Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

This study explored whether a daytime nap aids children's acquisition of letter-sound knowledge, which is a fundamental component for learning to read. Thirty-two preschool children in Sydney, Australia (M[subscript age] = 4 years;3 months) were taught letter-sound mappings in two sessions: one followed by a nap and the other by a wakeful period.…

Natural languages contain systematic relationships between verb meaning and verb argument structure. Artificial language learning studies typically remove those relationships and instead pair verb meanings randomly with structures. Adult participants in such studies can detect statistical regularities associated with words in these languages and…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

In this study, we explored enacted task characteristics (ETCs) that supported students' quantitative reasoning (QR). We employed a design-based methodology; we conducted a teaching experiment with eight secondary school students. Through ongoing and retrospective analyses, we identified ETCs which supported students' quantitative reasoning. The…

The purpose of the study is to evaluate how prospective mathematics teachers (PMTs) modify tasks to facilitate students' learning of pattern generalization through the use of their mathematical knowledge for teaching. Case study, which is a type of qualitative research method, was used to determine the mathematical characteristics that PMTs use…

The present study investigates the effect of high variability phonetic training (HVPT) on the discrimination of second language (L2) vowel contrasts by adult speakers who live in a country where the L2 is dominant. The same subjects who participated in a previous discrimination task were trained in the discrimination of four L2 vowel contrasts…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…

The objective of this article is to describe types of mathematical reasoning evidenced by a middle school mathematics teacher, when answering two generalization questions in a figural pattern generalization task, related to quadratic sequences. Reasoning is delimited from teacher's arguments, reconstructed from a theoretical-methodological…

Generalization is the ability to apply regularities to novel instances, for example, correctly guessing that the plural for the novel English word 'wug' should be 'wugs'. Early language learners make overgeneralization errors like 'mouses', applying regularities beyond their attested uses. Theories concerned with the question of how learners learn…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

This study employed a multisite design to investigate the differential impact of deductive and guided inductive instruction for second language (L2) grammar development in ecologically valid classroom contexts. Students (n = 138) from eight intact third-year L2 Spanish classes in three public high schools in the United States received deductive…

The acquisition of a new morphological rule can be influenced by numerous factors, including the type of feedback provided during learning. The present study aimed to test the effect of different feedback types on children's ability to learn and generalize an artificial morphological rule (AMR). Two groups of eight-year-olds learned to judge and…

The present study explores the ways in which young EFL learners draw on lived experiences, viewed as interactional experiences in L1 or L2 which they have participated in or observed, to ground their metapragmatic understandings. Building on previous research with adult (e.g. McConachy 2018) and young learners (Savic 2021; Savic and Myrset 2021),…