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The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks.

The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student completed a written assessment of mathematical knowledge. A system code (e.g. FR = failure to regroup) has been used to grade the tests. A reliability check has been performed on 65 per cent randomly selected exams.

Data frequency analyses reveal that the most common type of error was miscalculation for both addition (n = 164; 38.6 per cent) and subtraction (n = 180; 21.7 per cent). The second most common error type was related to failure to regroup in addition (n = 74; 17.5 per cent) and subtraction (n = 139; 16.3 per cent). Frequency of error types by grade level has been provided. Findings from the hierarchical regression analyses indicate that students’ performance differences emerged as a function of error types which indicated students’ types of difficulties.

There are several limitations of this study: the use of a convenient sample; all schools were located in the northern region of Portugal; the limited number of problems; and the time of the year of assessment.

Students’ errors suggested that their performance in calculation tasks is related to conceptual and procedural knowledge and skills. Error analysis allows teachers to better understand the individual performance of a diverse group and to tailor instruction to ensure that all students have an opportunity to succeed in mathematics.

Error analysis helps teachers uncover individual students’ difficulties and deliver meaningful instruction to all students.

This paper adds to the international literature on error analysis and reinforces its value in diagnosing students’ type and severity of math difficulties.

The purpose of this paper is to propose physically based varying fidelity surrogates to be used in structural design optimization of space trusses. The main aim is to demonstrate its efficiency in reducing the number of high fidelity (HF) runs in the optimization process.

In this work, surrogate models are built for space truss structures. This study uses functional as well as physical surrogates. In the latter, a grid analogy of the space truss is used thereby reducing drastically the analysis cost. Global and local approaches are considered. The latter will require a globalization scheme (sequential approximate optimization (SAO)) to ensure convergence.

Physically based surrogates were proposed. Classical techniques, namely Taylor series and kriging, are also implemented for comparison purposes. A parameter study in kriging is necessary to select the best kriging model to be used as surrogate. A test case was considered for optimization and several surrogates were built. The CPU time is reduced when compared with the HF solution, for all surrogate‐based optimization performed. The best result was achieved combining the proposed physical model with additive corrections in a SAO strategy in which C1 continuity was imposed at each trust region center. Some guidance for other engineering applications was given.

This is the first time that physical‐based surrogates for optimum design of space truss systems are used in the SAO framework. Physical surrogates typically exhibit better generalization properties than other surrogates forms, produce faster solutions, and do not suffer from dimensionality curse when used in approximate optimization strategies.

This study examines the destigmatization of second-hand consumption in a developing country through the lens of social practice theory. It explores media and institutional discourses surrounding children’s thrift stores, identifying key argumentative emphases that reshape perceptions of the second-hand market.

The methodology involves leveraging journalistic and institutional materials to gain insights into the practices molding the second-hand market. Content analysis is used to identify these sources’ pivotal themes and recurring categories, which were then divided into objects, doing and meanings, forming the basis for creating a “gear of practice.”

The findings reveal a complex network of practices that underpin the destigmatization of second-hand consumption. Specifically, they identify three circuits of practices forming a “gear of practice,” where suppliers, thrift store owners and customers play interchangeable roles, with their actions shaping the meanings and perceptions associated with second-hand goods.

This study introduces the innovative “gear of practice,” which represents a theoretical contribution to understand how practices intersect, considering the perspectives of various stakeholders. Furthermore, this framework advances theoretical discussion by providing insights into how businesses can navigate sustainable consumption trends, considering the role of consumer participation and organizational practices (doings), infrastructure investment and product attributes (objects) and diverse meanings (e.g. sustainability, economic advantage and participation in a new trend) in destigmatizing second-hand markets.