Introducing equations in early algebra

Radford, Luis

doi:10.1007/s11858-022-01422-x

Cited by 9 publications

(2 citation statements)

References 18 publications

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“…In the Numbers disciplinary area, over 50% of the students showed a good performance in only one of the attributes, at most, with the attribute of stablishing medium level relationships between numerical and algebraic expressions showing the highest frequency of success. These findings are interesting, considering the relationship that exists between the type of cognitive processes involved in the development of arithmetic and algebraic reasoning (Radford, 2022). As stated by Nunes and colleagues (2016), arithmetic reasoning can be understood as a cognitive generalization of numerical sense.…”

Section: Discussionmentioning

confidence: 74%

Nonparametric cognitive diagnosis of profiles of mathematical knowledge of teacher education candidates

et al. 2023

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Traditionally, the selection process of teacher candidates has emphasized the assessment of subject matter and pedagogical knowledge using psychometric methodologies, which simply organize candidates in continuous scales and require a large number of samples. However, these methods do not allow for the identification of candidates’ knowledge profiles and learning paths, which would help develop programs tailored to support students in their training process. In this study, an evaluation instrument was developed by using the nonparametric approach to model diagnostic classifications and was then validated on a sample of 119 participants. This instrument allows for disaggregating candidates’ initial knowledge and establishing relationships between its components. The results showed that candidates present a variety of profiles, which may consider more than one attribute. Not only does it provide a score that can be used for selection processes, it also provides useful information for initial teacher training methods.

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Section: Discussionmentioning

confidence: 74%

Nonparametric cognitive diagnosis of profiles of mathematical knowledge of teacher education candidates

et al. 2023

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“…When considering theories on teaching and learning, a more profound conceptualization is required, one that acknowledges the inherently social nature of these processes (Ernest, 2019), addresses responsibility and care (Ernest, 2019), and upholds a commitment to the content of mathematics education research, as seen in this study, or mathematics in the context of teaching the subject. An intriguing candidate for such a concept is the recently introduced notion of communitarian ethics by Radford (2022). Ethical action revolves around discerning right and wrong or good and bad behavior, which may be grounded in values embedded in design decisions.…”

Section: Reflection On Ethicsmentioning

confidence: 99%

Design research on an online summer school in mathematics education

Bikner-Ahsbahs

2024

EDeR

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Design research in education pursues two goals simultaneously: the development of a design and a local theory that clarifies how the design can achieve the intended effects and under what conditions. The results are obtained in an iterative cyclical process including both the implementation of the design and the research on its implementation. Each cycle contains a prospective phase, in which the design is determined, and a reflective phase, in which the implementation of the design is examined. The nested connection of theory and design development leads to a reciprocal relationship between the two final products. This article introduces an example of design research from mathematics education, in which an online summer school for doctoral students was to be framed in response to the sudden lockdown situation at the outbreak of the Covid-19 pandemic. At short notice, the original summer school was moved into the virtual space of a digital conference system resulting in new framework conditions; previous design principles were adapted and a rhythmical organization of space and time was theorized and implemented. Rhythm analyses show that design decisions to realize ontological, epistemological and axiological commitments intertwined and thus fostered students’ interactive learning processes. Consequently, the suggestion is made to merge the three commitments into a three-dimensional framework concept of ethico-onto-epistemological commitments. Such a framework concept would have the function of reconciling ethical, ontological and epistemological dimensions in design research in the pursuit of robust teaching-learning processes and incorporating the ethical responsibilities of design researchers conceptually for both design and local theory.

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Algebra Education and Digital Resources: A Long-Distance Relationship?

Haspekian,

Kieran,

Drijvers

et al. 2023

Springer International Handbooks of Education

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This chapter considers the general question of how technology impacts mathematical contents for the case of algebra and addresses it from the conceptual notion of instrumental distance. It first provides an overview of perspectives on the teaching and learning of algebra in primary and secondary education. Next, it presents the theoretical lens of instrumental distance, used to study how these algebraic contents are transformed by digital tools. Using three examples of digital resources that cover different school levels and different types of design, the chapter shows that this lens indeed reveals how digital technology may create distance with respect to the regular algebraic contents and procedures carried out in the paper-and-pencil environment. The results thus raise awareness not only of new potentialities, but also of the complexity generated by technology. They suggest that being aware of the instrumental distance would be beneficial while developing digital resources and professional development programs that aim to integrate digital technologies into the teaching and learning of algebra.

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Introducing equations in early algebra

Cited by 9 publications

References 18 publications

Nonparametric cognitive diagnosis of profiles of mathematical knowledge of teacher education candidates

Nonparametric cognitive diagnosis of profiles of mathematical knowledge of teacher education candidates

Design research on an online summer school in mathematics education

Algebra Education and Digital Resources: A Long-Distance Relationship?

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