the student way.

ARI LAB serves as an example of an educational technology which supports such a transition.

There are stages of students’ progression through the arithmetic problem solving domain:

1. producing oral solution using common sense made within the manipulatives and natural language. This is a very concrete stage of reasoning. (Coins microworld in AriLab).

2. producing written verbal solution using the decimal positional notations for numbers. At this stage students are moving towards using symbols for numbers (Abacus microworld in AriLab) and developing algorithms which they describe in own words.

3. converting written verbal expression into arithmetical relation. At this stage student learn how to use mathematical symbols (+,-,*,/) to express their strategy.

Students communicate and compare their solution, and come to realize that there are many possible strategies and thus many possible mathematical expressions for the same answer. (Spreadsheet microworld).

4. generalization of the strategies to the extend that students may use a variable in place of concrete number. The spreadsheet microworld would facilitate this ability. Students refer to a number by the sell name and write expressions like the following: A5/6*B5 in place of 27,000/6*14. Students naturally develop an algebraic solution.

Due Jan 29: First part (pages 657-672)

Hershkowitz R. et al (2002) Mathematics curriculum development for

computerized environment: a designer-researcher-teacher-learner activity.

Make your notes about important points in this reading for the in-class discussion on Jan 29^th . The whole paper on this article will be due Feb 5^th.