Neural Analogical Matching

Analogy is core to human cognition. It allows us to solve problems based on prior experience, it governs the way we conceptualize new information, and it even influences our visual perception. The importance of analogy to humans has made it an active area of research in the broader field of artificial intelligence, resulting in data-efficient models that learn and reason in human-like ways. While cognitive perspectives of analogy and deep learning have generally been studied independently of one another, the integration of the two lines of research is a promising step towards more robust and efficient learning techniques. As part of a growing body of research on such an integration, we introduce the Analogical Matching Network: a neural architecture that learns to produce analogies between structured, symbolic representations that are largely consistent with the principles of Structure-Mapping Theory.Comment: AAAI versio

Making mathematics on paper : constructing representations of stories about related linear functions

This dissertation takes up the problem of applied quantitative inference as a central question for cognitive science, asking what must happen during problem solving for people to obtain a meaningful and effective representation of the problem. The core of the dissertation reports exploratory empirical studies that seek to answer the descriptive question of how quantitative inferences are generated, pursued, and evaluated by problem solvers with different mathematical backgrounds. These are framed against a controversy, described in Chapter 2, over the theoretical and empirical validity of current cognitive science accounts of problems, solutions, knowledge, and competent human activity outside of laboratory or school settings.Chapter 3 describes a written protocol study of algebra story problem solving among advanced undergraduates in computer science. A relatively open-ended interpretive framework for "problem-solving episodes" is developed and applied to their written solution attempts. The resulting description of problem-solving activities gives a surprising image of competence among an important occupational target for standard mathematics instruction.Chapter 4 follows these results into detailed verbal problem-solving interviews with algebra students and teachers. These provide a comparison across settings and levels of competence for the same set of problems. The results corroborate similar generative activities outside the standard formalism of algebra across levels of competence. Notable among these nonalgebraic problem-solving activities are "model-based reasoning tactics," in which people reason about quantitative relations in terms of the dimensional structure of functional relations described in the problem. These tactics support different activities within surrounding solution attempts and usually describe "states" in the problem's situational structure.Chapter 5 holds these activities accountable to local combinations of notation and quantity, reinterpreting results for model-based reasoning in an ecological analysis of material designs for constructing and evaluating quantitative inferences. This analysis brings forward important relations between what material designs afford problem solvers and the complexity of episodic structure observed in their solution attempts. The dissertation closes with a reappraisal of the relationship between knowledge, person, and setting and, I will argue, puts us on a more promising track for a descriptively adequate theoretical account of constructing mathematical representations that support applied quantitative inference

The Material Theory of Induction

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it.The content of that logic and where it can be applied are determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference

Implicit association test as an analogical learning task

The Implicit Association Test (IAT) is a popular tool for measuring attitudes. We suggest that performing an IAT could, however, also change attitudes via analogical learning. For instance, when performing an IAT in which participants categorize (previously unknown) Chinese characters, flowers, positive words, and negative words, participants could infer that Chinese characters relate to flowers as negative words relate to positive words. This analogy would imply that Chinese characters are opposite to flowers in terms of valence and thus that they are negative. Results from three studies (N = 602) confirmed that evaluative learning can occur when completing an IAT, and suggest that this effect can be described as analogical. We discuss the implications of our findings for research on analogy and research on the IAT as a measure of attitudes

The development and validation of an automatic-item generation measure of cognitive ability

Cognitive ability is perhaps the most studied individual difference available to researchers, being measured quickly and effectively while demonstrating a predictable influence on many life outcomes. Historically, the evolution of the psychometric study of cognitive abilities has pivoted on the development of new and better methodologies allowing for a more complete and efficient capture of intellect. For instance, recent advances in computer and Internet technology have largely replaced traditional pencil-and-paper methods, allowing for innovative item development and presentation. However, concerns regarding the potential adverse impact and test security of online measures of cognitive ability, particularly in unproctored situations, are well documented and have limited the use of such measures in organizational settings. Methods, such as the use of multiple test forms and computer adaptive testing coupled with item exposure algorithms, have addressed some test-security concerns. However, these methods require the costly and tedious development of extensive item pools. The burgeoning area of automatic item generation potentially addresses many of the test-security and item-development concerns through the creation of assessment items based solely on an item model and a computer algorithm. Moreover, once the elements that contribute to item difficulty are calibrated, the psychometric properties of the items are known, meaning that little to no human review of the items is required before their use. The purpose of the current study was to develop an experimental non-verbal measure of cognitive ability through automatic item generation, using an innovative item type. Using a sample of 333 adults, the results of the current analysis support the proposed cognitive model\u27s ability to explain item difficulty. Likewise, the temporal stability and predictive validity of the experimental measure are supported. In doing so, the experimental measure answers some of the test-security and item-generation concerns that are associated with the development and administration of cognitive-ability measures in organizational settings

