How teacher questioning can reduce the cognitive demand of mathematical tasks

Objective: A set of 4 driving related tasks were used to evaluate the potential for a modified Detection Response Task (DRT) to simultaneously measure visual and cognitive task demands. Background: The accurate assessment of cognitive and visual tasks demands in driving has become increasingly important. As of yet, no simple, cost effective approach has been found to measure visual demands in complex, multimodal tasks. Methods: Two experiments are presented which evaluate an extension of the standard DRT methodology. The discriminate sensitivity of the experiments is tested using an integrated testing configuration, which systematically increased visual demand across four conditions. Results: Results suggest that the standard DRT configurations are highly tuned to selectively evaluate cognitive demand but that a variant of the system may be able to simultaneously evaluate changes in both visual and cognitive task demands. Conclusions: These data suggest that the simple, rapid, and reliable assessment of both visual and cognitive task demands is possible, even in highly fluid systems with non-constant visual task requirements.

The assessment of task demand caused by in-vehicle systems is crucial to avoid distraction while driving. The Box Task (BT) in combination with a tactile Detection Response Task (DRT) provides a method for measuring both visual-manual and cognitive secondary task demand. In the present study, the impact of cognitive, auditory-verbal tasks on the BT + DRT performance was investigated. Thirty-two participants had to perform an easy as well as a difficult version of an n-back task and a memory scanning task while simultaneously performing the BT + DRT. There was only a slight effect of cognitive task demand on the BT performance parameters, while the DRT proved to be highly sensitive to cognitive task demand. Therefore, it is assumed that the method is suitable for a differentiated measurement of task demand dimensions.

This study looked at how student teachers created and altered mathematical assignments using their pedagogical and subject-specific knowledge of mathematics. It also looked at the connection between instructor expertise and a task's cognitive requirements. The framework of Hill, Ball, and Schilling outlines many domains of knowledge in mathematics for instruction. The Stein, Smith, Henningsen, and Silver framework also characterizes the cognitive demands of mathematical tasks in research. Findings show that when student teachers lack the expertise in other areas, particularly subject matter expertise, required to accomplish specific educational tasks, they focus on knowledge of shared content. was shown. When the student's teacher changed the task, the cognitive demands of that task often decreased. These declines are often related to a lack of subject matter expertise.

본 연구의 목적은 스토리텔링 수학 교과서 개발과 학교 현장에서 스토리텔링 교과서 활용의 방향성을 제시하기 위해, 2009 개정 교육과정에 따른 중학교 2학년 수학 교과서 5종을 연구 대상으로 수학 과제 유형에 따른 인지적 노력 수준, 답안 유형, 스토리텔링 유형을 분석하였다. 연구 결과, 첫째, 수학 과제의 인지적 노력 수준은 공통적으로 모든 교과 내용 영역에서 PNC(Procedures without Connections) 과제가 가장 많은 비중을 차지하였고, 수학적 내용 과제에서는 인지적 노력이 낮은 수준의 과제(Low-Level)가 많았고, 수학적 활동 과제에서는 인지적 노력이 높은 수준의 과제(High-Level)가 더 많았다. 둘째, 학생들에게 요구하는 답안 유형은 모든 영역에서 단답형이 가장 많았고, 수학적 내용 과제의 대부분은 단답형, 수학적 활동 과제는 단답형과 설명형이 많았다. 마지막으로 스토리텔링의 유형은 실생활 연계형이 가장 많은 비중을 차지하고 있었고, 수학적 활동 과제의 수가 수학적 내용 과제의 수보다 휠씬 적었다. 그러나 스토리텔링 유형이 반영된 과제에서는 수학적 활동 과제의 비율이 수학적 내용 과제의 비율보다 더 높았다. 이러한 연구 결과를 바탕으로 향후 다른 학년의 스토리텔링 수학 교과서를 개발하고 학교 현장에 적용할 때, 수학 과제 유형에 따른 인지적 노력 수준, 답안 유형, 스토리텔링 유형에 대해서 균형성과 다양성을 고려해야할 필요성을 제시할 수 있다. The purpose of this research is to analyze cognitive demands, answer types, and storytelling types on the basis of mathematical tasks in five different mathematics textbooks based on 2009 revised curriculum in order to suggest directions for the development and use of storytelling mathematics textbooks in school. Results show that first, PNC (Procedures without Connections) task was the largest category in cognitive demands of all mathematical tasks, Low-Level task was larger than others in cognitive demands of mathematical content tasks, and High-Level task was larger than others in cognitive demands of mathematical activity tasks. Second, a short-answer type was the largest category in answer types of all mathematical tasks, the majority of mathematical content tasks were a short-answer type, and the majority of mathematical activity tasks were both short-answer and explanation-answer types. Finally, storytelling connected to real-life was the largest category in storytelling types, and the number of mathematical activity tasks was less than that of mathematical content tasks. However, in the tasks reflected on storytelling, the percentage of mathematical activity tasks was higher than that of mathematical content tasks. Based on the results, while developing storytelling mathematics textbooks and using storytelling textbooks in school, it suggests to consider the need for balance and diversity in cognitive demands, answer types, and storytelling types according to mathematical tasks.

