Qualitative Reasoning

This document discusses the core Semantic Technologies in DynaLearn: i) The semantic repository, which supports the online storage and access of qualitative reasoning models, ii) the grounding process, which establishes semantic equivalences between the concepts in the models and the concepts in a background knowledge source, and iii) the use of ontology matching techniques for discovering similarities between the grounded models, in order to support knowledge-based feedback during the modelling process.

The reasoning is one of the many skills that must be mastered by students when working on math problems. One type of reasoning in mathematics is creative reasoning. Creative reasoning is classified into Local Creative Reasoning (LCR) and Global Creative Reasoning (GCR). The reasoning is called Local Creative Reasoning (LCR) if, in the problem-solving process, the steps are still memorizing or imitating, and only a small part uses creative reasoning. Meanwhile, the reasoning is called the Global Creative Reasoning (GCR) type if the problem-solving is not based on an algorithm and, as a whole, requires creative reasoning. This research aims to identify the types of creative reasoning of Islamic elementary school students in solving geometrical problems. This study used the descriptive qualitative method. The subjects of this study were fifth-grade students of MI Nurul Ulum Moropelang, consisting of 2 students with high mathematical abilities, 2 students with moderate mathematical abil...

This paper presents an approach to the computational use of drawings through the development of complexity measures, defined as the information content of the description of a drawing's structure. As such it is the function of the representation used. The paper presents examples of the use of such measurements applied to design drawings of architects.

Qualitative formalisms, suited to express qualitative temporal or spatial relationships between entities, have gained wide acceptance as a useful way of abstracting from the real world. The question remains how to describe spatio temporal concepts, such as the interaction between disconnected moving objects, adequately within a qualitative calculus and more specifically how to use this in geographical information systems. In this paper, the Basic Qualitative Trajectory Calculus (QT CB) for representing and reasoning about moving objects is presented. QT CB enables comparisons between positions of objects at different time points to be made. The calculus is based on few primitives (i.e., distance and speed constraints), making it elegant and theoretically simple. To clarify the way in which trajectories are represented within QT CB, specific cases of movements (e.g. circular movement) are presented. To illustrate the naturalness of QT C, a "predator-prey" example is studied.

Quantitative and qualitative models. Basic forms of qualitative space. Code and numerical patterns in qualitative space. Qualitative process models. Latent and contradicting models. Completeness and acceptability measure of qualitative models. Examples of qualitative models of production parameters of the oil well log, seismic signals from the oil deposits and laser welding process. Quacol algebra and possibilities of its extensions. Criteria for usage of specific algebraic operations. Comparison of model structures from the standpoint of accuracy, simplicity and solution stability. Conversion of qualitative models to its quantitative counterparts and determination of mean value and amplification factor of the quantitative model. Comparison of the interim step of the Medusa-T and Medusa-H algorithms. Numerical limits of circular qualitative models.

Quantitative and qualitative models. Basic forms of qualitative space. Code and numerical patterns in qualitative space. Qualitative process models. Latent and contradicting models. Completeness and acceptability measure of qualitative models. Examples of qualitative models of production parameters of the oil well log, seismic signals from the oil deposits and laser welding process.Quacol algebra and possibilities of its extensions. Criteria for usage of specific algebraic operations. Comparison of model structures from the standpoint of accuracy, simplicity and solution stability. Conversion of qualitative models to its quantitative counterparts and determination of mean value and amplification factor of the quantitative model. Comparison of the interim step of the Medusa-T and Medusa-H algorithms. Numerical limits of circular qualitative models.

