In this paper, I propose a new construct named "analytic equation sense" to conceptually model a desired way of reasoning that involves students' algebraic manipulations and use of equivalent expressions. Building from the analysis of two existing models in the field, I argue for the need for a new model and use empirical evidence to…

During language acquisition children generalise at multiple layers of granularity. Ambridge argues that abstraction-based accounts suffer from lumping (over-general abstractions) or splitting (over-precise abstractions). Ambridge argues that the only way to overcome this conundrum is in a purely exemplar/analogy-based system in which…

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an…

This article reviews two aspects of human learning: (1) people draw inferences that appear to rely on hierarchical conceptual representations; (2) some categories are much easier to learn than others given the same number of exemplars, and some categories remain difficult despite extensive training. Both of these results are difficult to reconcile…

Humans are sensitive to the properties of individual items, and exemplar models are useful for capturing this sensitivity. I am a proponent of an extension of exemplar-based architectures that I briefly describe. However, exemplar models are very shallow architectures in which it is necessary to stipulate a set of primitive elements that make up…

The syntactic behaviour of human beings cannot be explained by analogical generalization on the basis of concrete exemplars: analogies in surface form are insufficient to account for human grammatical knowledge, because they fail to hold in situations where they should, and fail to extend in situations where they need to. [For Ben Ambridge's…

Ambridge argues that the existence of exemplar models for individual phenomena (words, inflection rules, etc.) suggests the feasibility of a unified, exemplars-everywhere model that eschews abstraction. The argument would be strengthened by a description of such a model. However, none is provided. I show that any attempt to do so would immediately…

The authors argue that Ambridge's radical exemplar account of language cannot clearly explain all syntactic priming evidence, such as inverse preference effects ("greater" priming for less frequent structures), and the contrast between short-lived lexical boost and long-lived abstract priming. Moreover, without recourse to a level of…

Ambridge calls for exemplar-based accounts of language acquisition. Do modern neural networks such as transformers or word2vec -- which have been extremely successful in modern natural language processing (NLP) applications -- count? Although these models often have ample parametric complexity to store exemplars from their training data, they also…

This commentary critiques Ambridge's radical exemplar model of language acquisition using research from the Longitudinal Study of Early Language, which has tracked the language development of 30+ children with Autism Spectrum Disorders (ASD) since 2002. This research has demonstrated that the children's capacity for abstraction at the grammatical…

Ambridge reviews and augments an impressive body of research demonstrating both the advantages and the necessity of an exemplar-based model of knowledge of one's language. He cites three computational models that have been applied successfully to issues of phonology and morphology. Focusing on Ambridge's discussion of sentence-level constructions,…

In 'Against Stored Abstractions,' Ambridge uses neural and computational evidence to make his case against abstract representations. He argues that storing only exemplars is more parsimonious -- why bother with abstraction when exemplar models with on-the-fly calculation can do everything abstracting models can and more -- and implies that his…

Ambridge argues that there is widespread agreement among child language researchers that learners store linguistic abstractions. In this commentary the authors first argue that this assumption is incorrect; anti-representationalist/exemplar views are pervasive in theories of child language. Next, the authors outline what has been learned from this…

A characterization of the modelling process in science is proposed for science education, based on Mario Bunge's ideas about the construction of models in science. Galileo's "Dialogues" are analysed as a potentially fruitful starting point to implement strategies aimed at modelling in the classroom in the light of that proposal. It is…

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…