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Young children, who are exposed to Latin script letters, experience difficulties in distinguishing between the reversible letters b and d and may therefore transform b into d (and vice versa). When children begin to write, in cultures with left-to-right writing/reading systems, they also often turn Arabic digits in the direction of writing/reading, thus, for example, producing ε instead of 3. However, two different terms or processes, namely, confusion and reversal, are used in the literature to label these apparent transformations. This study aimed to provide empirical evidence that the two processes are indeed very different. The sample consisted of 529 first graders (Mage = 6.21 years) who participated in the French National Assessment at the beginning of the school year. Simple linear, Bayesian, and logistic regression modeling of the left–right reversal rate in writing digits as a function of the confusion rate in children's recognition of the letters b and d showed a negative relationship between the two rates, and a nonparametric test yielded a significant negative correlation (rS(318) = –0.373, p <.001). These results seem to rule out the possibility that the same process leads to reversing characters (letters or digits) in writing and misrecognizing b as d (or vice versa). This is the first study reporting strong empirical evidence that the processes of reversal and confusion are very different. Consequently, it would be a mistake to treat confusion between b and d as the reversal of b into d (and vice versa). [ABSTRACT FROM AUTHOR]

The question of teaching a standard written algorithm for the four arithmetical operations in the first years of elementary school is increasingly raised as a consequence of the possibility of using calculators, tablets, and computers. This article first presents arguments both against and for maintaining this teaching in the first school years. Then, it presents an analysis of the procedure—whether it implies the standard algorithm or not—used by second grade students to solve a subtraction verbal problem. The 4720 students involved in the research were divided in a control group (n = 2101) and an experimental group (n = 2619) in which the standard written algorithm (SWA) was taught, or not taught, respectively. The effectiveness of algorithm use was analyzed not only in terms of accuracy of the answers, but also for its influence on the choice of the correct arithmetical operation and for its choice by the students as a function of their ability. The SWA was strongly associated with the use of the false arithmetical operation (effect size ϕ = 0.79)—addition instead of subtraction—but was chosen by students of all levels of ability. The latter result suggests that the SWA is well suited for the most advanced students but far less for the others who use it mechanically and without reflection. [ABSTRACT FROM AUTHOR]

Ensuring students correctly understand the notion of equality is a fundamental problem in teaching mathematics. Is it possible to teach arithmetic in such a way that students do not misinterpret the equal sign "=" as indicating the result of an arithmetic operation and, consequently, viewing the arithmetic operation symbols (+, -, or x) as systematically meaning perform a computation? The present paper describes the implementation of an experimental arithmetic teaching program (called ACE) drawn up in conjunction with teachers and focusing on these issues. We assessed the program's impact via an experiment involving 1140 experimental group students and 1155 control group students, and using a pretest/posttest design. The experimental group students achieved higher composite arithmetic scores, combining all four subdomains (arithmetic writing, mental computation, word-problem solving, and estimation), than control group students. The effect size, computed using individuals' posttest scores adjusted for pretest scores was d = 0.559. The ACE program was effective in all four subdomains tested; however, it was particularly successful in the arithmetic writing subdomain, especially in writing equalities. The program's effect not only held one year later, it was cumulative, as the benefits produced by following the program in both first and second grade were almost double those of following the program in just one grade. [ABSTRACT FROM AUTHOR]

Recent research has established that 5- to 6-year-old typically developing children in a left-right writing culture spontaneously reverse left-oriented characters (e.g., they write instead of J) when they write single characters. Thus, children seem to implicitly apply a right-writing rule (RWR: see Fischer & Koch, 2016a). In Study 1, the reversal of all asymmetrical digits and capital letters by 356 children was modeled with a simple Rasch model, which describes reversal as the outcome of two competing responses, correct writing and writing in the cultural direction of writing. It accounts for the high frequency of reversals of the left-oriented characters (3, Z, J, 1, 2, 7, 9), as predicted by the RWR. Study 2 investigated letter reversals when children spontaneously write their name from right to left. Most of the 204 children in the study radically changed the direction of the RWR by reversing mainly the right-oriented letters (B, C, D, E, F, G, K, L, N, P, R, S). Hence, a more universal formulation of the RWR would be as an implicit rule orienting characters in the writing direction. This reformulated rule is consistent with the 'spatial agency bias' model (Suitner & Maas, 2016), according to which writing direction affects thoughts and actions. Visual and motoric statistical learning may favor bootstrapping of the rule. Taken together, these data demonstrate the prominent role of culture in a phenomenon-character reversal or mirror writing-which has often been presented uniquely as biologically determined. [ABSTRACT FROM AUTHOR]

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