Team cognition is an important indicator to reflect the trend of single pilot operation (SPO) human-machine system team performance. How to measure team cognition to explore different function allocation decisions before the implementation of prototypes or simulators has become a significant step in the early SPO human-machine system design. Therefore, this article proposed a team cognition measurement method based on the social network analysis (SNA) method, namely cognitive social network analysis (CSNA). The CSNA method firstly identified the nodes, edge directions and channel resource values of each task; secondly calculated the cognitive demands of each task based on multiple resource theory; thirdly summed the cognitive demands of the same task to construct the association matrix; and finally calculated global and nodal network metrics. The results of the study showed that (1) the CSNA method could identify design flaws of the initial SPO human-machine system; (2) the CSNA method increased the ability to identify the changes in both the cognitive demands of tasks and the overall workloads of human agents compared to the SNA method; (3) the CSNA method could help researchers make reasonable design suggestions to improve the team performance of the redesigned SPO human-machine system. The above results not only verify the feasibility of the CSNA method, but also show that the CSNA method is superior to the current SNA method.

본 연구의 목적은 수학적 과제의 인지적 수준에 대한 교사의 수업반성이 수학 수업에 어떠한 영향을 주는지 분석하여 초등 교사의 수학 수업에 시사점을 제공하는 것이다. 이를 위해 수학 수업에서 과제 설정과 과제 실행단계 동안, 수학적 과제의 인지적 수준의 변화와 변화에 영향을 준 교실 요인을 분석하고, 이에 대한 수업반성을 거쳐 실시한 수학 수업에서 과제 설정과 과제 실행 단계동안, 수학적 과제의 인지적 수준의 변화 양상 및 변화에 영향을 준 교실 요인을 분석하였다. 그 결과, 수학적 과제의 인지적 수준이 쇠퇴했던 수학 수업이 수업반성을 통해 수학적 과제의 인지적 수준이 높게 유지하는 수학 수업으로 변화하였다. The purpose of this study is to offer the implication for elementary school mathematics teaching by analyzing teachers' reflection on the cognitive demands of mathematical tasks they give in class. During the setup phase and the implementation phase in math class, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes. After teachers' reflection on teaching, the researchers analyzed the change of cognitive demands on mathematical tasks and the factors which had influence on such changes in math classes. As a result, before teachers' reflection on the cognitive demands of mathematical tasks, the higher-level demands of mathematical tasks had a tendency to decline. However, after teachers' reflection on the cognitive demands of mathematical tasks, higher-level demands of mathematical tasks were maintained.

Manually Controlled Rendezvous and Docking (manual RVD) is a complex and demanding task for astronauts. The design quality of the display interface is critical for astronauts’ performance in manual RVD tasks. Present study aimes to improve the design of the display interface for manual RVD based on the analysis of the cognitive demands of the task. The cognitive demands of the RVD task on the human operators were analyzed by theoretical analysis and imperial research, and the cognitive demands were taken into consideration in the ergomomic design of the display interface for RVD tasks. Theoretical analysis and experimental data suggest that spatial transformations are highly demanded, and speed perception may be difficult for the operators. The arrangement of the display and the characteristics of the elements on the display were designed to facilitate human perception, judgement and decision, and several design schemes were proposed. The overall display interface which we designed demonstrated satisfying qualities. Analysis of the cognitive processes and cognitive demands of the manual RVD task provided important guide for the design of the RVD interface. The display interface we designed successfully supported the manual RVD tasks in China’s SZ-9 and SZ-10 missions.

