Abstract
The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge, which need to be diagnosed aiming to assist them in developing the required knowledge to teach according to that perspective. This study aims to understand what aspects of functional thinking Spanish and Portuguese elementary PTs exhibit at the beginning of their teacher education program. The findings show that although PTs from both countries use different strategies to generalize functional relationships, the occurrence of successful strategies is low. Also, most participants provide local approaches in their interpretation of relationships between variables and reveal difficulties in understanding and connecting different representations of functions. These difficulties show that PTs lack important knowledge about functional thinking. By providing a framework concerning the functional thinking required for PTs to teach within an early algebra perspective, we shed light on a necessary step for teacher education programs to diagnose PTs’ functional thinking and to assist them in developing the needed mathematical knowledge to teach accordingly.
Highlights
Abstrak Pentingnya pengenalan ide-ide aljabar siswa sebelum pendidikan menengah telah terungkap dalam penelitian literatur ini
By providing a framework concerning the functional thinking required for prospective teachers (PTs) to teach within an early algebra perspective this paper intends to shed light on a necessary step for teacher education programs to diagnose PTs’ functional thinking and to assist them in developing the needed mathematical knowledge to teach according to that perspective
Most participants provide local approaches in their interpretation of relationships between variables and reveal difficulties in understanding and connecting different representations of functions. These findings show that regardless of PTs’ school experiences in mathematics and the differences among the curriculum in both countries, PTs lack important knowledge about functional thinking when they start their preparation to become elementary teachers
Summary
Abstrak Pentingnya pengenalan ide-ide aljabar siswa sebelum pendidikan menengah telah terungkap dalam penelitian literatur ini. To better document the PTs’ functional thinking and difficulties, Lannin et al (2006) emphasize the need to be attentive to the commonly used frameworks to classify students’ approaches to pattern generalization and to adapt them for characterizing PTs’ knowledge regarding functional thinking This recommendation is important in countries like Portugal and Spain where the elementary mathematics curriculum emphasizes ideas with some resonance with an early algebra perspective, regarding functional thinking, but where there is not a consolidated practice around that perspective in schools (Morales et al, 2018; Oliveira & Mestre, 2014). By providing a framework concerning the functional thinking required for PTs to teach within an early algebra perspective this paper intends to shed light on a necessary step for teacher education programs to diagnose PTs’ functional thinking and to assist them in developing the needed mathematical knowledge to teach according to that perspective
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