Abstract:

For many students, algebra is a boring and obscure domain. We developed an app for making it more pleasant by verifying permanently the student’s calculations during the resolution of exercises. This is a transfer of the main functionality of the Aplusix Windows software we developed in 2000, which was experimented in several countries and is always used in school and at home, see http://aplusix.com/en. With the new app, the student is given exercises like “Factor x(2x-6)+(x-3)(x+1)” and “Solve 5/(2x+3)+2/(3x-4)=0”. Formulas are displayed as usual in math (exponents, fraction bar, square roots). The student produces freely calculation steps using the special virtual keyboard of the app for entering characters and math operators, and an advanced math editor. At each entry, the app displays a feedback on the status of the formula of the step when it is invalid (e.g., unbalanced bracket) and of its relation to the previous step when it is valid (equivalent or not equivalent). Furthermore, it indicates when the exercise is solved.

Two specific applications have been developed by the Aristod Company (http://www.aristod.com):
(1) a player called Aplusix Web implemented in JavaScript, running on computers, tablets and smartphones;
(2) an authoring tool which is an extension of the EpsilonWriter software, running on computers.

The authoring tool is used by teachers to generate Aplusix exercises (http://epsilonwriter.com/en). They have to enter lists of exercises, each exercise having a type of exercise (Calculate / Expand and simplify / Factor / Solve equation, inequality, simultaneous equations) and a formula. An advanced formula generator is used for producing many exercises form a pattern. Teachers can easily type 5 patterns, generate 100 exercises from each, and set the file to provide randomly 10 exercises to the student. Files are stored on a web server to be available immediately for everybody.

The player is currently a web app running in a browser (http://aplusix.org) and using the Training mode described above. During the beginning of 2016, a Test mode with scores and feedbacks at the end of the activity will be added. Standalone apps will be developed for Apple Store and Google Store. They will be usable offline, containing the player and many exercises.

The first experiments in secondary schools of this new app, on tablets and smart-phones, are encouraging. Aplusix Web helped them to work their technical knowledge on algebraic expressions and equations in a pleasant context: “We like to work with this digital device. We feel more motivated. It’s much more playful than a textbook.” The feedback allows them to train in autonomy in the classroom and at home, and highlights misconceptions, for instance: 3x=1 is not equivalent to x=1-3 and 4(x-3) is not equivalent to 4x-3. From these feedbacks, students either ask the teacher why it is not equivalent, or correct themselves without any intervention. We noticed an improvement in their skills.

In conclusion, Aplusix Web appears as an efficient tool enhancing students’ autonomy like its predecessor (Chaachoua & al., 2004) but also now as a practical and funny tool usable everywhere at any time because many secondary students own a smart-phone.

References:
[1] Chaachoua, H., Nicaud, J. F., Bronner, A., & Bouhineau, D. (2004). Aplusix, a learning environment for algebra, actual use and benefits. In 10th International Congress on Mathematical Education.

Keywords:

Algebra, smart-phones, tablets.