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Many researchers have investigated flexibility of strategies in various mathematical domains. This study investigates strategy use and strategy flexibility, as well as their relations with performance in non-routine problem solving. In this context, we propose and investigate two types of strategy flexibility, namely inter-task flexibility (changing strategies across problems) and intra-task flexibility (changing strategies within problems). Data were collected on three non-routine problems from 152 Dutch students in grade 4 (age 9–10) with high mathematics scores. Findings showed that students rarely applied heuristic strategies in solving the problems. Among these strategies, the trial-and-error strategy was found to have a general potential to lead to success. The two types of flexibility were not displayed to a large extent in students’ strategic behavior. However, on the one hand, students who showed inter-task strategy flexibility were more successful than students who persevered with the same strategy. On the other hand, contrary to our expectations, intra-task strategy flexibility did not support the students in reaching the correct answer. This stemmed from the construction of an incomplete mental representation of the problems by the students. Findings are discussed and suggestions for further research are made.

In this article we review the research on the flexible or adaptive use of solution strategies in school mathematics, with a focus on the most recent work in the field. After a short introduction, we provide an overview of the various ways in which strategy flexibility has been conceptualized and investigated in the research literature. Then we review the research that has looked at the relationship between strategy flexibility and task proficiency, followed by studies that analyzed the association of strategy flexibility and other learner variables, including learners’ age, general mathematical ability, prior knowledge, executive functions, gender, and affect. Studies addressing the socio-cultural and educational embeddedness of strategy flexibility are reviewed next, and, finally, we discuss the intervention studies that have tried to stimulate learners’ strategy flexibility by means of various instructional approaches. While this review reveals that strategy flexibility is increasingly recognized as an important and valuable construct in research and practice of mathematics education, and that recently substantial progress has been made in our understanding of this construct, there are many aspects of it that are still not well-understood and that need further investigation.

In this paper, the multidigit arithmetic-related strategy adaptivity, strategy flexibility and solution accuracy of Danish compulsory school students is examined. Participants, 749 grade three, 731 grade six and 818 grade eight, were drawn from twenty demographically different schools. Drawing on a tri-phase assessment tool, each student completed a series of tasks designed to elicit shortcut strategies. First, students solved each task by means of their preferred strategy; those using shortcut strategies were construed as adaptive for that task. Second, students solved the same tasks by means of whatever alternative strategies they had available; those offering at least two strategies were construed as flexible for that task. Third, for each task, students were asked to indicate which of their strategies they believed was optimal. Across all grades, students were more flexible than adaptive. Overall, sixth graders exhibited higher levels of flexibility than third graders and marginally lower levels than eighth graders. Sixth graders exhibited higher levels of adaptivity than those in either grade three or grade eight. Students’ accuracy, which improved with maturation, was influenced positively by both adaptivity and flexibility, with flexibility having the greatest influence in grade three and adaptivity in grade six. The findings raise further questions concerning, inter alia, culture’s influence on students’ strategy choices and the interaction of adaptivity, flexibility and maturity on accuracy.

Due to the popularization and development of new energy vehicles (NEVs) worldwide, power batteries that have been used are being retired and replaced. In China’s battery recycling industry, the legal NEV battery recycling enterprises are at a negative financial performance. Based on theory of organizational adaptation, the key to innovation performance and sustainable development is recognition of the environment and strengthening organizational flexibility. This study empirically explores the bidirectional dynamic relationships among heterogeneous environmental uncertainties, innovation activities, firm growth and strategic flexibility in Chinese NEV battery recycling firms. A total of 1040 sample data were collected from 2015 to 2021. The research results demonstrate that environmental uncertainty (EU), strategic flexibility (SF) and innovation activities (INNO) all had impacts on firm growth (FG). Specifically, INNO had strongly negative effects in the short term, and in the long term, it will bring a positive effect to FG; the impact of EPU was more important than market uncertainty (MU) to FG and innovation activities. This could be due to the dependence of the Chinese NEV battery recycling industry on government policy. However, MU has a strong impact on SF. Moreover, the levels of SF should be reasonable, otherwise it could be a burden to enterprises. There also exists the bidirectional dynamic relationships between FG and INNO. This study contributes a non-core perspective to strategic flexibility research by revealing the complex environmental mechanism, and to the Chinese NEV battery recycling industry we provide a theoretical basis and practical guidance for government and firms on how to apply SF to promote innovation and realize growth in the present business environment.

This study aims to determine the effect of an instruction dealing with non-routine problem solving on fifth graders' strategy flexibility and success in problem-solving. For this aim, a quasi-experimental pre-test- post-test design without a control group was designed. The sampling method of the research is convenience sampling. There were 65 fifth graders (11–12 years of age) who came from two different classes of a public middle school located in Istanbul/Turkey. The instruction carried out by the first researcher in the students' classrooms lasted ten weeks (20 lesson hours). Pre-test and post-test consisted of eight non-routine problems which can be solved by using guess and check, make a systematic list, work backward, look for a pattern, simplify the problem, and make a drawing strategies. The results showed that instruction that focuses on non-routine problem solving could improve students' strategy flexibility in this area. Besides, non-routine problem-solving instruction was associated with a significant positive improvement in students' problem-solving achievement. Based on these results, some educational implications and suggestions for future studies were discussed.