BackroundIn the mathematics education literature, there is a limited number of comprehensive studies that examine the dynamic relationship between teacher efficacy beliefs and psychological variables such as curiosity and anxiety within the context of primary education. However, these variables have a wide sphere of influence, extending from instructional quality to student achievement, and they interactively shape teacher behaviors. Therefore, investigating the impact of primary teachers’ mathematical curiosity and teaching anxiety on their beliefs about mathematics teaching efficacy emerges as a necessity for supporting professional development, restructuring teacher education programs more effectively, and contributing to the improvement of mathematics instruction. In line with this need, the present study aims to reveal the relationship between primary school teachers’ beliefs about their mathematics teaching efficacy, their mathematical curiosity, and their mathematics teaching anxiety. Moreover, the study seeks to determine the influence of the psychological variables-curiosity and anxiety-on mathematics teaching efficacy beliefs within the context of mathematics instruction.MethodThe research, which was designed according to a cross-sectional research model, was conducted in accordance with the relational survey model, one of the quantitative research approaches. The research focuses on primary school teachers working in primary schools in a medium-sized city in the eastern region of Türkiye in 2024. The sample consists of 893 primary teachers, selected from the population through a disproportionate cluster sampling method. Among the teachers in the study sample, 43.6% were female and 56.4% were male; 65.5% held a bachelor’s degree, while 34.5% had completed graduate education. In terms of professional seniority, 31.9% had 1–5 years of experience, 27.8% had 6–10 years, 14.9% had 11–15 years, 15.6% had 16–20 years, and 9.8% had 21 years or more of teaching experience. Data were collected using four instruments: a “Personal Information Form,” the “Mathematical Curiosity Scale,” the “Primary Teachers’ Mathematics Teaching Anxiety Scale,” and the “Mathematics Teaching Efficacy Belief Scale.” Since the overall Cronbach’s alpha coefficients of the scales used in the study were greater than α > .70, the scale data were considered to be reliable. Since the research data met the normality criteria, inferential statistical methods such as Independent Samples t-Test, One-Way ANOVA, Pearson Correlation, and Multiple Linear Regression Analysis were used.ResultsThe study revealed significant differences in primary school teachers’ mathematics teaching efficacy beliefs, mathematical curiosity, and mathematics teaching anxiety based on gender, educational background, and professional seniority (p. < 05). Male teachers, those with postgraduate education, and more experienced teachers demonstrated higher levels of efficacy beliefs and curiosity, alongside lower levels of mathematics teaching anxiety. The findings reveal that primary teachers’ beliefs about their mathematics teaching efficacy are significantly related to their mathematical curiosity and teaching anxiety (p < .01; .30 < r < .70). Moreover, the predictors-mathematical curiosity and teaching anxiety-were found to have a significant impact on teaching efficacy beliefs (Corrected R2 = .475; p < .05). Furthermore, the study found that low levels of mathematics teaching anxiety have a positive effect on mathematics teaching efficacy beliefs, which is an unexpected result.ConclusionsIn conclusion, it has been determined that emotional states such as curiosity and anxiety are significant predictors of elementary school teachers’ mathematics teaching efficacy beliefs. These results offer important insights for educational stakeholders regarding primary teachers’ beliefs about mathematics teaching efficacy, their mathematical curiosity, and their mathematics teaching anxiety. The results indicate that teachers’ efficacy beliefs are significantly related to, and potentially shaped by, the variables of curiosity and anxiety. Identifying mathematics teaching efficacy beliefs in the context of teacher development and their influence on learning environments can enable targeted support for teachers with low self-efficacy through various teacher training instruments. Moreover, such interventions may help prevent teachers from beginning and ending their lessons with diminished confidence and motivation.