Literature suggests that people typically understand knowledge by induction and produce knowledge by synthesis. This paper revisits the various modes of reasoningexplanatory abduction, innovative abduction, deduction, and inductionthat have been proposed by earlier researchers as crucial modes of reasoning underlying the design process. First, our paper expands earlier work on abductive reasoningan essential mode of reasoning involved in the process of synthesisby understanding its role with the help of the "SAPPhIRE" model of causality. The explanations of abductive reasoning in design using the SAPPhIRE model have been compared with those using existing models. Second, the paper captures and analyzes various modes of reasoning during design synthesis with the help of the "Extended Integrated Model of Designing". The analysis of participants' verbal speech and outcomes shows the model's ability to explain the various modes of reasoning that occur in design. The results indicate the above models to provide a more extensive account of reasoning in design synthesis. Earlier empirical validation of both the models lends further support to the claim of their explanatory capacity. According to , reasoning refers to the mental processes involved in generating and evaluating logical arguments. Reasoning consists of three parameters: (1) "premises", (2) "results" or "conclusions", and (3) "a rule" or "material implication" or "warrant" that allows

Literature suggests that people typically understand knowledge by induction and produce knowledge by synthesis. This paper revisits the various modes of reasoning – explanatory abduction, innovative abduction, deduction, and induction – that have been proposed by earlier researchers as crucial modes of reasoning underlying the design process. First, our paper expands earlier work on abductive reasoning – an essential mode of reasoning involved in the process of synthesis – by understanding its role with the help of the “SAPPhIRE” model of causality. The explanations of abductive reasoning in design using the SAPPhIRE model have been compared with those using existing models. Second, the paper captures and analyzes various modes of reasoning during design synthesis with the help of the “Extended Integrated Model of Designing”. The analysis of participants' verbal speech and outcomes shows the model's ability to explain the various modes of reasoning that occur in design. The ...

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial understanding denotes when the definition or the concept image has correct parts but essential parts are missing or incoherencies occur. Some students confused continuity with differentiability or perceived it as a graph not having holes, which is also reported by other studies. Another misconception that emerged is to perceive points on the x-axis as non-continuous. The partial understandings of asymptotes were related to the vertical asymptote as it was confused with a function property. Some students referred to the definitions when correctly solving some of the tasks and some students with coherent concept images were successful solving some of the tasks even when they did not refer to the definitions.

In this paper we describe an application of weighted abductive theorem proving that is used to create a model of students' qualitative reasoning for the Why2-Atlas tutoring system. The system encourages a student to write an essay in natural language so that the essay provides both an explanation as well as an answer to a qualitative mechanics problem. The student's essay is first mapped into a first-order predicate logic representation, which the abductive theorem prover treats as a goal (observation) in order to generate a proof that explains the essay. The resulting proof (1) provides an evaluation of the correctness of the student's essay, and, in the event the essay contains errors, (2) provides a diagnosis of the observed errors that help identify possible tutoring actions. We describe the knowledge representation, rules and weighted abductive theorem proving framework, outline previous and upcoming evaluations, and discuss possible future directions.

program. Two approaches are discussed: (1) based on theorem-proving method and (2) based on PROLOG language. Limitations of using theorem-proving software are discussed as well as how the actual implementation was done. Chapter VIII discusses further limitations of theorem-proving software not discussed in Chapter VII and the modifications that can be made for future enhancements of the diagnostic program. R ep ro d u ced with p erm ission o f th e copyright ow ner. Further reproduction prohibited w ithout perm ission.

The foreign language (FL) classroom can be an anxious environ- ment where students feel uncomfortable having to communicate in a language in which they feel inadequate and have little practice. Low self-efficacy in skill-specific tasks is oftentimes the culprit. While there are a number of factors involved in successful language learning, this study examines how practice affects students’ sense of self-efficacy in the foreign language classroom. Using self-efficacy theory and design-based research, this qualitative study ‘flipped’ the classroom to focus on student input and output practice in class with grammar instruction video-recorded for homework. Data were recursively collected and analyzed from ten courses over three semesters. Classroom observations and reflection were triangulated with interviews and focus groups. Findings suggest that practice and self-efficacy in the FL classroom are indeed linked and that other factors such as peer familiarity and grading also play a role...

Despite mathematical reasoning being a proficiency included in mathematics curricula around the world, research has found that primary teachers struggle to understand, teach, and assess mathematical reasoning. A detailed rubric involving the three reasoning actions of analysing, generalising and justifying at five proficiency levels was refined according to feedback from teachers. At different stages of the study, teachers used the rubric to assess their students’ reasoning and provided feedback about its usefulness.

