Doctor of Philosophy

dissertationOut of the three major constituents of cognitive load theory, intrinsic is the most crucial as it relates to difficulty of learning material. Difficulty of learning material is determined by two factors: the learner's prior knowledge and interacting elements present in the task. The proposed study investigated the role of two formats of worked examples (full and worked) in mathematical problem solving taking into account the learner's prior knowledge and difficulty of the presented material. One hundred and sixty participants were recruited for the study. The participants solved algebraic systems of equations by either using full or completion worked examples approach. Participants were identified as low-prior-knowledge learners or high-prior-knowledge learners based on their performance on the prior knowledge test, using a median split method in which the top one-third and lower one-third participants were retained, with the middle one-third excluded from final analyses. Results indicated that both low- and high-prior-knowledge learners found completion worked examples to be beneficial in solving easy problems and full worked examples in solving difficult problems. This finding is contradictory to the expertise reversal effect. Significant positive correlation was found between intrinsic and germane cognitive load while a significant negative correlation was found between extraneous and germane cognitive load. Both of these significant correlations are aligned with proposals from previous research. Results of the motivation questionnaire indicated that interest was significantly positively correlated with germane load implying that interest in the instructional domain is an important determinant in effecting germane load

Implementing MAS agreement processes based on consensus networks

[EN] Consensus is a negotiation process where agents need to agree upon certain quantities of interest. The theoretical framework for solving consensus problems in dynamic networks of agents was formally introduced by Olfati-Saber and Murray, and is based on algebraic graph theory, matrix theory and control theory. Consensus problems are usually simulated using mathematical frameworks. However, implementation using multi-agent system platforms is a very difficult task due to problems such as synchronization, distributed finalization, and monitorization among others. The aim of this paper is to propose a protocol for the consensus agreement process in MAS in order to check the correctness of the algorithm and validate the protocol. © Springer International Publishing Switzerland 2013.This work is supported by ww and PROMETEO/2008/051 projects of the Spanish government, CONSOLIDER-INGENIO 2010 under grant CSD2007-00022, TIN2012-36586-C03-01 and PAID-06-11-2084.Palomares Chust, A.; Carrascosa Casamayor, C.; Rebollo Pedruelo, M.; Gómez, Y. (2013). Implementing MAS agreement processes based on consensus networks. Distributed Computing and Artificial Intelligence. 217:553-560. https://doi.org/10.1007/978-3-319-00551-5_66S553560217Argente, E.: et al: An Abstract Architecture for Virtual Organizations: The THOMAS approach. Knowledge and Information Systems 29(2), 379–403 (2011)Búrdalo, L.: et al: TRAMMAS: A tracing model for multiagent systems. Eng. Appl. Artif. Intel. 24(7), 1110–1119 (2011)Fogués, R.L., et al.: Towards Dynamic Agent Interaction Support in Open Multiagent Systems. In: Proc. of the 13th CCIA, vol. 220, pp. 89–98. IOS Press (2010)Luck, M., et al.: Agent technology: Computing as interaction (a roadmap for agent based computing). Eng. Appl. Artif. Intel. (2005)Mailler, R., Lesser, V.: Solving distributed constraint optimization problems using cooperative mediation. In: AAMAS 2004, pp. 438–445 (2004)Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95(1), 215–233 (2007)Pujol-Gonzalez, M.: Multi-agent coordination: Dcops and beyond. In: Proc. of IJCAI, pp. 2838–2839 (2011)Such, J.: et al: Magentix2: A privacy-enhancing agent platform. Eng. Appl. Artif. Intel. 26(1), 96–109 (2013)Vinyals, M., et al.: Constructing a unifying theory of dynamic programming dcop algorithms via the generalized distributive law. Autonomous Agents and Multi-Agent Systems 22, 439–464 (2011

Beyond deficit-based models of learners' cognition: Interpreting engineering students' difficulties with sense-making in terms of fine-grained epistemological and conceptual dynamics

Researchers have argued against deficit-based explanations of students' troubles with mathematical sense-making, pointing instead to factors such as epistemology: students' beliefs about knowledge and learning can hinder them from activating and integrating productive knowledge they have. In this case study of an engineering major solving problems (about content from his introductory physics course) during a clinical interview, we show that "Jim" has all the mathematical and conceptual knowledge he would need to solve a hydrostatic pressure problem that we posed to him. But he reaches and sticks with an incorrect answer that violates common sense. We argue that his lack of mathematical sense-making-specifically, translating and reconciling between mathematical and everyday/common-sense reasoning-stems in part from his epistemological views, i.e., his views about the nature of knowledge and learning. He regards mathematical equations as much more trustworthy than everyday reasoning, and he does not view mathematical equations as expressing meaning that tractably connects to common sense. For these reasons, he does not view reconciling between common sense and mathematical formalism as either necessary or plausible to accomplish. We, however, avoid a potential "deficit trap"-substituting an epistemological deficit for a concepts/skills deficit-by incorporating multiple, context-dependent epistemological stances into Jim's cognitive dynamics. We argue that Jim's epistemological stance contains productive seeds that instructors could build upon to support Jim's mathematical sense-making: He does see common-sense as connected to formalism (though not always tractably so) and in some circumstances this connection is both salient and valued.Comment: Submitted to the Journal of Engineering Educatio

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

A Relationship Between Problem Solving Ability and Students' Mathematical Thinking

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student's are better trained in problem solving than information system department students. So, to improve students' mathematical thinking, its would be better, at fisrtly enhance the problem solving ability

Research questions and approaches for computational thinking curricula design

Teaching computational thinking (CT) is argued to be necessary but also admitted to be a very challenging task. The reasons for this, are: i) no general agreement on what computational thinking is; ii) no clear idea nor evidential support on how to teach CT in an effective way. Hence, there is a need to develop a common approach and a shared understanding of the scope of computational thinking and of effective means of teaching CT. Thus, the consequent ambition is to utilize the preliminary and further research outcomes on CT for the education of the prospective teachers of secondary, further and higher/adult education curricula

Learning by Seeing by Doing: Arithmetic Word Problems

Learning by doing in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children\u27s ability to see significant abstract structures in mathematical situations. The reflection necessary for such seeing is motivated by activities and contexts that emphasize affective and social aspects. Natural language, as a representation already familiar to children, is key in these activities, both as a means of mathematical expression and as a link between situations and various abstract representations. These tools support children\u27s ownership of a mathematical problem and its expression; remote sharing of problems and data; software interpretation of children\u27s own word problems; play with dynamically linked representations with attention to children\u27s prior connections; and systematic problem variation based on empirically determined level of difficulty