The finite-to-finite strand of a learning progression for the concept of function: A research synthesis and cognitive analysis

In this paper we report validation efforts around the finite-to-finite strand of a provisional learning progression (LP) for the concept of function. We regard an LP as an empirically-verified account of how student understandings form over time and in response to instruction. The finite-to-finite strand of the LP was informed by literature on students’ thinking and learning related to functions as well as the Algebra Project’s curricular approach, which is designed for students who are traditionally underserved by mathematics education. Developing and validating an LP is a multi-step, cyclic process. Here we report on one step in this process, an item and response analysis. Data sources include 680 students’ responses to 13 multipart computer-delivered tasks. Results suggest that revisions to the items, associated scoring rubrics, and in some instances the LP are warranted. We illustrate this task, rubric, and LP revision process through an item analysis for a selected task.     

Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program

We report on a teaching experiment intended to foster a concept of multiplication that would both subsume students’ multiple-groups concept of whole number multiplication and provide a conceptual basis for understanding multiplication of fractions. The teaching experiment, which used a rigorous single-subject methodology, began with an attempt to build on students’ multiple-groups concept by promoting generalizing assimilation. This was not totally successful and led to a redesign aimed at promoting reflective abstraction. Analysis of this latter phase led to several significant conclusions, which in turn led to a revised hypothetical learning trajectory. The revised trajectory aims to foster a concept of multiplication as a change in units.     

Prerequisites between learning objects: Automatic extraction based on a machine learning approach

One standing problem in the area of web-based e-learning is how to support instructional designers to effectively and efficiently retrieve learning materials, appropriate for their educational purposes. Learning materials can be retrieved from structured repositories, such as repositories of Learning Objects and Massive Open Online Courses; they could also come from unstructured sources, such as web hypertext pages. Platforms for distance education often implement algorithms for recommending specific educational resources and personalized learning paths to students. But choosing and sequencing the adequate learning materials to build adaptive courses may reveal to be quite a challenging task.In particular, establishing the prerequisite relationships among learning objects, in terms of prior requirements needed to understand and complete before making use of the subsequent contents, is a crucial step for faculty, instructional designers or automated systems whose goal is to adapt existing learning objects to delivery in new distance courses. Nevertheless, this information is often missing. In this paper, an innovative machine learning-based approach for the identification of prerequisites between text-based resources is proposed. A feature selection methodology allows us to consider the attributes that are most relevant to the predictive modeling problem. These features are extracted from both the input material and weak-taxonomies available on the web. Input data undergoes a Natural language process that makes finding patterns of interest more easy for the applied automated analysis. Finally, the prerequisite identification is cast to a binary statistical classification task. The accuracy of the approach is validated by means of experimental evaluations on real online coursers covering different subjects.     

Single-machine group scheduling with general deterioration and learning effects

In this paper we consider single-machine group scheduling problems with effects of learning and deterioration at the same time. By effects of learning and deterioration, we mean that the group setup times are general linear functions of their starting times and the jobs in the same group have general position-dependent and time-dependent learning effects. The objective of scheduling problems is to minimize the makespan and the sum of completion times, respectively. We show that the problems remain solvable in polynomial time under the proposed model.     

The optimal sequential information acquisition structure: A rational utility-maximizing perspective

We consider a rational utility maximizer decision maker (DM) who must gather two pieces of information from a set of multidimensional products before making a choice. We analyze the resulting sequential information acquisition process where the DM tries to find the best possible product subject to his information acquisition constraint. In addition, we introduce publicly observable signals that allow the DM to update his expected utility functions following a standard Bayesian learning rule. Even though it seems intuitively plausible to assume that the transmission of positive and credible information may lead DMs to accept any product signaled more eagerly, this paper illustrates how transmitting credible positive information is not sufficient to decrease the rejection probability faced by the information sender on its set of products. A significant difference in product rejection probabilities arises depending on the characteristic on which signals are issued, as will be illustrated numerically for both risk-neutral and risk-averse DMs.     

Channel estimation techniques for linear precoded systems: Supervised, unsupervised, and hybrid approaches

Linear precoding is an attractive technique to combat interference in multiple-input multiple-output systems because it reduces cost and power consumption at the receiver. Frequency division duplex systems with linear precoding acquire the channel state information at the receiver side by using supervised algorithms. Such methods make use of pilot symbols periodically provided by the transmitter. Next, this channel state information is sent to the transmitter side through a low-cost feedback channel. Thus, the available channel information allows the transmitter to adapt signals to the channel conditions. Given that pilot symbols do not convey user data, they penalize throughput, spectral efficiency, and transmission energy consumption of the system. In this work, we propose to mitigate the aforementioned limitations by combining both supervised and unsupervised algorithms to acquire the channel state information needed by the transmitter. The key idea consists in introducing a simple criterion to determine whether the channel has suffered a significant variation which requires the transmission of pilot symbols. Otherwise, when small fluctuations happen, an unsupervised method is used to track these channel variations instead. This criterion will be evaluated by considering two types of strategies for the design of the linear precoders: Zero-Forcing and Wiener criteria.     

Variable selection for QSAR by artificial ant colony systems

Derivation of quantitative structure-activity relationships (QSAR) usually involves computational models that relate a set of input variables describing the structural properties of the molecules for which the activity has been measured to the output variable representing activity. Many of the input variables may be correlated, and it is therefore often desirable to select an optimal subset of the input variables that results in the most predictive model. In this paper we describe an optimization technique for variable selection based on artificial ant colony systems. The algorithm is inspired by the behavior of real ants, which are able to find the shortest path between a food source and their nest using deposits of pheromone as a communication agent. The underlying basic self-organizing principle is exploited for the construction of parsimonious QSAR models based on neural networks for several classical QSAR data sets.     

Robust learning in social networks via matrix scaling

The influence vanishing property in social networks states that the influence of the most influential agent vanishes as society grows. Removing this assumption causes a failure of learning of boundedly rational dynamics. We suggest a boundedly rational methodology that leads to learning in almost all networks. The methodology adjusts the agent's weights based on the Sinkhorn-Knopp matrix scaling algorithm. It is a simple, local, Markovian, and time-independent methodology that can be applied to multiple settings.     

Automatic segmentation of hippocampal subfields based on multi-atlas image segmentation techniques

The volume of hippocampal subfields is closely related with early diagnosis of Alzheimer＇s disease. Due to the anatomical complexity of hippocampal subfields, automatic segmentation merely on the content of MR images is extremely difficult. We presented a method which combines multi-atlas image segmentation with extreme learning machine based bias detection and correction technique to achieve a fully automatic segmentation of hippocampal subfields. Symmetric diffeomorphic registration driven by symmetric mutual information energy was implemented in atlas registration, which allows multi-modal image registration and accelerates execution time. An exponential function based label fusion strategy was proposed for the normalized similarity measure case in segmentation combination, which yields better combination accuracy. The test results show that this method is effective, especially for the larger subfields with an overlap of more than 80%, which is competitive with the current methods and is of potential clinical significance.