[MATHLINK] Call for Papers in JNC on the Development of Mathematical Understanding

[Jo-Anne LeFevre]

We are pleased to announce a special thematic section of the Journal of Numerical Cognition on the Development of Mathematical Understanding. Please see the details on the JNC Website:

(Call for Papers: The Development of Mathematical Understanding| Journal of Numerical Cognition (psychopen.eu)<https://can01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fjnc.psychopen.eu%2Findex.php%2Fjnc%2Fannouncement%2Fview%2F89&data=05%7C02%7CJoAnneLefevre%40cunet.carleton.ca%7Cc1b24e18b1ad494adb4108dc187b8c69%7C6ad91895de06485ebc51fce126cc8530%7C0%7C0%7C638412166116822830%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=DZpmd1GrLozxgCwgf4rpcKfCtt9ircnAnTgjN3gucy0%3D&reserved=0>


Interested authors should submit an abstract (300 – 500 words) via email to Daniel B. Berch (dbb6h at virginia.edu<mailto:dbb6h at virginia.edu>) that summarizes the proposed content and foci of the paper. These abstracts will form the basis for selection to submit a complete manuscript. The deadline for submission of these abstracts is March 15, 2024. Accepted papers will be due February 15, 2025.
Special Issue Editors: Daniel B. Berch, Jo-Anne LeFevre, Helena Osana, Bert DeSmedt
Background
Although the study of children’s conceptual knowledge in mathematics has received an increasing amount of attention over the past several decades, most cognitive and developmental psychologists have used the terms “knowledge” and “understanding” interchangeably, rarely explicating differences in the ways they may be defined or measured. That said, Bisanz and LeFevre (1992) put forward a very useful, two-dimensional classification scheme for assessing the understanding of elementary mathematics consisting of 1) the type of activity involved (applying, justifying, and evaluating solution procedures) and 2) the degree of generality with which these activities are executed (i.e., narrow, or broad). More recently, Crooks & Alibali (2014) provided a comprehensive review and incisive analysis of the numerous and heterogenous ways in which conceptual knowledge has been characterized and measured, concluding that only some of these definitions and assessments appear to be a good fit for this construct if it is divided into two facets: knowledge of 1) general principles, and 2) the principles underlying procedures. However, if as these authors recommend, the tasks that should be used for measuring the acquisition of what they consider as knowledge are those suggested by Bisanz and LeFevre (e.g., applying, justifying, evaluating), then successful performance may more appropriately be interpreted as having demonstrated the attainment of understanding. That is, in comparison with mathematical knowledge, mathematical understanding can be thought of as a higher-order intellectual achievement and epistemic state that requires an ability to ‘grasp’, to varying degrees and in different forms (e.g., why, how, of), conceptual relations between mentally represented mathematical ideas or objects (see Hannon, 2021 for a review of contemporary epistemological perspectives on distinguishing between knowledge and understanding).
Interestingly, the construct of mathematical understanding has long been regarded as the sine qua non of teaching and learning in the mathematics education community. Indeed, math educators almost universally claim that achieving a deep understanding of mathematics is the ultimate goal of instruction. Concomitantly, mathematics education scholars and researchers have written extensively about the nature and acquisition of mathematical understanding (Hiebert & Carpenter, 1992; Sierpinska, 1990,1994; Skemp, 1976), most often developing their theories and designing educational practices from a constructivist perspective (Cai & Ding, 2017; Pirie & Kieren, 1994). On one hand, their emphasis on students’ descriptions of and explanations for their problem solutions in this literature has provided a valuable resource for examining mathematical understanding. On the other hand, this body of work is limited in some important ways that preclude a fuller account of the cognitive processes underlying the development of children’s understanding of mathematics.
Aims of the special issue
The primary aims of this special issue are to provide readers with a collection of papers representing diverse disciplinary perspectives that not only can contribute robust empirical findings regarding the development of mathematical understanding, but also expand our toolkit for measuring this construct as well as advance our knowledge of its theoretical underpinnings. We also hope these articles will stimulate future examination of a topic that is of interest to cognitive, developmental, and educational psychologists and mathematics education researchers.

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