Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5

A case study of two 5th-Grade children, Jason and Laura, is presented who participated in the teaching experiment, Children’s Construction of the Rational Numbers of Arithmetic. The case study begins on the 29th of November of their 5th-Grade in school and ends on the 5th of April of the same school year. Two basic problems were of interest in the case study. The first was to provide an analysis of the concepts and operations that are involved in the construction of three fractional schemes: a commensurate fractional scheme, a fractional composition scheme, and a fractional adding scheme. The second was to provide an analysis of the contribution of interactive mathematical activity in the construction of these schemes. The phrase, “commensurate factional scheme” refers to the concepts and operations that are involved in transforming a given fraction into another fraction that are both measures of an identical quantity. Likewise, “fractional composition scheme” refers to the concepts and operations that are involved in finding how much, say, 1/3 of 1/4 of a quantity is of the whole quantity, and “fractional adding scheme” refers to the concepts and operations involved in finding how much, say, 1/3 of a quantity joined to 1/4 of a quantity is of the whole quantity. Critical protocols were abstracted from the teaching episodes with the two children that illustrate what is meant by the schemes, changes in the children’s concepts and operations, and the interactive mathematical activity that was involved. The body of the case study consists of an on-going analysis of the children’s interactive mathematical activity and changes in that activity. The last section of the case study consists of an analysis of the constitutive aspects of the children’s constructive activity, including the role of social interaction and nonverbal interactions of the children with each other and with the computer software we used in teaching the children.     

Evaluation of three interventions teaching area measurement as spatial structuring to young children

We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on correctness to include analyses of children’s use of procedural and conceptual knowledge and examined individual differences in strategy shifts before and after transitions, enabling a more detailed examination of the hypothesized necessity of development through each level of a learning trajectory. The two experimental interventions focused on a dynamic conception of area measurement while also emphasizing unit concepts, such as unit identification, iteration, and composition. The findings confirm and extend earlier results that seeing a complete record of the structure of the 2D array—in the form of a drawing of organized rows and columns—supported children’s spatial structuring and performance.     

A bicriteria parallel machine scheduling with a learning effect of setup and removal times

In studies on scheduling problems, generally setup times and removal times of jobs have been neglected or by including those into processing times. However, in some production systems, setup times and removal times are very important such that they should be considered independent from processing times. Since, in general jobs are done according to automatic machine processes in production systems processing times do not differ according to process sequence. But, since human factor becomes influential when setup times and removal times are taken into consideration, setup times will be decreasing by repeating setup processes frequently. This fact is defined with learning effect in scheduling literature. In this study, a bicriteria m-identical parallel machines scheduling problem with a learning effect of setup times and removal times is considered. The objective function of the problem is minimization of the weighted sum of total completion time and total tardiness. A mathematical programming model is developed for the problem which belongs to NP-hard class. Results of computational tests show that the proposed model is effective in solving problems with up to 15 jobs and five machines. We also proposed three heuristic approaches for solving large jobs problems. According to the best of our knowledge, no work exists on the minimization of the weighted sum of total completion time and total tardiness with a learning effect of setup times and removal times.     

Creating awareness on bullying and cyberbullying among young people: Validating the effectiveness and design of the serious game Conectado

Serious games have proven to be educational tools with numerous positive effects, capable of promoting learning, changing behavior, or improving training and skills development, among other effects. Serious games can also be applied to address and prevent social problems. This study describes the experiments and analyses we have carried out to test the effectiveness of Conectado, a serious game created to prevent bullying and cyberbullying in schools by increasing awareness of the problem in players. We have used the results from these experiments to answer different research questions regarding the game’s acceptance and effectiveness, validating several characteristics of the game design. We have also studied the influence of players’ characteristics on the effect of the game, as well as the relationship between the in-game behaviors of players and their degree of awareness. We have verified a positive effect of the game in terms of an increase of awareness regarding bullying and cyberbullying for all target users, and have provided further insight into how this increase is related to different players’ characteristics and behaviors.     

The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities

The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.     

