- Margarida César1 and Ricardo Machado2
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1Psychologist; retired full professor, Universidade de Lisboa, Portugal, 2Invited professor, Escola Superior de Educação de Lisboa (ESELx); tutor, Universidade Aberta de Lisboa, and researcher at CICS.NOVA, Universidade Nova, Portugal
We live in
intercultural societies and schools. In schools there are pupils with distinct
mother languages (L1) that shape their mathematical performances (César, 2024b;
César & Machado, 2024, submitted). Pupils whose L1 is ideographic, like
Creole (Cape Verde), usually prefer global approaches to problem solving,
spatial or geometrical reasoning, and graphic representations as solving
strategies. Those whose L1 is phonetic, like Portuguese, usually prefer
step-by-step approaches to problem solving, analytical reasoning, and
arithmetic or algebraic solving strategies, the ones most teachers value more.
The rejection of their natural approaches, reasoning, and solving strategies makes
pupils who participate in Cape Verde culture lose their voice, underachieving
in their mathematical performances (César, 2009, 2013a, 2024a, 2024b; César
& Machado, 2024, submitted). The Interaction and Knowledge (IK)
project lasted 12 years and involved around 600 classes, taught by 69
Mathematics teacher/researchers who participated in the IK team. The IK used
collaborative and dialogical work, implicit messages, inter- and
intra-empowerment mechanisms (César, 2009, 2024b), and bi-univocal cultural mediation
(César, 2017) as tools to give pupils a voice and to increase their
mathematical performances, contributing to an intercultural and inclusive
education. We focus on data from the action-research projects (Hamido &
César, 2009) and we assume an interpretative paradigm (Denzin, 2002). Data
treatment and analysis was based on a narrative analysis (Clandinin &
Conelly, 1998). The analysis of some examples of answers given to an instrument
to evaluate pupils’ abilities and competencies (IACC), elaborated by the IK
team, as well as the performances regarding some tasks used in class,
illuminate how important it is that Mathematics teachers respect pupils’
approaches, reasoning, and solving strategies. This is an essential feature to
empower them, to promote equity and social justice, thus contributing to an
intercultural and inclusive education.
Keywords: Mother language (L1), Mathematics learning, inter- and intra-empowerment mechanisms, life trajectories of participation, bi-univocal cultural mediation