Attention to mathematical reasoning in curriculum standards is part of an international trend, but identifying and understanding reasoning continues to challenge teachers.We report on one component of an Australia-wide initiative supporting teachers to implement innovative pedagogies. This paper contains insights from design research that focused on trialling classroom materials to support elementary teachers in their planning and assessment of mathematical reasoning. Findings confirmed planning is a critical step to developing learning experiences that elicit student reasoning, including consideration to task modifications and teacher questioning. Teachers' capacity to assess their students' reasoning was explored using the purposefully designed Assessing Mathematical Reasoning Rubric. The results reveal the complexity involved in constructing accurate judgements of students' reasoning capabilities, particularly appreciating the non-linear nature of mathematical reasoning and the need to draw on multiple sources of evidence. Implications for supporting teachers in their planning for, and assessing of, mathematical reasoning are raised.

Background and objective: Major depressive disorder causes more human suffering than any other disease affecting humankind. It has a high prevalence and it is predicted that it will be among the three leading causes of disease burden by 2030. The prevalence of depression, all of its social and personal costs, and its recurrent characteristics, put heavy constraints on the ability of the public healthcare system to provide sufficient support for patients with depression. In this research, a model for continuous monitoring and tracking of depression in both short-term and long-term periods is presented. This model is based on a new qualitative reasoning approach. Method: This paper describes the patient assessment unit of a major depression monitoring system that has three modules: a patient progress module, based on a qualitative reasoning model; an analysis module, based on expert knowledge and a rules-based system; and the communication module. These modules base their reasoning mainly on data of the patient's mood and life events that are obtained from the patient's responses to specific questionnaires (PHQ-9, M.I.N.I. and Brugha). The patient assessment unit provides synthetic and useful information for both patients and physicians, keeps them informed of the progress of patients, and alerts them in the case of necessity. Results: A set of hypothetical patients has been defined based on clinically possible cases in order to perform a complete scenario evaluation. The results that have been verified by psychiatrists suggest the utility of the platform. The proposed major depression monitoring system takes advantage of current technologies and facilitates more frequent follow-up of the progress of patients during their home stay after being diagnosed with depression by a psychiatrist.

Probabilistic inference with a belief network in general is computationally expensive. Since the concept of structural relevance provides for identifying parts of a belief network that are irrelevant to a context of interest, it allows for alleviating to some extent the computational burden of inference: inference can be restricted to the network's relevant part. The structurally relevant part of a belief network, however, is not static. It may c hange dynamically as reasoning progresses. We address the dynamics of structural relevance and introduce the concept of an independence projection to capture these dynamics.

While much progress has been made on verification of discrete systems such as computer programs, work on formal verification of continuous, physical systems has been limited. We present a technique for verification of safety properties of such systems. Our algorithm treats safety as a reachability problem, and attempts to prove that a system cannot evolve from an abstract initial state into a state in which the safety condition does not hold. This approach is inspired by qualitative simulation techniques and makes use of trajectories comprised of a sequence of qualitative states and state transitions. The applicability of the technique, however, is not limited to qualitative problems, as we can use any amount of quantitative mathematics in the system description. This paper describes the technique, presents example problems, and discusses its limitations as well as potential for use in device engineering.

Modeling is regarded as fundamental to human cog-nition and scientific inquiry (Schwarz and White2005). It helps learners express and externalize their thinking, visualize and test components of their theories, and make materials more interesting. Particularly, the impor-tance of learners constructing conceptual interpretations of system behavior has been pointed out many times (Mettes and Roossink [1981], Elio and Sharf [1990], Ploetzner and Spada [1998], Frederiksen and White [2002]). Modeling envi-ronments can thus make a significant contribution to the improvement of science education. A new class of knowledge construction tools is emerging that uses logic-based (symbolic, nonnumeric) representations for expressing conceptual systems knowledge (Forbus et al. 2005, Leelawong and Biswas 2008, Bredeweg et al. 2009). Dif-ferent from the numeric-based tools (Richmond and Peter-son 1992, Pratap 2009), these tools employ a qualitative vocabulary (Forbus 2008) for users to construct the...

