Electronic forums & algebraic communication

Pili Royo

DIPE

IES Montilivi

Girona- 2006PDTR

Moodle & algebraic communication

ALGEBRAIC CO-CONSTUCTION THROUGH CONVERSATION IN

VIRTUAL ENVIRONMENTS(STUDENTS 13-14 YEARS OLD)

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.

TASKS

• Analysis of the effective interactions in the co-construction of knowledge through the forums .

• Analysis of individual process

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)

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)

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.

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.

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

Phase I

Phase II

“THE SCREEN ACTIVITIES”

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?

DISCUSSION

A. FROM THE FORUMSB. FROM THE WRITTEN INDIVIDUAL

TESTC. FROM THE SURVEYD. THE ROLE OF THE TEACHER

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

Significative learning is produced

Significative learning is produced

B. DISCUSSION

Written

individual test

After forums

Students doing Arithmetic relations

Just good students do this in control group

Just students with difficulties

do this in experimental group

Problem G.

Middle level students solving by using symbolic language skills

Problem G

Other methods just in the experimental group

Problema G

Explicit explanations were found in the experimental group (I)

Even without a good symbolic manipulation

Explicit explanations were found in the experimental group (II)

Explicit explanations were found in the experimental group (III)

Traditional methods without self-control were used by control group (III)

Problema G.

Many relations were found even without good final results

Many relations were found

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

They achieve self-confidence on their

own strategies

Some conversation constrictionsThe need of complementary

ressources (inside moodle, but out of the forum)

The need of variability observations

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

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

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