The document discusses a study focused on algebraic communication and co-construction of knowledge through conversation forums in a virtual environment (Moodle) for students aged 13-14. It outlines the methodology, including data collection from forums, written tests, and student surveys, to analyze interactions and learning outcomes. The findings suggest that significant learning occurs through collaborative discussions, and the role of the teacher is crucial in facilitating these interactions.

1. Electronic forums & algebraic
communication
Pili Royo
DIPE
IES Montilivi
Girona- 2006
PDTR

2. Moodle & algebraic communication
ALGEBRAIC CO-CONSTUCTION
THROUGH CONVERSATION IN
VIRTUAL ENVIRONMENTS
(STUDENTS 13-14 YEARS OLD)

3. ABSTRACT
The aims of the study are:
• Analyzing the hypothetical
trajectories observed in
conversation forums on the virtual
environment Moodle.
• And to find the characteristics of
forum as learning mediator of
algebra.

4. TASKS
• Analysis of the effective
interactions in the co-
construction of knowledge
through the forums .
• Analysis of individual process

5. FRAMEWORK (I)
• Algebra as a set of assertions in which it is
possible to produce meaning in terms of
numbers and arithmetical operations (Lins and
Giménez , 1997)
• Constructivist conception of teaching and
learning (Coll, 2002) and coconstruction ( )
• The forum of conversation, as a CMO form, can
turn out a useful instrument to solve or discuss
problems jointly (Balacheff y Soury 1998, Murillo
2004, Hoyles, Noss…1999, Trouche 2004)

6. FRAMEWORK (II)
• Algebra learning and teaching should be
based on problem situations leading to
symbolizing. But we also have to take into
account the different ways present in
algebraic thinking in early grades:
analyzing relationships between
quantities, noticing structure, studying
change, generalizing, problem solving,
modelling, justifying, proving, predicting,
(Kieran, 2004, pg 149)

7. FRAMEWORK (III)
•
The condition of transformation agents assigned
to the TIC, is worthy to be taken into account for
conceiving deliberate interventions to change the
pedagogical models, the practices in the
classroom and the curricular contents in
educative systems, in order to lead to the
students towards a significant and satisfactory
learning (Rojano, 2003, pg 138)
• Translating word problems into equations
involves one of fundamentals issues of transition
from arithmetic to algebra, in terms of symbolism
as well as reasoning.

9. METHODOLOGY
• Population:
3 groups of 2nd course of ESO (13-14 years old) , pertaining to a public secondary
school, during the course 2005-06.
• Context. Environment
The whole class attended the computer classroom once a week.
Of the participant groups in the experience. Three of them followed the elaborated
curricular material with regard to the project . The other group served as reference
group.
At the end of this experience, the students responded to a written individual test.
• Data analysis
As data, the dialogues of the forums and the results of the written individual test have
been collected. The analysis of these data was made based on some of the
investigation questions. Students have also answered a survey about their assessment
of the tool.

10. PHASES
2. Using conversation forums to discuss
and to look for strategies of resolution of
algebraic problems, in a collaborative
environment.
1. Design & Implementation of a moodle –
algebra course

11. Phase I

13. Phase II

14. “THE SCREEN ACTIVITIES”

15. THE PROBLEMS
of the forums
• A PING-PONG MATCH
If in a ping-pong championship n players play, which is
the total number of parties that will gamble?
 HENS AND PIGS
In a farm there are 18 animals, hens and pigs all
together. The number of legs is 50. How many hens
and how many pigs are they?
• DIVISIONS
Which is the smaller number of three numbers that
when dividing it successively by 4 by 5 and 6, always
obtains 3 of remainder?

16. DISCUSSION
A. FROM THE FORUMS
B. FROM THE WRITTEN INDIVIDUAL
TEST
C. FROM THE SURVEY
D. THE ROLE OF THE TEACHER

17. DISCUSSION
• Children read the interventions of their partners much
more times than they write in the forum. This can be
associated at more reflexive interventions when they do.
• The coexistence of both types, actual and online
interventions, must be taken into account as a better way
than only one of them.
• Interactions between students of similar and different
cognitive levels take place.
• In the design of these forums, the teacher has to
consider the difficulty of some mathematical expressions.
• Significant learning is produced. It is possible to see it
through the evolution on the interventions and through
the results on the written individual test.
A.FROM THE FORUMS

18. Significative learning is produced

19. Significative learning is produced

20. B. DISCUSSION
Written
individual test
After forums

21. Students doing Arithmetic relations
Just good students do this in control group
Just students with difficulties
do this in experimental group
Problem G.

22. Middle level students solving by
using symbolic language skills
Problem G

23. Other methods just in the experimental
group
Problema G

24. Explicit explanations were found in the
experimental group (I)
en without a good symbolic manipulation

25. Explicit explanations were found in the
experimental group (II)

26. Explicit explanations were found in the
experimental group (III)

27. Traditional methods without self-control
were used by control group (III)
Problema G.

28. Many relations were found even
without good final results

29. Many relations were found

30. Some talks and strategies during the
experiment were “applied” to a new situation

31. They achieve self-
confidence on their
own strategies

32. Some conversation constrictions
The need of complementary
ressources (inside moodle, but out
of the forum)
The need of variability observations

33. Activity 1
• Show the multiplication x (y + 2) by filling in the
rectangle. What is your answer? Change the value of x by
dragging the x-slider. X(y+2)=
http://matti.usu.edu/nlvm/nav/vlibrary.html
ALGEBRA AND GEOMETRY

35. DISCUSSION
• Children didn’t percieve 7 weeks (once
a week) as a long time doing the task.
As they say, it allows you “to take your
time”.
• Children think this way is better than
others because they have access to
more “opinions”.
C. FROM THE SURVEY

36. D. THE ROLE OF THE TEACHER
• Design and organization of the learning experience.
• Selection of representative algebraic problems to
encourage discourse.
• Guide and scaffolding when necessary.
• Promoting the participation of all the students
• Promoting on a progressive way the abstraction and the
generalization.
• Promoting the reflection, the conjecture and the
experimentation.
• Assessment and evaluation of the activity.
DISCUSSION