DynaLearn is an Interactive Learning Environment that facilitates a constructive approach to developing a conceptual understanding of how systems work. The software can be put in different interactive modes facilitating alternative learning experiences, and as such provides a toolkit for educational research.

In this deliverable, we introduce three new virtual character support types (Critic, Quiz and Diagnosis) which are linked to different kinds of conceptual knowledge (such as semantic feedback or multiple choice questions) generated within the DynaLearn software. We show how this knowledge is extracted and transformed into characterspecific dialogs that are presented by the virtual characters but also encourage the learner to engage and participate. For this process, we rely on the architecture and dialog management system developed in earlier deliverables. Finally, we investigate how different characters and support types can be combined with each other to from integrated dialogs to even further support and engage learners.

In this document we present two different use cases of the DynaLearn software which involve virtual characters: The Teachable Agent and the Basic Help. We elaborate on how the necessary knowledge for these use cases is extracted from the CM component, how it is represented and how it is turned into presentations by the virtual characters that are engaging and helpful for the learners. We also describe how the different parts of the dialog system presented in Deliverable 5.2 aid us in achieving this task.

De plus en plus d'objets mobiles sont équipés de capteurs qui facilitent la surveillance de leur évolution et permettent la réception, le stockage et la visualisation en temps réel de leur position. Actuellement, la fouille de données dans des historiques de déplacements volumineux offre des perspectives intéressantes dans le domaine de l'étude du comportement de ces objets. À partir de résultats d'analyses statistiques sur des ensembles de trajectoires, des patrons spatio-temporels (trajectoires médianes, couloirs spatiotemporels, routes types) ont été définis. En s'appuyant sur ces patrons, il est possible de détecter en temps réel des situations inhabituelles et d'en qualifier le comportement. Dans cet article, cette méthode est appliquée aux déplacements de navires dans un espace maritime ouvert afin de détecter des comportements inhabituels (retard, hors route, etc.).

When we use Case-Based Reasoning (CBR) for practical applications, it is often the case to implement two kinds of problem solvers: casebased one and knowledge-based/conventional one. The complex integration of such plural reasoners often causes serious VV~T problems: performance of problem solving, quality of solutions, and so on. In this paper, we ~ldress the performance validation problems of a CBR system. This paper presents a blackbox validation approach to quantitatively analyze the performance and proposes three kinds of performance measures. The proposed measures are then applied to validating a CBR system: IRS-CHR (Intelligent Information Retriever with a Case-Based Reasoner). From the experimental results, we conclude that (1) IRS-CBR has succeeded in both speed-up and memory-based learning, and (2) the proposed measures are useful for validating a CBR system.

Industrial process plants such as chemical refineries and electric power generation are examples of continuous-variable dynamic systems (CVDS) whose operation is continuously monitored for abnormal behavior. CVDSs pose a challenging diagnostic problem in which values are continuous (not discrete), relatively few parameters are observable, parameter values keep changing, and diagnosis must be performed while the system operates. We present a novel method for monitoring CVDSs which exploits the ...

In this paper, we present a framework abstracting motion by creating a qualitative representation of classes describing motion, and use the continuity constraints implicitly embedded in the semantics of these classes to create a framework that enables plausible reasoning about them. In particular, we propose a topology-based calculus of motion whose primitive is a motion class. We subsequently construct a set of primitive motion classes that exhaustively describes the change in topology between two moving objects, and show how compound motion classes are formed from these primitive motion classes using continuity constraints we make explicit. We use composition tables to define queries in the spatio-temporal domain and enable the extension of the classes to reason about the change in topology among three objects as they move.