桉树杂交种与其亲本的近红外光谱判别

研究桉树控制授粉后目标性状的基因作用方式是探索其基因重组规律的重要内容。常规的数量统计分析精度往往不高,而DNA分析的专业要求高,且费时费力。该研究利用近红外光谱(NIRs)研究不同基因型桉树杂交种、亲本及杂交种与亲本间近红外光谱信息的关系,探索NIRs用于桉树杂交种与其亲本判别的可行性和准确性。以控制授粉的桉树亲本及其杂交F1代材料为对象,每种基因型从各自田间试验分别选取10个单株,采集树冠中上部新鲜健康叶片。用手持式近红外仪Phazir Rx(1624)采集桉树杂交种与其亲本叶片的NIRs信息。每单株选10片完全生理成熟的健康叶片,避开叶脉扫描其正面光谱5次,以50条NIRs信息的均值代表单个叶片的NIRs信息,最终每个基因型获得10条NIRs信息。对原始NIRs采用二阶多项式S.G一阶导数预处理。预处理后的NIRs用于多元统计分析,首先对桉树杂交亲本和子代样本进行主成分分析(PCA),直观展示不同基因型的分类情况。然后运用簇类独立软模式(SIMCA)和偏最小二乘判别分析(PLS-DA)两种有监督的判别模式验证NIRs用于桉树杂交种与其亲本树种的分类判别效果。PCA结果显示,不同的亲本间、杂交种间及杂交种与亲本间样本的主因子得分可以清晰地将各基因型分开。SIMCA模式判别分析中,桉树杂交种样本到亲本PCA模型的样本距离显示,待判别样本能够形成单独的聚类,且能直观反映两者的遗传相似。PLS-DA判别结果显示,桉树杂交亲本的PLS模型能通过预测其杂交子代的响应变量将其与亲本准确分开。结果表明,桉树叶片的NIRs信息可以准确地反映桉树杂交子代遗传信息的传递规律,NIRs判别模型可以准确地将各种基因型予以区分。因此,NIRs信息不仅可用于桉树杂交种和纯种的定性判别,还可以分析桉树基因重组过程中加性遗传效应的大小,从而为桉树遗传基础分析及其育种改良研究提供理论支撑。     

An automated patient monitoring using discrete‐time wireless sensor networks

In recent years, Internet of Things (IoT) devices are used for remote health monitoring. For remotely monitoring a patient, only the health information at different time points are not sufficient; predicted values of biomarkers (for some future time points) are also important. In this article, we propose a powerful statistical model for an efficient dynamic patient monitoring using wireless sensor nodes through Bayesian Learning (BL). We consider the setting where a set of correlated biomarkers are measured from a patient through wireless sensors, but the sensors only report the ordinal outcomes (say, good, fair, high, or very high) to the sink based on some prefixed thresholds. The challenge is to use the ordinal outcomes for monitoring and predicting the health status of the patient under consideration. We propose a linear mixed model where interbiomarker correlations and intrabiomarker dependence are modeled simultaneously. The estimated and the predicted values of the biomarkers are transferred over the internet so that health care providers and the family members of the patient can remotely monitor the patient. Extensive simulation studies are performed to assess practical usefulness of our proposed joint model, and the performance of the proposed joint model is compared to that of some other traditional models used in the literature.     

Single-machine and two-machine flowshop scheduling with general learning functions

We show that the O(n log n) (where n is the number of jobs) shortest processing time (SPT) sequence is optimal for the single-machine makespan and total completion time minimization problems when learning is expressed as a function of the sum of the processing times of the already processed jobs. We then show that the two-machine flowshop makespan and total completion time minimization problems are solvable by the SPT sequencing rule when the job processing times are ordered and job-position-based learning is in effect. Finally, we show that when the more specialized proportional job processing times are in place, then our flowshop results apply also in the more general sum-of-job-processing-times-based learning environment.     

自监督学习子空间模式识别方法的统计特性分析

本文研究了神经网络无导师自监督学习子空间模式识别方法的收敛性问题，证明了学习子空间法的变换矩阵收敛于模式的自相关矩阵估计；证明了一类Ｋｏｈｏｎｅｎ自监督学习子空间方法的收敛性；给出了子空间旋转变化所引起的子空间特征谱分布的近似表达式，同时给出了子空间扰动的上界定理。