New measurement paradigms

This collection of New Measurement Paradigms papers represents a snapshot of the variety of measurement methods in use at the time of writing across several projects funded by the National Science Foundation (US) through its REESE and DR K–12 programs. All of the projects are developing and testing intelligent learning environments that seek to carefully measure and promote student learning, and the purpose of this collection of papers is to describe and illustrate the use of several measurement methods employed to achieve this. The papers are deliberately short because they are designed to introduce the methods in use and not to be a textbook chapter on each method. The New Measurement Paradigms collection is designed to serve as a reference point for researchers who are working in projects that are creating e-learning environments in which there is a need to make judgments about students’ levels of knowledge and skills, or for those interested in this but who have not yet delved into these methods

Math empowerment: a multidisciplinary example to engage primary school students in learning mathematics

This paper describes an educational project conducted in a primary school in Italy (Scuola Primaria Alessandro Manzoni at Mulazzano, near to Milan). The school requested our collaboration to help improve upon the results achieved on the National Tests for Mathematics, in which students, aged 7, registered performances lower than the national average the past year. From January to June, 2016, we supported teachers, providing them with information, tools and methods to increase their pupils’ curiosity and passion for mathematics. Mixing our different experiences and competences (instructional design and gamification, information technologies and psychology) we have tried to provide a broader spectrum of parameters, tools and keys to understand how to achieve an inclusive approach that is ‘personalised’ to each student. This collaboration with teachers and students allowed us to draw interesting observations about learning styles, pointing out the negative impact that standardized processes and instruments can have on the self‐esteem and, consequently, on student performance. The goal of this programme was to find the right learning levers to intrigue and excite students in mathematical concepts and their applications. Our hypothesis is that, by considering the learning of mathematics as a continuous process, in which students develop freely through their own experiments, observations, involvement and curiosity, students can achieve improved results on the National Tests (INVALSI). This paper includes results of a survey conducted by children ‐’About Me and Mathematics‘

The role of procedural similarity, self-explanation and self-constructed diagrams in analogical problem solving

This study aimed to investigate the precise role of self-support methods, such as self-explanation and self-constructed diagrams, as an alternative to external methods in enhancing the cognitive processes considered crucial for effective transfer performance in analogical problem-solving that depicts a multi-step process involving source problems and target problems. This was achieved by systematically examining how type of representation (Verbal & Pictorial) and levels of similarity (Principle, Strategy, and Procedural) interact with self-support methods (Self-explanation (SE) and Self Constructed Diagrams (SCD)) in influencing transfer performance. Three experiments were conducted each addressing a set of issues related to the purpose of the study. Experiment 1 (N = 48) was conducted to identify the cognitive processes and their sub-processes involved in analogical problem solving using pictorial representation and also investigated the specific effects of the self-explanation method on transfer process. This experiment consisted of two experimental conditions; self-explanation (SE) (expermintal group) and verbalization (VB) (control group), and three levels of similarity (i.e., procedural, strategy, and principle). Procedural similarity combined with the SE method was found to have a positive significant influence on the transfer process compared to the principle and strategy levels and VB condition. However, the verbal protocols also revealed that despite the inherent advantages of SE the percentage of complete solvers was low. This was attributed to some difficulty arising from adapting information from a pictorial source to solve a verbal target. Experiment 2 (N = 84) investigated the effect of verbal and pictorial types of representation on transfer performance in a within-subjects design, where each participant solved a pictorial source (PS) and verbal source (VS) problem, and their verbal target analogues. The mean performance of the pictorial representation was higher compared to verbal representation. Transfer performance was higher in the procedural level than the strategy level. This indicated that information from PS tends to be utilized more effectively than VS in retrieving and applying that information to the target problem. Thus having ensured that pictorial representation was an advantage in problems depicting a multistep to be implemented, Experiment 3 was conducted. Experiment 3 (N = 160) aimed at finding whether self-constructed diagrams (SCD) are a better alternative to external support in facilitating the cognitive processes crucial for transfer in analogical problem-solving. As predicted, a significant difference was found between the experimental (SCD) and No Diagrams (ND) control groups in the transfer performance. No significant within subject difference in the transfer performance of verbal and pictorial source representations was found in the SCD condition. An interesting finding was that transfer performance was significantly higher in the verbal representation and strategy level of similarity in the SCD condition than ND. Theoretically, this suggests that because visual memory is more easily accessible than auditory memory, SCD may play a critical role in creating accessible information from the source problem for effective feedback to help solve the target problem. It was concluded that explaining by diagrams helps in identifying the various elements of the problem that stimulate the memory and motivate the person to recall what he drew earlier while solving the target problem. This study contributed to the field of research on the cognitive processes involved in problem-solving by analogy. The methodology employed in each of the experiments was unique in terms of coding and scoring the protocols, which generated strong and reliable results. The outcome of the study was a dynamic model “The Generative Procedural Model of Analogical Problem-solving” which contributed to our understanding of not only how information is processed from verbal and pictorial representations during problem-solving by analogy but also the potential of a self-method in optimizing the processes of noticing, retrieving, and implementing a learned solution process successfully