ED6639 Technology and the teaching and learning of mathematics.

 

Winter 2008 with Margo Kondratieva.

 

Meeting 1. on January 15.

 

Different roles of technology in intellectual human development:

  •  facilitate mathematical computing;
  •  be a field of application of mathematical knowledge;
  • allow to model, build, investigate, and research;
  • assist in learning and teaching mathematics;

 

Technology may assist in teaching mathematics as a tool for:

  • fast arithmetic calculations (calculators);
  • algebraic manipulations (computer algebra systems);
  • storage and analysis of numerical data (statistics software);
  • multiple representation of mathematical objects (graphing calculators);
  • experimenting with data and figures (Geometer’s Sketchpad, Smartboard)
  • communication (email);
  • search of mathematical information (web).

 

Recent development of technology based on new generation of computers and Internet push our perception of mathematical activity beyond the limits of traditional educational forms offering new opportunities of doing and learning mathematics for everybody.

 

Technology gives an opportunity to make a challenging task accessible at the lower school level, to bring everybody to the wonderful and fascinating world of mathematics through the freedom of entertainment, the freedom of learning, freedom of fun, and freedom of challenge.

 

The freedom of choice offered by technology opens a unique source for combining in one activity entertainment with learning, fun with challenge.

 

“Technology breaks the walls of the classroom” is an expression used by Jean Marie De Koninck, one of the authors of the project ShowMath

http://www.smac.ulaval.ca/showmath/, at the meeting of CMS in Winter 2004.

 

“In Mathematics, as in other disciplines, the web based educational resources expand our concept of the classroom itself, changing what gets learned and how, affecting student-teacher relationship, and providing a new types of mathematical activities and resources.”

They give an opportunity to “differentiate mathematical challenge to meet educational needs of all group of learners”.  (G. Klotz in The digital classroom: how technology is changing the way we teach and learn, D.T. Gordon (Ed), 2003)

 

Technology enhances environment can offer an opportunity to access the traditional forms of mathematical activities as well as new forms that can not be realized in the traditional classroom setting.

 

As noted by S.Kennewell,

 

“ICT (information communication technology) can bring a difficult task within the ZPD (Zone of Proximal Development in Vygotskian sense) of more pupils through screen cues that provide scaffolding not available from the teacher. Task can be motivated and enjoyable because of interactivity. Conjecture and risk taken are encouraged. Pupils can learn constructively from their mistakes.  This fosters perseverance which enables pupils to meet the high expectations placed on them and appreciate the role of personal effort in achieving success” (p.96, in  Meeting the standards in using ICT for secondary teaching: a guide to the ITT NC, 2004).

 

You are invited to continue investigation at the following  websites:

 

http://wims.unice.fr/wims/ Web Interactive Mathematics Server

go to  Interactive Exercises

 

then go to

1) Ruler and compass (e.g. level 3: barycenter of a triangle)

2) Graphing functions (e.g. recognize graph after transformations)

3) Magic rectangles (arithmetic game)

------or any you want in fact!

 

How do you like to interact with this educational software? How can you use it for your teaching  practice?

 

A sample of Geometry software can be found at Geometer’s Sketchpad Resource Center

(you need a Java support on your computer to have a dynamical feature)

http://www.dynamicgeometry.com

 

http://www.dynamicgeometry.com/javasketchpad/gallery/

Visit dynamical example:

1) centroid (this is another name for barycenter of a triangle)

2) nine points triangle,

3) Napoleon’s Theorem.

4)  sine waver, 

5) maximizing box volume,

6) Sliding Rod problem .

Do they make sense for you? Do you have any teaching ideas of using them?

Ask me if you got interested and need math help.

 

 

Here is a summary of our collective ideas in favor and against using technology in mathematics classroom. It may undergo some changes as we proceed through the course.

 

ten reasons in favor of technology use

ten reasons why not use technology

1. Technology may promote logical thinking and focus on task (not on operations, which could be performed using a calculator).

1. Inappropriate use of technology could distract learners from intended learning goals.

2. Technology may provide visual understanding.

2. Students may develop dependence from technology and be unable to perform successfully without it.

3. Technology may assist children with various physical disabilities (kinesthetic hands on).

3. Students may never master basic arithmetic skills and do not form a number sense (if they always use calculator for basic operation.)

4. Technology has a potential to meet needs of all learners (provide adequate challenge for kids of various mental abilities).

4. Students may become very slow in mental arithmetic as a result of using calculators when it is unnecessary.

                                             

5. Technology may increase confidence and provide motivation for learners.

5. Cost. Not every school and not every student can afford buying some pieces of technology.

6. Technology may support fun and stimulating activities.

6. Time. It may require a lot of extra time for teacher to prepare technology based lesson.

7. Technology may allow more time for teacher for one-on-one interaction with each student.

7. Many teachers do not have enough knowledge and experience with modern educational technology.

8. Technology may provide instant feedback to the learner.

8. Many teachers lack didactical approach

to implementation of technological tools in school curriculum.

9. Technology may increase meaningful communication in the classroom

(students will ask questions and share ideas based on their practices).

9. Mathematical content may be lost while students focus on other aspects, such as winning a game or technicalities of the tool.

10. Students need technology skills for their life and future profession.

10.  Technology is not always reliable. It may not work the way you need and this is very frustrating.

 

P.S.

Reading Chapter 29 you may wonder about the ARI-LAB project.

Some information can be found at web:

 

http://www.itd.cnr.it/arilab/_english/strut_ita.html ARI-LAB structure

 

http://www.itd.cnr.it/arilab/_english/demo.html ARI-LAB demo download