Opinions of teachers who used Aplusix

Sandrine Lunel, teacher at the high school Aristide Bergès de Seyssinet-Pariset, France, after one year of use of Aplusix (2003-2004).

 

Aplusix was used in the computer room, with grade 10 students, in particular for the resolution of equations, inequations, systems of equations and also word problems leading to equations, inequations, systems of equations. The initial level of the class was heterogeneous with weak students on algebraic calculations and students feeling comfortable with algebraic calculations but not with the process of solving by equivalence. As soon as we began the field of algebraic calculations, Aplusix has been proposed to the students as a tool. It does not require particular prerequisite, except mastering the mouse. The objective was to help them better manipulate algebraic expressions.

Several type of sessions were implemented:

• With half-class, with one student per computer, first with the permanent verification of the calculation, then with the verification on request;
• With half-class, with one student per computer, with word problems; the choice of the tool (paper-pencil or software) was free;
• In individualized help: to help them to overcome certain difficulties, using autonomously Aplusix as a microworld with particular exercises in ordre to improve a technique.

The discovery of the software is rather natural and requires little help from the teacher. Significant improvements occur during the first session. The use of the virtual keyboard is more and more efficient.

The comparison between a session wit Aplusix and a paper-pencil session clearly shows the pedagogical interest of the software.

Sessions with Aplusix:

• The students work from the beginning to the end of the session, without demotivation; they are more autonomous and more confident;
• The experiment of several methods for the same exercise are facilitated and allows comparisons;
• The possibility to use calculation commands like 'expand' or 'reduce' allows to work on one difficulty at a time;
• The teacher can circulate more easily, provide punctual hint and give advices.

Paper-pencil session:

• The teacher validates or not the result;
• There remains problems in the presentation;
• Weak students are quickly demotivated;
• The teacher spend a lot of time to help weak student and to search calculation errors.

From a session to another, the students gained autonomy, improved their skills and manipulate algebraic expressions more rigorously. Certain sorts of error almost disappeared. More over, the notion of equivalent expressions seamed to get meaning.

The preparation of a session with Aplusix is rather easy: the exercise editor allows to create quickly a personal list of exercises or word problems.

The balance sheet is also very positive for the students:

• For good students: possibility to attempt more problems with a validation of the result by the software, incitation to choose an efficent method;
• For the othe students: reduction or disparition of certains errors, getting confident, more efficient work on precise subjects.
• For all: the transfer to paper is very good. The students work more with equivalent expressions and think to reduce the result.

Florence Gervais, teacher at the high school Jacques Prévert de Gaillard, France, after one year of use of Aplusix (2003-2004).

Aplusix has been used at grade 9, for remediation sessions, with 15 students, one student per computer.

Several exercises were proposed on a chosen theme. Each student works at his/her rhythm, autonomously, with an immediate correction conversely to paper-pencil sessions.
The students are active during the entire session and are enthusiastic. I often heard: "that's it, I have understood!"

With Aplusix, the student is obliged to correct his/her errors and, as a consequence, to analyse them. Thanks to this process, a large part of the group improved their skills and methodology.

Jean-Marc Gervais, teacher at the high school Jean Monnet, Annemasse, France, after one year of use of Aplusix (2003-2004).

My colleague Saïd Mouffak showed me how he used the software with his students; I have been attracted because:

• The discovery is very quick and one works immediately an efficient way.
• Each student can follow a personalised route and concentrate on his/her errors, analyse them.

I essentially used Aplusix in a grade 10 class for factoring polynomial expressions and solving systems of equations:

• With half-classes, which allows to have one student per computer,
• Sometimes in individualized help to obtain remediation to particular difficulties and consolidate some fragile knowledge.

I think that the main positive points are:

• The students' motivation is real, even for daunting exercises. They all are hard at work on them.
• A minimum of time is spent to learn how to use the software.
• The rigour demanded by the software (notation, parentheses, etc.) is accepted without discussion.
• The transfer on paper is correct, particularly at the level of the notation. In a few disappointing cases, it seams that a too punctual work, without perspectives is the reason. A classical paper-pencil context would not have avoided this issue. The remedy consists of better present the long term goals and to make the students aware of the intermediary accomplished progresses.
• The student can work on any exercise, not necessarily on a prepared one. This is very useful for the individualized help. Conversely, the teacher can prepare sessions in which the steps and the context (with or without verification, etc.) are chosen in advance.

I will continue to use Aplusix as a tool totally integrated in the curriculum. This use will be enlarged by word problems

Saïd Mouffack, teacher at the high school Jean Monnet, Annemasse, France, after two years of use of Aplusix (2002-2003 and 2003-2004).

Aplusix was used in the computer room, with grade 10 students, for each theme of algebra of the curriculum.

• The discovery of the system does not present any difficulty and is very quick;
• The use of the system on the network of the school is appreciated because it permits individual and collective use;
• The possibility to set the parameters of the system according to the goals of the learning is appreciated too;
• All the students worked from the beginning to the end of the Aplusix sessions, contrarily to the traditional paper-pencil sessions;
• Students in difficulty have shown motivation to solve exercises, on their own, out of the lesson; they chose exercises in their text book and solved them with Aplusix;
• The students needed less help from the teacher when they were working with Aplusix, they gained autonomy for solving problems;
• The transfer to the paper-pencil environment is good: progresses are made at the syntactical level; after two sessions devoted to systems of equations (Aplusix obliges the students to make steps with equivalent systems), 90% of the students wrote equivalent systems in the paper-pencil environment;
• At the end of the year, the students had better results in comparison to those of the years without Aplusix.

Pascal Chantrieux, teacher at the high school "à l'Hôpital et à Domicile" (at the Hospital and at home), (LCHD) of Grenoble, France, for children having long illnesses, after one year of use of Aplusix in 2003-2004.

LCHD uses Aplusix for ill children in two main situations:

• Student, in a classroom, who alternatively take a lesson (alone or in a group of 2 or 3) and work in semi-autonomy;
• Isolated student, at home or in a sterile room of the hospital, who alternatively take a individual lesson (by teleconference: the use of Aplusix is shared between the teacher and the student) and work in autonomy.
• The student has often less time to work than a usual student, and the duration of its stay in the LCHD is not always known in advance. One has to do simple and efficient actions.
• Up to now, the use of Aplusix at the LCHD is basic: a brief explanation of the functionalities allows an immediate use of Aplusix, generally in anonymous mode, to work on numerical calculations (fractions, square roots), algebraic calculations or equations. The first exercises are solved with the presence of the teacher (physical or at distance) who provides the exercises, and quickly the student works in semi-autonomy or autonomy with exercises provided by the teacher or by its own initiative.
• Some features of the software are particularly interesting for the specific students of LCHD:
• Lightness: the discovery is very quick, the manipulations are simple for the students (the virtual keyboard is appreciated for the laptop we lend to the students)
• Efficiency: Aplusix saves the teacher time; it favours the student’s autonomy, promotes an exploratory behaviour, asks interesting questions (0.33 is refused for 1/3 and 1,414 is refused for square root of 2)
• Attraction: the students like to use the system, even those who would not have been motivated by the same exercises on paper;
• Flexibility: the system is easy to used in an individualized way or at distance;
• Reliability: its rigour and logic allow letting, in confidence, the student work alone.