Virtual Reality vs Real Virtuality in Mathematics Teaching and Learning

1

• Virtual Reality vs Real Virtuality in
  Mathematics Teaching and Learning
• Pavel Boytchev, boytchev_at_fmi.uni-sofia.bg
• Toni Chehlarova, tchehlaroval_at_mail.bg
• Evgenia Sendova, jsendova_at_mit.edu

2

• Developing an Active LearningEnvironment for
  Stereometry
• (Socrates Program, MINERVA, 2005-2007)
• Computer applications based on Elica-Logo
  enhancing the scientist in the students
• Didactical scenarios consonant with the needs of
  students for self-expression

3
The Tradition
Studying Solids
4
(No Transcript)
5
(No Transcript)
6
Cubix Editor 1.2

• Calculating the volume and the surface of cubical
  constructions

7
Modeling rotational solids
8
Math Wheel 1.1

• Building rotational solids with the option of
  calculating the volume and the surface

9
Origami Nets 1.0

• Constructing nets of solids

10
Developing Activities

• Goal
• Problem formulated as a challenge
• System of problems
• Reflection

11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
Ancient Chineese vase
15
Seeing the architecture with new eyes
16
Visual modeling in an IT textbook for 6 grade

• Create compositions by means of the Cubix Editor
  in the style of Vasarelly

• Make the construction with the minimal number of
  cubes?

17
The applications support additional set of
activities

• Tessellating the plane
• Exploring the relation between numbers and their
  geometric representation
• Developing the notion of a good
  definition-description
• Finding the right level of formalization when
  describing a structure
• Art (under constrains)

18
Exploring relationships between numbers and
geometrical figures

• Find the volume of the cubes below. Predict the
  number in 20th place of the sequence.
•  

19
DALEST in Teacher education

• Teacher training courses for ICT teachers in the
  junior high school
• at the University of Sofia
• at the South-Western University of Blagoevgrad
• A short course for in-service teachers in
  mathematics and informatics from the country in
  the frames of Computer environments for the
  mathematics education

20
DALEST workshop
21
A DALEST puzzle for the expert
22
Sessions in Plovdiv
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
Sessions in Sofia
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
Free style constructions
33
Finding meaningful representations
34
(No Transcript)
35
Elaborating the descriptions
36
What do the students think? the first
impressions
37
I liked all the programs since they are fun and
require a lot of logical thinking. I like
mathematics especially when it is fun and
engaging.
The Origami Nets program is superb it has
absolutely no shortcomings and those who havent
tried it will be sorry Origami Nets are also
enjoyable and I can have fun and learn new things
at the same time.
Thanks to these (DALEST) classes the figures are
already turning in my mind
38
If only we could have every class as this one!..
What I liked the most was to figure out myself
what to do..
? How exactly?
39
What did researchers find

• The option of folding a rectangle immediately
  after being constructed contributes to
  experimenting with different styles of
  constructing the net
• It turned out to be suitable to provide them with
  figures which could be turned into nets after
  concrete operations (such as adding, removing or
  shifting some of their parts) and encourage them
  to create their own problems
• The kids combine debugging with degoaling when
  the object they are constructing is not what they
  have aimed at they are able to see another
  possibility.
• It is very useful to shuttle between using and
  developing the software.

40

• www.elica.net
• e-mail elica_at_fmi.uni-sofia.bg
• Welcome to our site! ?