Classification and Analysis of Pre-Service Teachers’ Errors in Solving Fermi Problems

Fermi problems are useful for introducing modelling in primary school classrooms, although teachers’ difficulties in problem solving may hinder their successful implementation. These difficulties are associated with the modelling process, but also with the estimation and measurement skills required by Fermi problems. In this work, a specific categorization of errors for Fermi problems was established, and it allowed us to analyse the errors of N = 224 pre-service primary school teachers. The results showed that prospective teachers make a large number of errors when solving this type of task, especially conceptual ones, which are associated with the process of simplifying/structuring the real situation and the mathematization process. They also showed that there is a significant relationship between the characteristics of the problem context and the error categories. Knowing the types of errors that prospective teachers make and designing task sequences that make them emerge so that prospective teachers learn from them could be an effective way to improve initial teacher education in modelling and estimation problem solving.

Music Modulates Cognitive Flexibility? An Investigation of the Benefits of Musical Training on Markers of Cognitive Flexibility

Cognitive flexibility enables the rapid change in goals humans want to attain in everyday life as well as in professional contexts, e.g., as musicians. In the laboratory, cognitive flexibility is usually assessed using the task-switching paradigm. In this paradigm participants are given at least two classification tasks and are asked to switch between them based on valid cues or memorized task sequences. The mechanisms enabling cognitive flexibility are investigated through two empirical markers, namely switch costs and n-2 repetition costs. In this study, we assessed both effects in a pre-instructed task-sequence paradigm. Our aim was to assess the transfer of musical training to non-musical stimuli and tasks. To this end, we collected the data of 49 participants that differed in musical training assessed using the Goldsmiths Musical Sophistication Index. We found switch costs that were not significantly influenced by the degree of musical training. N-2 repetition costs were small for all levels of musical training and not significant. Musical training did not influence performance to a remarkable degree and did not affect markers of mechanisms underlying cognitive flexibility, adding to the discrepancies of findings on the impact of musical training in non-music-specific tasks.

Problematics for Conceptualization of Multiplication

This chapter addresses the problematics for the conceptualization of multiplication in school mathematics and fundamental difficulties, which include semantics for defining multiplication meaningfully, syntax in relation to languages, and difficulties that originate from historical transitions. The chapter discusses the contradictions or inconsistencies in the various meanings of multiplication in school mathematics situations. Many of these problems of multiplication are originated from European languages. This discussion of these problematics provides some answers to the questions posed in Chap. 2 and provides bases for the necessity to consider the Japanese approach described in Chaps. 4, 5, 6, and 7 of this book. The terminology of multiplication discussed here is related to mathematical usages of multiplication in relation to situations and models. Educational terminology used for multiplication to explain the curriculum and task sequences for designing lessons are discussed in Chap. 4 of this book.

Optimization of Remanufacturing Disassembly Line Balance Considering Multiple Failures and Material Hazards

End-of-life (EOL) electromechanical products often have multiple failure characteristics and material hazard attributes. These factors create uncertain disassembly task sequences and affect the remanufacturing cost, environmental sustainability, and disassembly efficiency of the remanufacturing disassembly line system. To address this problem, a novel multi-constraint remanufacturing disassembly line balancing model (MC-RDLBM) is constructed in this article, which accounts for the failure characteristics of the parts and material hazard constraints. To assign the disassembly task reasonably, a disassembly priority decision-making model was presented to describe the relationship between the failure layer, the material hazards layer, and the economic feasibility layer. Furthermore, the multi-objective non-dominated sorting genetic algorithm II (NSGA-II) optimization for the MC-RDLBM is improved. To increase the convergence speed of the algorithm, an initial population construction method is designed, which includes the component failure and material hazards. Moreover, a novel genetic algorithm evolution rule with a Pareto non-dominant relation and crowded distance constraint is established, which expands the search scope of the chromosome’s autonomous evolution and avoids local convergence. Furthermore, a Pareto grade-based evaluation strategy for non-dominant solutions is proposed to eliminate the invalid remanufacturing disassembly task sequences. Finally, a case study verified the effectiveness and feasibility of the proposed method.

CoBuilt 4.0: Investigating the potential of collaborative robotics for subject matter experts

Human-robot interactions can offer alternatives and new pathways for construction industries, industrial growth and skilled labour, particularly in a context of industry 4.0. This research investigates the potential of collaborative robots (CoBots) for the construction industry and subject matter experts; by surveying industry requirements and assessments of CoBot acceptance; by investing processes and sequences of work protocols for standard architecture robots; and by exploring motion capture and tracking systems for a collaborative framework between human and robot co-workers. The research investigates CoBots as a labour and collaborative resource for construction processes that require precision, adaptability and variability. Thus, this paper reports on a joint industry, government and academic research investigation in an Australian construction context. In section 1, we introduce background data to architecture robotics in the context of construction industries and reports on three sections. Section 2 reports on current industry applications and survey results from industry and trade feedback for the adoption of robots specifically to task complexity, perceived safety, and risk awareness. Section 3, as a result of research conducted in Section 2, introduces a pilot study for carpentry task sequences with capture of computable actions. Section 4 provides a discussion of results and preliminary findings. Section 5 concludes with an outlook on how the capture of computable actions provide the foundation to future research for capturing motion and machine learning.

