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:
Technology may assist in teaching mathematics as a tool
for:
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
(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