The Cross-Modal Relationship Between Language and Mathematics: A Bi-Directional Training Paradigm

The cross-modal relationship between language and mathematics is extensively debated (see for review, Peng et al., 2020). The present research examined the nature of this cross-modal relationship across three experiments. Experiment 1 examined whether training participants in linguistic problem-solving facilitates performance in mathematical problems. Participants were 156 adults recruited using Amazon Mechanical Turk and randomly assigned to one of three linguistic training conditions (i.e., linguistic reasoning, structural priming, or no-training) and tested on mathematical problems. No significant difference in mathematical performance was found across training conditions [F(2, 153) = 1.69, p = .18]. Experiment 2 examined whether training participants to solve mathematical problems facilitates performance in linguistic problems. Participants were 144 adults assigned to one of three mathematical training conditions (i.e., mathematical reasoning, structural priming, or no-training) and tested on linguistic problems. Results showed a significant difference in linguistic performance across training conditions [F(2, 142) = 3.86, p = .02, η2 = .05]. Post-hoc analysis revealed a significant difference between the structural priming (M = 9.37, SD = 1.99) and no-training conditions (M =8.04, SD=2.66). Experiment 3 examined whether the explicitness of mathematical training differently impacts linguistic problem-solving. Participants were 75 undergraduate students assigned to one of three mathematical training conditions (i.e., explicit training, structural priming, or no-training) and tested on linguistic problems. A significant difference between training conditions was found [F(2, 72) = 5.40, p = .006, η2 = .13]. Post-hoc analysis showed a significant difference between explicit instruction (M = 9.00, SD = 2.61) and no-training (M =7.32, SD=2.88), as well as structural priming (M = 9.40, SD = 1.32) and no training (M =7.32, SD=2.88). Implications of these results and avenues for future research are discussed

Quand l'adaptation des cas par révision des croyances et l'extrapolation analogique se rencontrent

National audienceCase-based reasoning, where cases are described in terms of problem-solution pairs case = $(x,y)$, amounts to propose a solution to a new problem on the basis of past experience made of stored cases. On the one hand, the building of the solution to a new problem may be viewed as a form of belief revision of the solution of a retrieved case (whose problem part is similar to the new problem) constrained by domain knowledge. On the other hand, an extrapolation mechanism based on analogical proportions has been proposed. It exploits triplets of cases ($case^a$ ,$case^b$ ,$case^c$) whose descriptions of problem parts $x^a$ , $x^b$ , $x^c$ form an analogical proportion with the new problem xtgt, in such a way that “xa is to xb as xc is to $x^{tgt}$”. Then, the analogical inference amounts to compute a solution $y^{tgt}$ of xtgt by solving (when possible) an equation expressing that “$y^a$ is to $y^b$ as $y^c$ is to $y^{tgt}$” (where $y^a$ , $y^b$ and $y^c$ are respectively the solution parts of $case^a$ ,$case^b$ ,$case^c$). The paper investigates how the belief revision view and analogical extrapolation relate. Besides that it constitutes an unexpected bridge between areas which ignore each other, it casts some light on the adaptation mechanism in case-based reasoning.The paper is illustrated by a running exampleLe raisonnement à partir de cas vise à résoudre des problèmes en s'appuyant sur une base de cas, où un cas est un couple problème-solution (x, y). D'un côté, l'élaboration d'une solution au problème à résoudre (ou problème cible) peut être vue comme une forme de révision des croyances de la solution du cas remémoré (dont la partie problème est similaire au problème cible), contrainte par les connaissances du domaine. D'un autre côté, un mécanisme d'extrapolation fondé sur les proportions analogiques a été proposé récemment. Une proportion analogique est une relation entre 4 termes a, b, c, d qui se lit « a est à b ce que c est à d ». L'extrapolation analogique exploite des triplets de cas dont les parties problèmes forment une proportion analogique avec le problème cible. Puis, l'inférence consiste à résoudre une équation analogique entre les trois solutions des cas du triplet et l'inconnue de cette équation. Cet article étudie une relation entre ces deux approches de l'adaptation. En plus de constituer une passerelle inattendue entre ces deux domaines, il propose un nouvel éclairage sur le mécanisme d'adaptation en raisonnement à partir de cas. L'article est illustré à l'aide d'un exemple suivi

From Analogical Proportion to Logical Proportions

International audienceGiven a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( a∧b and a¯∧b¯), or dissimilarity indicators ( a∧b¯ and a¯∧b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations (a¯,b¯,c¯,d¯)). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions

Decision Making in the Sciences: Understanding Heuristic Use by Students in Problem Solving

The purpose of this study was to examine the use of heuristics by students and gain insight into the thought process behind their problem-solving skills. The study used an adaptive narrative as the information delivery medium. An adaptive narrative was chosen because it could be designed to simulate decision making processes encountered in real world situations. Students enrolled in an introductory biology major class were chosen for the study because their fields of interest all require complex problem solving and decision-making skills. It was of interest to investigate what decisions were made when heuristics were given and how that may influence their rationale in the decision-making process. The results of this study indicate that: heuristics can enable students to make correct decisions when the heuristics are based on already familiar concepts; although students self-reported low cognitive load challenges in the NASA TLX, most of the explanations were deemed poor when graded by rubrics; students had difficulty transferring information learned in the narrative and synthesizing a complete and complex explanation past three data points. This study provides evidence that greater practice in the transfer of information to novel settings is important in education in order for students to become proficient in complex decision-making