Previous articleNext article No AccessAttitudes of Prospective Teachers toward ArithmeticWilbur H. DuttonWilbur H. Dutton Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 52, Number 2Oct., 1951 Article DOIhttps://doi.org/10.1086/459310 Views: 8Total views on this site Citations: 32Citations are reported from Crossref Copyright 1951 The University of ChicagoPDF download Crossref reports the following articles citing this article:Rosetta Zan, Pietro Di Martino Students’ Attitude in Mathematics Education, (Feb 2020): 813–817.https://doi.org/10.1007/978-3-030-15789-0_146Kyoung Whan Choe, Jalisha B. Jenifer, Christopher S. Rozek, Marc G. Berman, Sian L. 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Extended performance of cognitively demanding tasks induces cognitive fatigue manifested with an overall deterioration of behavioral performance. In particular, long practice with tasks requiring impulse control is typically followed by a decrease in self-control efficiency, leading to performance instability. Here, we show that this is due to changes in activation modalities of key task-related areas occurring if these areas previously underwent intensive use. We investigated in 25 healthy adults the effects of extended practice with high cognitive demand (HCD) tasks on a Go-No Go task and the underlying electroencephalographic (EEG) activity. We compared these effects with those induced by practice with similar, but low cognitive demand (LCD) tasks. HCD tasks were followed by an increase in response inhibition failures. These were correlated with the appearance of a distinct neural signature on fast response trials, characterized by lower levels of beta ([13-30] Hz) EEG activity in the prestimulus period, and by a lack of EEG markers of preresponse processing in frontal areas. Moreover, HCD tasks were followed by a decrease in N200 during correct withholds while LCD tasks were followed instead by a lesser fraction of hits and a decrease in P300, suggesting a decrease in engagement. Overall, these results show that exertion of cognitive control determines the appearance of two distinct modalities of response with different processing speeds, associated with distinct underlying neural activity.

Effects of mental fatigue on exercise decision-making

This research investigates the impact of Augmented Reality (AR) based learning media on the understanding of mathematical concepts among primary school children. Employing a literature review method, the study outlines recent findings in literature concerning the application of AR in mathematics education. The results indicate that the use of AR can enhance motivation, active participation, and the understanding of mathematical concepts among primary school children. AR's ability to present material in a more concrete and applicable form has a positive impact on the understanding of concepts that are often challenging for students at their cognitive development level. Despite challenges in implementation and infrastructure development, this research provides a foundation for the integration of AR in mathematics education in primary schools. It is recommended that the implementation of AR be carefully considered in the primary school mathematics curriculum with adequate teacher training and appropriate infrastructure investment.

All students should be provided with opportunities to develop conceptual understanding prior to procedural fluency (NCTM 2014; CCSSI 2010). To develop students' conceptual understanding, teachers must learn such skills as how to select, plan, and enact cognitively demanding tasks (CDT) (Lambert and Stylianou 2013; Smith, Bill, and Hughes 2008) and to evaluate evidence of student learning (Hiebert et al. 2007). Therefore, teachers need opportunities to develop these skills to maximize their students' learning outcomes. Starting with a well-designed CDT is essential. In other words, before planning the Justin D. Boyle and Sarah B. Kaiser enactment of a task, teachers should analyze the task and make revisions to align it with student learning goals that promote conceptual understanding (Hiebert et al. 2007; Smith and Stein 2011).

This investigation describes secondary mathematics teachers’ learning and instructional change following their participation in a professional development workshop, the Enhancing Secondary Mathematics Teacher Preparation Project (ESP) (2004–2005), specifically focused on the selection and implementation of cognitively challenging mathematical tasks. Data consist of a pre/post-assessment of teachers’ knowledge of the cognitive demands of mathematical tasks and videotaped discussions and written artifacts from the professional development sessions. A mixed methods approach was used to identify connections between teachers’ learning and their experiences in the ESP workshop. Results indicate that ESP teachers developed new ideas about the influence of mathematical tasks on students’ learning. Increases in teachers’ knowledge of the cognitive demands of mathematical tasks were closely linked to ideas represented in frameworks and discussions from the ESP workshop and to teachers’ experiences in solving challenging mathematical tasks as learners.

The purpose of this study was to examine and analyze the cognitive demand of the mathematical tasks suggested in the middle school textbooks. In particular, it aimed to reveal the overall picture of the level of cognitive demand of the mathematical tasks in the strand of geometry in the textbooks. We adopted the framework for mathematical task analysis suggested by Stein & Smith(1998) and analyzed the mathematical tasks accordingly. The findings from the analysis showed that 95 percent of the mathematical tasks were at high level and the rest at low level in terms of cognitive demand. Most of the mathematical tasks in the textbooks were algorithmic and focused on producing correct answers by using procedures. In particular, the high level tasks were presented at the end of each chapter or unit for wrap up rather than as key resources.