Markov solution processes: Modeling human problem solving with procedural knowledge space theory

none3noStefanutti (2019) recently developed procedures and a related theory for deriving learning spaces from problem spaces. The approach provides a deterministic model for partially ordering individuals, on the basis of their performances in problem-solving tasks. This deterministic model accounts for both the accuracy of the responses and, especially, the sequence of ”moves” (observable solution process) made by the problem solver. A Markov model of the solution process of a problem-solving task is proposed, that provides a stochastic framework for the empirical test of the deterministic model and the related problem-space-derived learning space. This type of model allows for making predictions with respect to both the observable solution process, and the unobservable knowledge state on which the solution process is assumed to be based. The Tower of London test has been chosen as the problem-solving task for the empirical validation of the model. The results of a simulation study and of two different empirical studies are presented and discussed.noneStefanutti L.; de Chiusole D.; Brancaccio A.Stefanutti, L.; de Chiusole, D.; Brancaccio, A

Stat-Knowlab. Assessment and Learning of Statistics with Competence-based Knowledge Space Theory

An intelligent tutoring system for learning basic statistics, called Stat-Knowlab, is presented and analyzed. The algorithms implemented in the system are based on the competence-based knowledge space theory, a mathematical theory developed for the formative assessment of knowledge and learning. The system\u2019s architecture consists of the two assessment and learning modules that interact with each other in a continuous exchange of information about the current knowledge state of a student. This allows the system to personalize the student\u2019s learning, providing only with the learning objects that she is ready to learn. During the browsing of the system, several types of navigation data are recorded. In this work, we analyzed data from two studies that were aimed at examining the learning processes induced by the navigation of the system. The results of both studies highlighted that the system is useful for monitoring the student learning processes during a university course of basic statistics

Extending the Basic Local Independence Model to Polytomous Data

A probabilistic framework for the polytomous extension of knowledge space theory (KST) is proposed. It consists in a probabilistic model, called polytomous local independence model, that is developed as a generalization of the basic local independence model. The algorithms for computing \u201cmaximum likelihood\u201d (ML) and \u201cminimum discrepancy\u201d (MD) estimates of the model parameters have been derived and tested in a simulation study. Results show that the algorithms differ in their capability of recovering the true parameter values. The ML algorithm correctly recovers the true values, regardless of the manipulated variables. This is not totally true for the MD algorithm. Finally, the model has been applied to a real polytomous data set collected in the area of psychological assessment. Results show that it can be successfully applied in practice, paving the way to a number of applications of KST outside the area of knowledge and learning assessment

Modeling misconceptions in knowledge space theory

Building intelligent tutoring systems (ITSs) that are aware of the students\u2019 misconceptions has been one of the ambitions for many of the approaches to computerized assessment of knowledge and learning. In the present article we extend knowledge space theory (KST) to mistakes and misconceptions. The proposed approach completes and extends the work initiated by J. Lukas (1997, Modellierung von Fehlkonzepten in einer algebraischen Wissensstruktur [Modeling misconceptions in an algebraic knowledge structure], Kognitionswissenschaft, 6(4), 196\u2013204) on the application of information systems in KST for modeling misconceptions. The approach is divided into a deterministic and a probabilistic part. The notion of a \u201cpolytomous skill map\u201d (PSM) represents the cornerstone of the deterministic part. Properties of the PSM are established that assure a consistent link between item responses on the one hand and the (correct or buggy) cognitive rules applied by an individual on the other hand. A weaker notion of information system (named a \u201ccognitive rule system\u201d) is proposed for representing two types of dependencies among cognitive rules: precedence and compatibility. The probabilistic part consists of an extension of the basic local independence model to more than two response alternatives. This model can be used for knowledge diagnoses, as well as for empirically testing the deterministic assumptions from a PSM. An empirical application of this probabilistic model to the responses of 331 university students is illustrated and discussed using two different PSMs