This study aims to reveal the condition of students' reasoning abilities based on the way students argue. This research uses a qualitative-descriptive approach. The subjects in this study were 3 students of junior high school with high reasoning abilities and 3 students with low reasoning abilities who viewed the reasoning ability scores when providing problem solving solutions on the written test. The data obtained in this study were in the form of students' written test scores and the results of student interviews. Interviews were conducted to bring up students 'ability to argue that describe and reveal the condition of students' reasoning abilities in the process of solving problems. The results of students 'arguments are analyzed and adjusted to the model of StephenToulmin's argument which reveals that there are 6 components of the argumentation to show the seriousness of students in arguing in order to obtain valid argument results to assess students' reasoning abilities. The arguments from students succeeded in uncovering 4 conditions that describe the conditions of students' mathematical reasoning abilities. These conditions are: 1) Students who show high reasoning ability in written tests and are able to show their reasoning process in the arguments that are brought up, 2) Students who show low reasoning abilities in written tests but are able to show their reasoning processes in the arguments that are brought up, 3) Students which shows a high reasoning ability in a written test but have not been able to demonstrate the reasoning process in the arguments that are brought up, and 4) Students who show a low reasoning ability in a written test and have not been able to demonstrate their reasoning process in the arguments that are brought up.

This study aims to reveal the condition of students' reasoning abilities based on the way students argue. This research uses a qualitative-descriptive approach. The subjects in this study were 3 students of junior high school with high reasoning abilities and 3 students with low reasoning abilities who viewed the reasoning ability scores when providing problem solving solutions on the written test. The data obtained in this study were in the form of students' written test scores and the results of student interviews. Interviews were conducted to bring up students 'ability to argue that describe and reveal the condition of students' reasoning abilities in the process of solving problems. The results of students 'arguments are analyzed and adjusted to the model of StephenToulmin's argument which reveals that there are 6 components of the argumentation to show the seriousness of students in arguing in order to obtain valid argument results to assess students&#39...

Many real life optimization problems are defined in terms of both hard and soft constraints, and qualitative conditional preferences. However, there is as yet no single framework for combined reasoning about these three kinds of information. In this paper we study how to exploit classical and soft constraint solvers for handling qualitative preference statements such as those captured by the CP-nets model. In particular, we show how hard constraints are sufficient to model the optimal outcomes of a possibly cyclic CP-net, and how soft constraints can faithfully approximate the semantics of acyclic conditional preference statements whilst improving the computational efficiency of reasoning about these statements.

Objective: To get around students' reluctance, learning media is needed; one of them is the development of mathematics teaching materials. The development of teaching materials is needed to actualize subjects, especially mathematics, as a contextual subject. This goal is to improve students' reasoning abilities in understanding and solving the problems in daily life. The function of the model is as an intermediary between students' mathematical reasoning abilities and the questions presented in the development of teaching materials. More mathematical reasoning abilities are found in trigonometry material. Trigonometry is the science of measuring the angles and boundaries of triangles (used in astronomy and so on) in which there are solutions for other problems, such as measuring the height of mountains, buildings, towers, etc. Method: This research uses a qualitative method. Results: The teaching material Trigonometry research is valid for module material validation, gra...

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In this paper we construct an information-theoretic model of architectural drawings. This model is then used to quantify and measure the complexities and similarities of drawings. The approach is applied within a linear qualitative shape representation but can be generalized to other types of representation. The descriptive and analytic power of the proposed methods are demonstrated by studying the time evolution of the architectural plans produced by Aalto and Kahn and by comparing them to each other.

Recent advances in knowledge engineering have led to develop the qualitative (deep) model based diagnostic systems. As process knowledge accumulated, however, the diagnostic system remains strictly qualitative. This limits the usefulness of such systems. In this work, a framework is developed for integrating quantitative process knowledge into the qualitative model. Once quantitativeprocess information, e.g., steady-state gains, is available, it can be incorporated into the simplest qualitative process model called the signed directed graph. The quantitative process knowledge is described in terms of membership functions of fuzzy set theory. According to the measurement pattern, the truth value of a hypothesis (e.g., a fault origin) can be calculated based on the fuzzy logic. Consequently, the diagnostic resolution can be improved significantly. Furthermore, the proposed method becomes a strictly qualitative diagnostic system, i f no quantitative in formation is available. A chemical reactor example illustrates the design and performance of the qualitative/quantitative model-based diagnostic system. The proposed approach can also be extended to the multiple-fault situations in a straightforward manner.

