The Properties of Powers: Didactic Contract and Gender Gap
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The Properties of Powers: Didactic Contract and Gender Gap Federica Ferretti 1
& Chiara
Giberti 2
Received: 18 December 2019 / Accepted: 7 September 2020/ # The Author(s) 2020
Abstract National and international large-scale assessments of mathematics show that, in most nations, males achieve better results than females and Italy is one of the countries with a greater gap. Many research studies in mathematics education have analysed this issue, using both quantitative and qualitative methods to understand the sources and characteristics of this gap. This study focuses on a specific Grade 10 task that requires algebraic manipulations of powers with the same base. Item-level analysis enables the study of gender differences on specific content, before using the lenses of mathematics education theories to interpret macro-phenomena emergeing from standardized assessment results. The quantitative analysis, carried out using the Rasch statistical model, highlights a gender gap in favour of males in this task and, furthermore, a variance in choices of incorrect options between males and females; the interviews conducted provide a key to understanding this phenomenon in terms of didactic contract. Keywords Didactic contract . Gender gap . Large-scale assessment
Rationale. This research fits into a socio-constructivist perspective, according to which the student actively builds his/her own knowledge, interacting with the environment and organizing his/her mental constructs; the student does not simply receive information in a passive manner, but constantly re-elaborates each proposal independently. Social interaction plays a fundamental role within our study, framed by the didactic contract construct as defined by Brousseau (1988) and its features and results based on gender. Research (i.e. Lindberg, Hyde, Petersen & Linn, 2010; Primi, Busdraghi,
* Federica Ferretti [email protected]
1
Department of Education, University of Bologna, Bologna, BO, Italy
2
Department of Human and Social Sciences, University of Bergamo, Bergamo, Italy
F. Ferretti, C. Giberti
Tomasetto, Morsanyi & Chiesi, 2014) highlights that the gender gap is often affected by meta-cognitive aspects and that its characterization depends on factors not exclusively within the sphere of cognition. Specific studies (i.e. Cascella, Giberti, Bolondi, 2020; Leder, 1992; Leder & Forgasz, 2008; Organization for Economic Cooperation and Development [OECD], 2016a) highlight how variables linked to teaching practice, such as curriculum variables and assessment methods, might affect the gender gap in mathematics. One of the aims of this research study is to investigate, quantify and characterize macro-phenomena related to a gender gap which emerges from standardized assessments and may be framed within the context of the didactic contract. This research is carried out in accordance with the concept that standardized assessment results may be useful both for research and teachers, and can provide timely and efficient information to positively affect the
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