In this study, we used multivariate decoding methods to study processing differences between canonical (montring and count) and noncanonical finger numeral configurations (FNCs). While previous research investigated these processing differences using behavioral and event-related potentials (ERP) methods, conventional univariate ERP analyses focus…

In the context of our rapidly digitizing society, computational thinking stands out as an essential attribute for cultivating aptitude and expertise. Through the prism of computational thinking, learners are more adeptly positioned to dissect and navigate real-world challenges, poising them effectively to meet the exigencies of future societal…

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper…

As part of a broader information literacy agenda, academic libraries are interested in advancing algorithmic literacy. Folk theories of algorithmic decision-making systems, such as recommender systems, can provide insights into designing and delivering enhanced algorithmic literacy initiatives. Users of the Spotify music recommendation systems…

Eighteen college students solved addition problems using the Hutchings Low Fatigue Addition Algorithm, which requires a written record of running sums, and the standard algorithm, which does not. Students using the Hutchings algorithm had significantly higher reaction times to a tone, indicating that the Hutchings method requires less cognitive…

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…