In this paper we describe a part of the Why2-Atlas tutoring system that models students' reasoning in the domain of qualitative physics. The main goals of the model are (1) to evaluate correctness of the student's essay, and, in case the essay contains errors, (2) to direct remedial tutoring actions according to plausible errors in the student's reasoning. To meet these goals, a backchaining theorem prover generates a set of assumptions and a chain of reasoning (a proof) that plausibly led the student to write the observed essay. A proof can include correct as well as buggy reasoning steps and assumptions. After a proof is generated, it is analyzed for correctness and the analysis is used to generate appropriate feedback to the student. We describe the weighted abductive theorem proving framework, outline previous and upcoming evaluations and discuss possible future directions.

Introduction: Le but de cette étude était de déterminer la prévalence de l'hypotension orthostatique (HO) chez les hypertendus noirs africains traités, et rechercher ses facteurs favorisants. Méthodes: Il s'est agi d'une étude prospective transversale menée du 1 er février 2007 au 31 janvier 2009 à la clinique cardiologique du CHU Campus de Lomé, incluant des patients régulièrement traités pour hypertension artérielle. La pression artérielle et la fréquence cardiaque étaient mesurées en décubitus dorsal puis immédiatement en orthostatisme (1 ère et 3 ème minutes). Résultats: Sur une population de 394 patients hypertendus traités, 81 cas d'HO (20,5 %) ont été observés dont 53 (65,4 %) étaient symptomatiques. Il s'agissait de 188 femmes (49,2%) et de 206 hommes (50,8%). L'âge moyen des hypertendus était de 53,4 ans ± 11,2 avec des extrêmes de 26 ans et de 81ans. Les patients ayant présenté une HO avaient un âge moyen significativement plus élevé : 60 ans contre 51 ans chez les autres (p= 0,01). L'HO était plus fréquente chez les patients traités par antihypertenseurs centraux, les patients ayant présenté un accident vasculaire cérébral, les diabétiques, les obèses. Conclusion: L'hypotension orthostatique est fréquente chez les hypertendus noirs africains traités. Il faut la rechercher systématiquement chez tous les hypertendus surtout mal contrôlés car elle peut être non seulement un facteur de mauvaise observance thérapeutique, mais aussi un facteur de risque cardiovasculaire indépendant.

Approximate Reasoning is the process Ill" processes by which a possible imprecise conclusion is deduced from a collection of imprecise premises. Fuzzy logic plays the major role in approximate reasoning. It has the ability to deal with different types of uncertainty. An overview of the different aspects of the theory of appro:x:imate reasoning has been provided here based on the e:x:isting literature. Suitable iUustratioDB are included, whenever necessary, to make the concept clear. Some of the implementation of the theory to real life problems have been mentioned. Finally, a linguistic re cognition system based on approximate reasoning has heen described along with its implementation in bpeed1 recognition problem.

A pivotal difference between Artificial Neural Networks and Fuzzy Cognitive Maps (FCMs) is that the latter allow modeling a physical system in terms of concepts and causal relations, thus equipping the network with interpretability features. However, such components are normally described by quantitative terms, which may be difficult to handle by domain experts. In this paper, we explore a reasoning mechanism for FCMs based on the Computing with Words paradigm where numerical concepts and relations are replaced with linguistic terms. More explicitly, we include triangular fuzzy numbers into the qualitative reasoning process attached to our model, thus proving further interpretability and transparency. The simulations show the potential behind the symbolic reasoning mechanism proposed in this study.