On the polytomous generalization of knowledge space theory

One of the core assumptions of knowledge space theory (KST) is that the answer of a subject to an item can be dichotomously classified as correct or incorrect. Schrepp (1997) provided a very first attempt to generalize the main KST concepts to items with more than two response alternatives, but his work has not had a strong impact on the subsequent research on KST. The aim of the present article is to introduce a new formulation of the polytomous KST, starting from the work of Schrepp and broadening it to a wider extent. Schrepp's generalization is revisited, and the fundamental closure conditions are reformulated and decomposed into a necessary and sufficient set of four independent properties of polytomous knowledge structures. Among them, two special properties emerge in the polytomous case that in the dichotomous one are neither testable nor immediately visible, since necessarily true. These properties allow for a straight generalization of Birkhoff's Theorem with respect to quasi-ordinal knowledge spaces, and Doignon and Falmagne's Theorem for knowledge spaces. Such findings open the field to a systematic generalization of many KST concepts to the polytomous case

A class of k-modes algorithms for extracting knowledge structures from data

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The oncological multidimensional prognostic index is a promising decision-making tool: A real-world analysis in older patients with metastatic colorectal cancer

Background: Approximately 50% of colorectal cancers occur in older patients. In-ternational societies recommend geriatric tools to optimise treatment of older patients. Comprehensive Geriatric Assessment (CGA) is a multidimensional assessment used to classify patients as fit, vulnerable, or frail. The CGA-based oncological multidimensional prognostic index (onco-MPI) also classifies patients as high-, intermediate-, or low-risk based on tumour characteristics. We investigated the role of CGA and onco-MPI in older patients with meta-static colorectal cancer (mCRC) in a real-world setting. Methods: Data for consecutive mCRC patients aged >70 years were retrieved from a prospec-tively maintained database from 2010 to 2020. We analyzed patients' and tumours' character-istics, and the CGA domains. Onco-MPI was calculated by a validated algorithm derived from CGA domains. Pearson's test was used to verify whether onco-MPI scores and chemotherapy administration were correlated. Results: The study included 488 mCRC patients with a mean age of 76.1 years. According to CGA, 52% of patients were fit, 28% vulnerable, and 20% frail. According to onco-MPI, 9% were low, 54% intermediate, and 37% high-risk. The median OS was 22.7 months. The following factors improved OS: 0-1 ECOG PS, low onco-MPI, fit based on CGA, chemo-therapy administration, and doublet regimen. Chemotherapy administration significantly correlated with onco-MPI scores, leading to a survival gain regardless of the risk subgroups. First-line regimen had no impact on survival across the CGA and onco-MPI categories. Conclusion: CGA and onco-MPI scores confirmed their prognostic impact in older mCRC pa-tients and may aid in decision-making and subgroup stratification in dedicated trials. 2022 Published by Elsevier Ltd

Accreditation for excellence of cancer research institutes: recommendations from the Italian Network of Comprehensive Cancer Centers

A panel of experts from Italian Comprehensive Cancer Centers defines the recom- mendations for external quality control programs aimed to accreditation to excellence of these institutes. After definition of the process as a systematic, periodic evaluation performed by an external agency to verify whether a health organization possesses certain prerequisites regarding structural, organizational and operational conditions that are thought to affect health care quality, the panel reviews models internationally available and makes final recommendations on aspects considered of main interest. This position paper has been produced within a special project of the Ministry of Health of the Italian Government aimed to accredit, according to OECI model, 11 Ital- ian cancer centers in the period 2012-2014. The Project represents the effort under- taken by this network of Comprehensive Cancer Centers to find a common denomi- nator for the experience of all Institutes in external quality control programs. Fourteen shared \u201cstatements\u201d are put forth, designed to offer some indications on the main aspects of this subject, based on literature evidence or expert opinions. They deal with the need for \u201caccountability\u201d and involvement of the entire organization, the effectiveness of self-evaluation, the temporal continuity and the educational val- ue of the experience, the use of indicators and measurement tools, additionally for in- tra- and inter-organization comparison, the system of evaluation models used, the provision for specific requisites for oncology, and the opportunity for mutual ex- change of evaluation experiences