Abstract:

The use of a didactic Scratch application (https://scratch.mit.edu/projects/280886265/) developed by the first author in order to illustrate the concept of a vector equation of a straight line is analyzed in this paper. The research question that guided this work was as follows: “Does this application improve the knowledge of the students about this subject?”. In order to try to answer this question a pre-experimental study was carried out with a pre-test and a post-test. A Scratch application was then designed to illustrate a set generated by several points of a straight line from a point (x0,y0) and the multiple of a vector (u, v).
To make the application more appealing, a football field was placed as a background, and in the middle of the field was the origin of the referential After the introduction of the point (x0,y0) and the multiple of a vector (u, v), the students could see the straight line emerging from the various multiples of the vector that cross the football field. The visualization of the straight line generated by Scratch helped to make the concept of the vector equation less abstract. The student’s interaction with the Scratch application was made through a game. Thus, given a random point in the football field, the student would have to introduce a suitable vector so that the straight line formed by the generated point and the vector introduced defines the direction to the ball enter in the goal.
To assess the impact of the Scratch application on the students’ knowledge about the vector equation of a straight line, a group of 9 students of 12th grade of the Portuguese educational system was the group of participants of this pre-experimental study.
Analyzing the data, in terms of descriptive statistics, an average of 60% was obtained with a standard deviation of 37% in the pre-test and an average of 83%with a standard deviation of 18% in the post-test. Looking at the averages of the questions implemented, in all of them there was an improvement, especially the ones that implied defining vector equation of the straight lines, through the respective Cartesian equations.
In general, the study showed that the students who used this application had better results in the post-test than in the pre-test and, therefore, we can conclude that, in this case, the application of Scratch had a positive impact on knowledge respect to the vector equation of a straight line.

Keywords:

Scratch, mathematics, vector equation of a straight line.