Prospective high school mathematics teachers’ assessment of the epistemic suitability of a proportionality textbook lesson

Abstract

Background: Every teacher should be able to use curriculum materials to guide instructional design and make reasoned pedagogical decisions about the limitations these resources may have. Objectives: In this paper, we describe and analyse a formative intervention with prospective high school mathematics teachers, aimed at developing their competence of didactic suitability analysis of mathematics textbook lessons. Design: The methodology followed is didactic engineering, furthermore, the content analysis methodology is applied to examine the response protocols of the participants. Setting and Participants: The experience was carried out within the framework of a University Master's Degree in Compulsory Secondary Education and High School; the sample was made of 30 students. Data collection and analysis: We proposed these prospective teachers systematically and critically analyse a lesson on proportionality. The written reports of the lesson suitability produced by 14 work-teams are compared with the a priori analysis carried out by the researchers. Results:The results suggest that the prospective teachers usually make more descriptive and less analytical analyses even while using a guide. The participants did not clearly identify the epistemic deficiencies of the lesson, thus revealing their limited didactic-mathematical knowledge on proportionality and their lack of critical evaluation of the textbook. However, based on the analysis previously conducted, prospective teachers managed to be quite accurate in preparing their proposals for the use of the textbook lesson. Conclusions: In this article we show the interest and usefulness of providing future teachers with a tool to systematically analyse a specific textbook lesson. However, in order for future teachers to acquire the necessary skills in critical analysis of the lesson, it is necessary to reinforce their didactic-mathematical knowledge related to proportionality.

Developing reflective competence in prospective mathematics teachers by analyzing textbooks lessons

“…The research team is committed to reflect after each implementation in order to readapt the initially proposed design, if necessary. Thus, for the planning and design of the training experience described in this article, we relied on the retrospective analysis of interventions previously implemented with future Spanish teachers of primary education (Castillo & Burgos, 2022) and secondary education (Castillo et al, 2021(Castillo et al, , 2022c. As we show in the next section, the limitations found in those training actions were considered to improve the design and implementation of the new intervention.…”

“…In previous experimental cycles, it was observed that participants did not justify the level of compliance with each indicator in the TLAG-Proportionality (Castillo et al, 2021(Castillo et al, , 2022cCastillo & Burgos, 2022). For this reason, it was decided to include in the guide given to the PMT, in addition to the column for recording the numerical rating (0, 1, 2) of the degree of compliance with each indicator, another column in which they had to explain the reasons that had led them to assign that rating.…”

“…For this reason, it was decided to include in the guide given to the PMT, in addition to the column for recording the numerical rating (0, 1, 2) of the degree of compliance with each indicator, another column in which they had to explain the reasons that had led them to assign that rating. Moreover, in the new intervention, PMT were asked to apply the TLAG-Proportionality globally to the whole lesson, whereas in previous experiences the text was broken down by didactic configurations that constituted the units of analysis (Castillo et al, 2021(Castillo et al, ,2022cCastillo & Burgos, 2022). This change made it possible to alleviate the participants' workload and to see the exercise and evaluation tasks proposed in the lesson (normally separate) together with the conceptualization or exemplification tasks proposed by the author of the textbook.…”

Competencia de análisis y reflexión sobre la gestión de lecciones de libros de texto por maestros en formación

“…These suitability indicators must be enriched and adapted according to the specific mathematical content to be taught (Breda et al, 2017), but also to the type of instructional medium, understanding that both constrain aspects of the different components in didactic suitability. Thus, in Castillo et al (2021), the system of didactical suitability components and indicators of Godino (2013) is revised and particularised to develop a textbook lesson analysis guide for proportionality (TLAG-Proportionality) as a tool to guide the reflection of pre-service and in-service teachers on the instructional processes planned in textbook lessons on proportionality. This guide includes specific indicators based on an exhaustive review of research results and expert judgments assumed by the academic community (Breda et al, 2017), which allow identifying didactic-mathematical knowledge to be considered in the evaluation, redesign or management of proportionality teaching processes.…”

“…Some of the specific interventions developed in the field of teacher education based on the DMKC model have used the didactic competence tool, its components and indicators (Godino, 2013) to organise teachers' systematic reflection on their own practice or that of others and to develop the competence to evaluate planned or implemented instructional processes (Breda et al, 2018;Font et al, 2018;Giacomone et al, 2018;Hummes et al, 2019;Morales-López and Araya-Román, 2020;Pino-Fan et al, 2013). Some of these studies have dealt specifically with the mathematical content of proportionality (Burgos et al, 2018;Castillo et al, 2021;Esqué & Breda, 2021). Despite the longitudinal and cross-cutting importance of this content in the primary and secondary curricula, as well as being the bridge to advanced mathematical thinking, proportionality is often not adequately addressed in school mathematics textbooks at both stages (Ahl, 2016;Burgos, Castillo et al, 2020;Shield & Dole, 2013).…”