The sustainable utilization of forest biomass for bioenergy production is increasingly challenged by the variability and unpredictability of raw material availability. These challenges are particularly critical in regions like Central Portugal, where seasonality, dispersed resources, and wildfire prevention policies disrupt procurement planning. This study investigates two flexibility strategies—dynamic network reconfiguration and operations postponement—as policy relevant tools to enhance resilience in forest-to-bioenergy supply chains. A novel mathematical model, the mobile Facility Location Problem with dynamic Operations Assignment (mFLP-dOA), is proposed and solved using a scalable matheuristic approach. Applying the model to a real case study, we demonstrate that incorporating temporary intermediate nodes and adaptable processing schedules can reduce costs by up to 17% while improving operational responsiveness and reducing non-productive machine time. The findings offer strategic insights for policymakers, biomass operators, and regional planners aiming to design more adaptive and cost-effective biomass supply systems, particularly under environmental risk scenarios such as summer operation bans. This work supports evidence-based planning and investment in flexible logistics infrastructure for cleaner and more resilient bioenergy supply chains.

This study investigates elementary school children’s flexible use of mental calculation strategies on additions and subtractions in the number domain 20–100. Sixty third-graders of three different mathematical achievement levels individually solved a series of 2-digit additions and subtractions in one choice and two no-choice conditions. In the choice condition, children could choose between the compensation (56 + 29 = ?; 56 + 30 = 86, 86 − 1 = 85) and jump strategy (56 + 29 = ?; 56 + 20 = 76, 76 + 9 = 85) on each item. In the two no-choice conditions, children had to solve each item with either the compensation or the jump strategy. The results demonstrated that children of all achievement levels spontaneously applied both the compensation and the jump strategy to solve the items from the choice condition. Furthermore, they all executed the compensation strategy equally accurately, but faster than the jump strategy in the no-choice conditions. Finally, children neither took into account the expected task nor individual strategy efficiency characteristics during the strategy choice process. Results are discussed in terms of recent models of adaptive strategy choices and instructional practices in the number domain 20–100.

Flexible phase change composites (FPCCs) have garnered significant attention for their ability to combine high latent heat capacity with mechanical flexibility. This combination enables advanced thermal management in emerging fields such as flexible electronics, soft robotics, and wearable technologies. Traditional phase change materials (PCMs) excel in energy absorption and release. However, their rigidity limits their applicability in the sectors above. Existing reviews largely focus on encapsulation methods and traditional PCM applications, leaving a gap in the literature concerning flexibility enhancement strategies and FPCC‐specific applications. This review seeks to address this gap by presenting a comprehensive timeline of FPCC development, elucidating the principles of latent heat capacity, and systematically reviewing recent advancements in the field. Emphasis is placed on design strategies at both the structural level, such as fiber and foam configurations, and materials level, including physical blending and molecular engineering. Performance comparisons are provided, evaluating FPCCs in terms of both latent heat storage and mechanical flexibility. Furthermore, the review explores diverse applications of FPCCs in thermal energy storage, transfer, conversion, and release, underscoring their potential in cutting‐edge sectors. By highlighting FPCCs' versatility and interdisciplinary applications, this review aims to inspire further research and integration of FPCCs into domains requiring both mechanical flexibility and thermal energy management solutions. This review categorizes strategies for enhancing the flexibility of phase change materials into structural and material designs, focusing on strain and latent heat capacity as key properties. It also examines applications of flexible phase change composites (FPCCs) in thermal energy storage, transfer, conversion, and release. The goal is to inspire future research in emerging fields that demand integrated mechanical flexibility and thermal energy management.

Electricity supply chains involve more sources of uncertainty than typical production and manufacturing supply chains, owing to the intermittent nature of renewable energy generation. Therefore, it is critical but challenging to mitigate supply disruption risks by improving management methods. The extant literature has mainly investigated the sourcing strategies of manufacturers with price-taking suppliers. Where there is an option to source from multiple generators, including regular but unreliable generators and reliable backup generators, a flexible sourcing strategy is usually regarded as the best tactic for the grid operator. Our objective is to evaluate the costs and benefits of flexible sourcing and sole sourcing when generators are strategic price-setters. In this paper, we develop a Stackelberg game with wholesale prices contingent on the dominant grid operator’s sourcing strategy. We describe and analyze the resulting equilibriums under different scenarios. The results show that the grid operator does not necessarily benefit from a backup generator and that the flexible sourcing mode is not in fact optimal, except when the disruption ratio of the unreliable generator is medium and the penalty-sharing ratio of the unreliable generator is low. The model is applied to a numerical case study of a real-word electricity supply chain to illustrate the validity and effectiveness of the proposed conclusions.