The effects of different task sequences on novice L2 learners’ oral performance in the classroom

This study investigated the optimum task sequence for second language (L2) novice learners of English. One set of task sequences was manipulated using a deductive and theoretical SSARC (simplify–stabilize–automatize–restructure–complexify) model, and two sets of task sequences were manipulated based on a teacher’s inductive classroom observations. A total of 76 undergraduates at a private university in Korea were divided into three groups for the task sequences: task complexity (TC), guided planning with vocabulary (GPV), and guided planning with content (GPC). While the four oral tasks were sequenced according to the resource-directing dimensions [± elements] and [± reasoning] in all three groups, the TC group received pretask planning, the GPV group received teacher-led guided planning with words, and the GPC group received teacher-led guided planning with content for the resource-dispersing dimensions. Pretest and posttest of syntactic complexity, accuracy, and fluency were used as the main data. The analysis showed that the TC group outperformed the GPV and GPC groups significantly in increasing overall syntactic complexity, and the GPV group outperformed the GPC group significantly in improving speed fluency. Both sequencing TC and GPV tasks significantly increased syntactic complexity and speed fluency. Sequencing TC tasks decreased accuracy and increased dysfluency, whereas sequencing GPV tasks increased accuracy and decreased dysfluency. Meanwhile, sequencing GPC tasks did not produce overall positive effects on oral performance compared with the two other groups.

Opportunities for Reasoning: Digital Task Design to Promote Students’ Conceptions of Graphs as Representing Relationships between Quantities

We posit a dual approach to digital task design: to engineer opportunities for students to conceive of graphs as representing relationships between quantities and to foreground students’ reasoning and exploration, rather than their answer-finding. Locally integrating Ference Marton’s variation theory and Patrick Thompson’s theory of quantitative reasoning, we designed digital task sequences, in which students were to create different graphs linked to the same video animations. We report results of a qualitative study of thirteen secondary students (aged 15–17), who participated in digital, task-based, individual interviews. We investigated two questions: (1) How do students conceive of what graphs represent when engaging with digital task sequences? (2) How do student conceptions of graphs shift when working within and across digital task sequences? Two conceptions were particularly stable – relationships between quantities and literal motion of an object. When students demonstrated conceptions of graphs as representing change in a single quantity, they shifted to conceptions of relationships between quantities. We explain how a critical aspect: What graphs should represent, intertwined with students’ graph-sketching. Finally, we discuss implications for digital task design to promote students’ conceptions of mathematical representations, such as graphs.

Abstract sequential task control is facilitated by practice and embedded motor sequences

Everyday task sequences, such as cooking, contain overarching goals (completing the meal), sub-goals (prepare vegetables), and motor actions (chopping). Such tasks generally are considered hierarchical because superordinate levels (e.g., goals) affect performance at subordinate levels (e.g., sub-goals and motor actions). However, there is debate as to whether this hierarchy is “strict” with unidirectional, top-down influences, and it is unknown if and how practice affects performance at the superordinate levels. To investigate these questions, we manipulated practice with sequences at the goal and motor action levels using an abstract, or non-motor, task sequence paradigm (Desrochers et al., 2015; Schneider & Logan, 2006). In three experiments, participants performed memorized abstract task sequences composed of simple tasks (e.g., color/shape judgements), where some contained embedded motor response sequences. We found that practice facilitated performance and reduced control costs for abstract task sequences and subordinate tasks. The interrelation was different between the hierarchical levels, demonstrating a strict relationship between abstract task sequence goals and sub-goals and a non-strict relationship between sub-goal and motor response levels. Under some conditions, the motor response level influenced the abstract task sequence level in a non-strict manner. Further, manipulating the presence or absence of a motor sequence after learning indicated that these effects were not the result of an integrated representation produced by practice. These experiments provide evidence for a mixed hierarchical model of task sequences and insight into the distinct roles of practice and motor processing in efficiently executing task sequences in daily life.

Monitoring Multiple Deadlines Relies on Spatial Processing in Posterior Parietal Cortex

Proactively coordinating one's actions is an important aspect of multitasking performance due to overlapping task sequences. In this study, we used fMRI to investigate neural mechanisms underlying monitoring of multiple overlapping task sequences. We tested the hypothesis that temporal control demands in multiple-task monitoring are offloaded onto spatial processes by representing patterns of temporal deadlines in spatial terms. Results showed that increased demands on time monitoring (i.e., responding to concurrent deadlines of one to four component tasks) increasingly activated regions in the left inferior parietal lobe and the precuneus. Moreover, independent measures of spatial abilities correlated with multiple-task performance beyond the contribution of working memory. Together, these findings suggest that monitoring and coordination of temporally overlapping task timelines rely on cortical processes involved in spatial information processing. We suggest that the precuneus is involved in tracking of multiple task timelines, whereas the inferior parietal lobe constructs spatial representations of the temporal relations of these overlapping timelines. These findings are consistent with the spatial offloading hypothesis and add new insights into the neurocognitive mechanisms underlying the coordination of multiple tasks.