Critical Thinking Skills Profile of High School Students In Learning Science-Physics

This study aims to describe Critical Thinking Skills high school students in the city of Makassar. To achieve this goal, the researchers conducted an analysis of student test results of 200 people scattered in six schools in the city of Makassar. The results of the quantitative descriptive analysis of the data found that the average value of students doing the interpretation, analysis, and inference in a row by 1.53, 1.15, and 1.52. This value is still very low when compared with the maximum value that may be obtained by students, that is equal to 10.00. This shows that the critical thinking skills of high school students are still very low. One fact Competency Standards science subjects-Physics is demonstrating the ability to think logically, critically, and creatively with the guidance of teachers and demonstrate the ability to solve simple problems in daily life. In fact, according to Michael Scriven stated that the main task of education is to train students and or students to think critically because of the demands of work in the global economy, the survival of a democratic and personal decisions and decisions in an increasingly complex society needs people who can think well and make judgments good. Therefore, the need for teachers in the learning device scenario such as: driving question or problem, authentic Investigation: Science Processes

identifying archaeological knowledge using multi dimensional scaling and multiple constraint satisfaction

In this thesis, I look at the current state of research in two fields: the cognitive psychology of learning and expertise & the development of Intelligent Tutoring Systems, especially their methods of modelling the users knowledge state. Within these areas I proceed to examine the way that these theories have overlapped in the past and consider their recent divergence, suggesting that this parting of the ways is premature. I then consider other relevent research so as to suggest a hypothesis where a symbolic connectionist approach to the modelling of knowledge states could be a solution to previous difficulties in the field of Intelligent Tutoring. This hypothesis is then used to construct a method for its examination and also a computer program to analyse the collected data. I then undertake experimental work to validate my hypothesis, and compare my results and methods with a pre-established technique for interpreting the data, that of multi-dimensional scaling. Finally the method now shown to be feasible is discussed to indicate the its success and highlight its shortcomings. Further suggestions are also made as to further research avenues

From primitives to primates

Where do our images about early hominids come from? In this fascinating in-depth study, David Van Reybrouck demonstrates how input from ethnography and primatology has deeply influenced our visions about the past from the 19th century to this day – often far beyond the available evidence. Victorian scholars were keen to look at contemporary Australian and Tasmanian aboriginals to understand the enigmatic Neanderthal fossils. Likewise, today’s primatologists debate to what extent bonobos, baboons or chimps may be regarded as stand-ins for early human ancestors. The belief that the contemporary world provides ‘living links’ still goes strong. Such primate models, Van Reybrouck argues, continue the highly problematic ‘comparative method’ of the Victorian times. He goes on to show how the field of ethnoarchaeology has succeeded in circumventing the major pitfalls of such analogical reasoning. A truly interdisciplinary study, this work shows how scholars working in different fields can effectively improve their methods for interpreting the deep past by understanding the historical challenges of adjacent disciplines. Overviewing two centuries of intellectual debate in fields as diverse as archaeology, ethnography and primatology, Van Reybrouck’s book is one long plea for trying to understand the past on its own terms, rather than as facile projections from the present. David Van Reybrouck (Bruges, 1971) was trained as an archaeologist at the universities of Leuven, Cambridge and Leiden. Before becoming a highly successful literary author (The Plague, Mission, Congo…), he worked as a historian of ideas. For more than twelve years, he was coeditor of Archaeological Dialogues. In 2011-12, he held the prestigious Cleveringa Chair at the University of Leiden

Legal Rules, Legal Reasoning, and Nonmonotonic Logic

This dissertation develops, justifies, and examines the jurisprudential implications of a non-monotonic theory of common law legal reasoning. Legal rules seem to have exceptions but identifying all of them is difficult. This hinders attempts to formalize legal rules using classical logics. Non-monotonic logics allow defeasible inference, permitting rules that hold generally but can be defeated in the presence of exceptions. This ameliorates the problem of characterizing all exceptions to a rule, because exceptions can be added piecemeal while the rule remains. The first portion of the dissertation rebuts a prominent criticism leveled at a large class of theories of legal reasoning that includes my theory. The charge is that no coherent theory can recognize both (i) the difference between distinguishing and overruling, and (ii) the constraint of precedent. The critics argue that (ii) is more important than (i) and that (ii) can only be explained by monotonic legal rules. Drawing on cognitive psychology as well as legal theory, I show that coherent theories, such as my own, can accommodate both (i) and (ii). The second chapter provides motivation for understanding precedential constraint in terms of non-monotonic default rules and introduces my positive theory, which elaborates on John Horty's work in treating legal rules as prioritized defaults involving reasons. I motivate and implement a relaxation of Horty's restrictions on the form of rules to allow a more fine-grained characterization of precedent. Finally, I explore the relationship between these relaxations and the concept of precedent. The final section explains how my theory fits into the traditional jurisprudential ecosystem. I demonstrate that, contrary to assertions in the legal theory literature, this non-monotonic approach is entirely compatible with positivism's commitment to extracting rules from authoritative legal sources, namely court opinions. I also suggest how it might be attractive to law and economics theorists, pragmatists, and followers of Dworkin.PhDPhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110363/1/arigoni_1.pd