Many modern machine learning approaches require vast amounts of training data to learn new concepts; conversely, human learning often requires few examples-sometimes only one-from which the learner can abstract structural concepts. We present a novel approach to introducing new spatial structures to an AI agent, combining deep learning over qualitative spatial relations with various heuristic search algorithms. The agent extracts spatial relations from a sparse set of noisy examples of block-based structures, and trains convolutional and sequential models of those relation sets. To create novel examples of similar structures, the agent begins placing blocks on a virtual table, uses a CNN to predict the most similar complete example structure after each placement, an LSTM to predict the most likely set of remaining moves needed to complete it, and recommends one using heuristic search. We verify that the agent learned the concept by observing its virtual block-building activities, wherein it ranks each potential subsequent action toward building its learned concept. We empirically assess this approach with human participants' ratings of the block structures. Initial results and qualitative evaluations of structures generated by the trained agent show where it has generalized concepts from the training data, which heuristics perform best within the search space, and how we might improve learning and execution.

Roles that students take in solving problems can help in guiding and scaffolding their learning and meaning making. We present a case study -part of a UK-Israel research project -that focuses on the emerging roles spontaneously developed by Israeli eighth-grade students (14 years old) in solving a scientific-statistical inquiry task using TinkerPlots2. The task integrated four design approaches: Exploratory Data Analysis, Active Graphing, modeling, and gaming. We examine how this task design played a role in this emergence of students' roles and how they respectively adopted perspectives on uncertainty and modeling. Implications of the findings are discussed.

This paper presents a framework of an educational scenario for the teaching of electrical circuits at senior high schools. This scenario aims at the development of exploratory and critical thinking of students, the development of make-decision skills and knowledge transfer skills from one framework to another, the ability of collaboration and in common approach of problem solving. During the lessons, the student teams discover the formulas and principles of the total resistance, the voltage drop across the resistances, and the flowing current through the resistances, in series, in parallel, and in combination resistance circuits by comparing the circuits with each other and guided by the exploratory questions and scaffolding as well. At the end, the student teams solve an open-ended problem based upon their knowledge obtained through the activities. This framework has adopted and applied by educators with a great success.

The space-centered framework is a reasoning methodology for obtaining qualitative solutions to boundary value problems. The inference strategy uses backward-andforward propagation. The backward propagation assumes a component or connection qualitative state consistent with available knowledge about the component or connection. The forward propagation uses the topology of the structure and derives values without ambiguity consistent with the new information assumed by the backward propagation. The forward propagation considerably improves the inference efficiency. A computer program named Agrippa implements the famework. The framework is applied to the evaluation of the load transfer characteristics of two conceptual structural designs.

The purpose of this study was to study the impact of conformity to Statistical Reasoning Learning Environment (SRLE) principles on students' statistical reasoning in Advanced Placement statistics courses. A quasi-experimental design was used to compare teachers' levels of conformity to SRLE principles through a matching process used to mitigate the effects of nonrandom assignment. This matching process resulted in five pairs of similar teachers and schools who differed in self-reported beliefs in the effectiveness and application of SRLE principles. Increases in students' statistical reasoning were found at varying levels in both high and low conformity classrooms. Improvements among teachers with low conformity to SRLE principles were less varied and consistent with national averages for improvement by college students. Improvements in classes with high conformity to SRLE principles were more varied. Students of two teachers with high levels of conformity to SRLE principles showed large levels of improvement in statistical reasoning in comparison to national results. While the comparison between classrooms conformity to SRLE principles revealed no statistically significant differences in students' statistical reasoning ability, deeper analysis suggests that beliefs and practices aligned with SRLE principles have potential to increase students' statistical reasoning at rates above national averages.

In this paper we present the notion of structured reasoning through a model, called the Generic/Actual Argument Model (GAAM). The model which has been used as a computational representation for machine modelling of reasoning and for hybrid combinations of human and machine reasoning can be used as a coalescent framework for decision making. Whilst the notion of structuring reasoning is not new, structured reasoning is advanced as a technique where group consensus on reasoning structures at various levels can be used to facilitate the comprehension of complex reasoning particularly where there are multiple perspectives. For an issue, the approach provides a scaffolding structure for cognitive co-operation and a normative reasoning structure against which group participants can identify points of difference and points in common as well as the nature of the differences and similarities. Intragroup transparency characterized by the ability to recognise points in common and understand the nature of differences is important to the process of coalescing group decisions that carry maximum group support.