Insights into the reversal error from a study with South African and Spanish prospective primary teachers

This study, using a quantitative approach, examined Spanish and South African pre-service teachers’ responses to translating word problems based on direct proportionality into equations. The participants were 79 South African and 211 Spanish prospective primary school teachers who were in their second year of a Bachelor of Education degree. The study’s general objective was to compare the students’ proficiency in expressing direct proportionality word problems as equations, with a particular focus on the extent of the reversal error among the students’ responses. Furthermore, the study sought to test the explanatory power of word order matching and the static comparison as causes of the reversal error in the two contexts. The study found that South African students had a higher proportion of correct responses across all the items. While nearly all the errors made by Spanish students were reversals, the South African group barely committed reversal errors. However, a subgroup of the South African students made errors consisting of equations that do not make sense in the situation, suggesting that they had poor foundational knowledge of the multiplicative comparison relation and did not understand the functioning of the algebraic language. The study also found that the word order matching strategy has some explanatory power for the reversal error in both contexts. However, the static comparison strategy offers explanatory power only in the Spanish context, suggesting that there may be a difference in curriculum and instructional approaches in the middle and secondary years of schooling, which is when equations are taught.

Research on the peak prediction and intelligent computing of reversal error for the tilt feed system installed on the precision machine tools

To effectively predict the peak of reversal error of tilt feed system and reduce reversal error caused by friction and gravity components, a peak prediction method of reversal error for tilt feed system on the precision NC machine tool is proposed. According to the load, tilt angle, motion trajectory, maximum static friction torque and relevant dynamic characteristic information, the peak prediction formula of the reversal error for the tilt feed system is established by mathematical derivation based on the kinematics, dynamics and torque balance during the process of reversal. Thus, the peak of reversal error for the tilt feed system can be obtained. The experimental results show that this method can achieve a good prediction effect, and can predict the peak of reversal error before the machining. It provides a theoretical basis for the reversal error suppression.

The Students–Professors Problem—The Reversal Error and Beyond

This paper first introduces and reviews the existing research on the well-known “students–professors (S/P) problem”, which was first formulated in 1979. Next, it presents an empirical study of Danish upper secondary students’ answers to two mathematical modeling versions of the S/P-problem; a mathematization version (296 students), and a de-mathematization version (658 students). Besides reproducing several previously reported findings, e.g., the so-called reversal error, the study identifies new error types not previously reported in the literature. The mathematical modeling perspective adopted, along with a mixed-methods design, give rise to new potential explanations of the reversal error as well as explanations of the new error types. Our study shows that interpreting the linguistic formulation of the S/P-problem statement is not only related to language but is intrinsically of a mathematical – and cognitive – nature as well. Altogether, there is still more to be said about the S/P-problem forty years after its emergence. The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610104.

DEAF MIDDLE SCHOOL STUDENTS’ COMPREHENSION OF RELATIONAL LANGUAGE IN ARITHMETIC COMPARE PROBLEMS

This study examined the performance of deaf and hard of hearing middle school students on arithmetic compare word problems with relational statements. Thirteen prelingual, severe-to-profound deaf students were selected to participate. The results showed that the students were more likely to misunderstand a relational statement and make a reversal error when the required arithmetic operation was inconsistent with the statement’s relational term (e.g., choosing the operation of addition when the relational term was less than). There were no statistical differences in the number of reversal errors and on lexical markedness (i.e., marked vs. unmarked items). Finally, fraction-of-a-number relational terms exerted more influence on students’ abilities to solve word problems than did the lexical markedness. Findings are interpreted in light of the consistency effect hypothesis. Directions for future research and implications for instruction are also provided.

Childhood-Diagnosed ADHD, Symptom Progression, and Reversal Learning in Adulthood

Objective: ADHD persists in up to 60% into adulthood, and the reasons for persistence are not fully understood. The objective of this study was to characterize the neurofunctional basis of decision making in those with a childhood diagnosis of ADHD with either persistent or remitted symptoms in adulthood versus healthy control participants. Method: Thirty-two adults diagnosed with ADHD as children were split into persistent ( n = 18) or remitted ( n = 14) ADHD groups. Their neural activity and neurofunctional connectivity during a probabilistic reversal learning task were compared with 32 healthy controls. Results: Remitters showed significantly higher neural connectivity in final reversal error and probabilistic error conditions, and persisters depict higher neural connectivity in reversal errors than controls at a family-wise error (FWE) corrected whole-brain corrected threshold. Conclusion: Remitters may have utilized higher neural connectivity than controls to make successful decisions. Also, remitters may have utilized compensatory strategies to override any potential underlying ADHD deficits.