Abstract:

Percentage calculations require the development and comprehension of a variety of mathematical schemes. We presented percentage as equivalent to fractions of 100. For instance, 25% is equivalent to a fourth of 100, therefore students could compute 25% of any number as the fourth part of it. As we conceptualize knowledge organization as a social construction process the main objective is to make thinking patterns visible to students with the aim of improving achievement through the analysis of mistakes and misconceptions. The classroom percentage problems and the related assessment items developed were based on relational thinking and were designed in order to assess the following competencies: Identification and characterization of the essential elements involved in percentage calculations; analysis of the relationships that play a role in those calculations; construction of a mathematical relation between percentage and its fractional and decimal representations. Two groups of fifth-grade elementary school participated in our research. One group participated as a control group and this group only participated in the assessment tests. Every student solved the assessment items both before and after that the percentage learning group have participated in learning sessions concerning percentage calculations. Items responses were analyzed with an item analysis program designed by our research group. This program was developed to be used with the Microsoft excel application. We get as a result the item response curve, a difficulty parameter, and a discrimination parameter related to mathematical academic grade point average as an ability parameter. The percentage learning group shows an improvement related to percentage calculations compare to control group. Students with high academic grades develop greater increments.

Keywords:

Cognition, scheme, relational scheme, item response curve.