Personal Performance Shapers (PPS): Their Importance in Mathematics Achievement and in Pupils’ Empowerment

Migrations have increased in the last decades, particularly in Europe, bringing new challenges to schools and societies. In Portugal, despite the Constitution (Assembleia da República, 2005) that claims equal rights for everyone, gender and racial discriminations still exist. César and Machado (2024, submitted, in preparation) illuminated that the mother language (L1) shaped how pupils do and learn Mathematics. Pupils who participate in Cape Verdean culture and whose L1 is Creole prefer a global approach, spatial or geometric reasoning (Battista, 2007), and graphic representation solving strategies, usually not accepted at school – a subtle form of exclusion. Thus, they feel powerless and act as peripheral participants (César, 2009; Lave & Wenger, 1991). César (2009, 2013a, 2013b) showed that collaborative and dialogical work was effective to empower pupils from vulnerable minorities. Using inter-empowerment mechanisms, exploring different mathematical reasoning, and solving strategies, and developing bi-univocal cultural mediation (César, 2017; César & Machado, 2024) promoted pupils’ empowerment, and learning. The Interaction and Knowledge (IK) project lasted 12 years and had a 10-year-follow-up. We focus on data from the action-research projects, including 69 Mathematics teacher/researchers, and around 600 classes. The triangulation of sources, data collecting instruments, researchers, and theories were used as quality criteria. Data treatment and analysis were based on a narrative content analysis (Clandinin & Connelly, 1998). Some examples illuminate that changing the first week of classes and using personal performance shapers (PPS) to decide about the first dyads, were essential to empower pupils, and to increase their learning. Implicit messages and inter-empowerment mechanisms also played an important role. Collaborative and dialogical class work and research were important features to increase pupils’ empowerment, self-esteem, resilience, and school performances. These results were more striking when schools used bi-univocal cultural mediation.

Keywords: mathematics education, language (L1), collaborative and dialogical work, inter- and intra-empowerment mechanisms, life trajectories of participation, bi-univocal cultural mediation, personal performance shapers (PPS)