In this response to commentators, I agree with those who suggested that the distinction between exemplar- and abstraction-based accounts is something of a false dichotomy and therefore move to an abstractions-made-of-exemplars account under which (a) we store all the exemplars that we hear (subject to attention, decay, interference, etc.) but (b)…

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…

We present a framework designed to help categorize various sense making moves, allowing for greater specificity in describing and understanding student reasoning and also in the development of curriculum to support this reasoning. The framework disaggregates between the mechanisms of student reasoning (the cognitive "tool" that they are…

Critical thinking is a core skill within tertiary education, traditionally relying on such principles as logic and truth. Relativistic pedagogical frameworks, such as critical literacy, however, have become increasingly widespread within all levels of education and call into question such principles. In order to ascertain whether critical thinking…

By using high-leverage models to connect student learning experiences to overarching concepts in mathematics, teachers can anchor learning in ways that allow students to make sense of content on the basis of their own prior experiences. A rectangular area model can be used as a tool for understanding problems that involve multiplicative reasoning.…

While AI has become more prevalent in our society than ever, many young learners are found holding various naive, erroneous conceptions of AI due to the influence of their technology and media environments. To address this issue, this study seeks to propose a novel pedagogical solution to improve upper-elementary school students' scientific…

In this study, a research team made up of Métis artists and knowledge keepers, Anishinaabe and non-Indigenous educators, and a non-Indigenous university mathematics education researcher co-designed and delivered an Indigenous cultural mathematical inquiry in a Grade 5 classroom. We explored the connections between loom bead designs and…

This paper examines the relation between epistemology and higher education. We shall start by briefly examining three classical texts on the understanding of knowledge at universities, as well as noting some others, and go on to sketch a version of our own. Our argument is as follows: the world is such that the relationship between the university…

Drawing on prior research on indirect proof, this paper reports on a series of exploratory studies that examine the extent to which findings on students' ways of reasoning about contradiction and contraposition characterize students' views of indirect existence proofs. Specifically, Study 1 documents students' comparative selections and selection…

To promote learning and transfer of abstract ideas, contemporary theories advocate that teachers and learners make explicit connections between concrete representations and the abstract ideas they are intended to represent. "Concreteness fading" is a theory of instruction that offers a solution for making these connections. As originally…

This article concerns a lacuna in chemistry students' reasoning about chemical bonding. Although chemistry students are familiar with the charges that make up the atom--both positive and negative--they refer only to the attraction between unlike charges. Specifically, they ignore the repulsion between the positive nuclei. We named this disregard…

Learning from expository science texts is challenging. These studies explore whether difficulties can be attributed to poor memory or poor reasoning. To eliminate the need for memory during testing, some students took the tests with the texts available. To test for the effects of reasoning on performance, some students were prompted to engage in…

Introductory programming courses (CS1) are difficult for novices. Inspired by "Problem solving followed by instruction" and "Productive Failure" approaches, we define an original "necessity-driven" learning design. Students are put in an apparently well-known situation, but this time they miss an essential ingredient…

As a multifaceted concept, the learning of angle concepts takes years to achieve and is beset with challenges. This paper explores how the processes of constructing and validating a learning progression in geometric reasoning can be used to generate targeted teaching advice to support the learning of angle concept. Data from 1090 Year 4 to Year 10…

In this dissertation study, I report on six middle school students' construction and interpretation of graphs and associated dynamic situations. Constructing and interpreting graphs represents a critical moment in middle school mathematics due to its opportunity to provide a powerful foundation for learning. Nevertheless, researchers have…