<aside> <img src="/icons/info-alternate_gray.svg" alt="/icons/info-alternate_gray.svg" width="40px" /> Research Info.
Project: Metadidactial Analysis of Mathematical Teaching.
Author: Àlex Miró Mediano.
Supervisors: Marc Alier Forment, Javier Mora Serrano.
University: Universitat Politècnica de Catalunya.
Centre: Institut de Ciències de l’Educació.
Funding: FPI UPC Banco Santander 22.
Correspondance: [email protected].
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<aside> <img src="/icons/info-alternate_gray.svg" alt="/icons/info-alternate_gray.svg" width="40px" /> What’s on this page? This page reviews already completed research activities and discusses future research lines on the doctoral investigation conducted by Àlex Miró Mediano, under the title Metadidactical Analysis of Mathematics Teaching at UPC. The research began with the definition of the Mathematical Knowledge Matrix (MKM), a tool for assessing complexity in mathematics education. Initial findings suggested limitations in MKM for word problems, prompting deeper exploration and identification of several complexity sources through teacher interviews. Five variables were then defined to measure the identified sources of complexity. Variables were proven to be reliable, and the effect of each variable was studied. Future research includes analysing mathematics textbook editorials’ test data to extend current findings, and studying different learning sequences’ impacts on student outcomes, aiming to enhance math education.
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Index of Contents
1 Completed Actitivies and Research Outcomes
The Mathematical Knowledge Matrix (MKM) emerged as the first research outcome after reviewing cognitive load theory literature. The first research activity consisted in defining the MKM as ‘a tool to address difficulties in teaching and learning mathematics by focusing on the management of complexity and prior knowledge’.
Publications:
(1) Paper in Conference Proceedings: The MKM: Identify and Assess Complexity and Prior Knowledge in Your Math Didactics (Miró, Alier & Mora, 2023). TEEM 2023: 11th International Conference on Technological Ecosystems for Enhancing Multiculturality
(2) Conference Paper Presentation: Presenting the MKM: a tool for assessing math didactics through element interactivity and prior knowledge (Miró, Mora, & Alier, 2023). ICLTC: 15th International Cognitive Load Theory Conference.
The MKM was focused on interactivity between knowledge elements. We used it to evaluate the complexity of several tasks and we compared our results with the perspectives of experienced teachers and cognitive load theory experts. The MKM was found to be invalid for word problems complexity assessment because it did not measure several complexity sources related to them. Therefore, in our second research activity, we studied these complexity sources in greater depth, as follows.
This research explored the complexity of secondary school mathematics through the perspectives of experienced in-service teachers and the framework of cognitive load theory. The research identified several sources of complexity in learning mathematics and compared them with the definitions of complexity within cognitive load theory. Semi-structured interviews with N = 11 secondary school mathematics teachers were conducted. The findings offered insights into the nature of the difficulties students encounter while learning mathematics and thus provided an approximation to the sources of complexity that should be considered when assessing secondary school mathematics.
Publications:
(3) Paper in Indexed Journal (Manuscript submitted under peer review): Why is Secondary Mathematics Difficult to Learn? Form the Perspectives of In-Service Teachers and Cognitive Load Theory (Miró, Alier, Chen, Mora & Castro-Alonso, 2024).
(4) Data set: Data for: Why Is Secondary School Mathematics Difficult to Learn? From the Perspectives of In-Service Teachers and CLT. https://doi.org/10.5064/F6MAO6TQ.