abstract: The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens’ Categorization Practice Utility (MS-CPU), an example-tracing intelligent tutoring system that serves as practice for the first step (problem categorization) in a larger comprehensive story problem-solving pedagogy that purports to raise the level of story problem-solving performance. During the analysis phase of this project, knowledge components and particular competencies that enable learning (schema building) were identified. During the development phase, a tutoring system was designed and implemented that algorithmically teaches these competencies to the student with graphical, interactive, and animated utilities. Because the tutoring system provides a much more concrete rather than conceptual, learning environment, it should foster a much greater apprehension of a story problem-solving process. With this experience, the student should begin to recognize the generalizability of concrete operations that accomplish particular story problem-solving goals and begin to build conceptual knowledge and a more conceptual approach to the task. During the formative evaluation phase, qualitative methods were used to identify obstacles in the MS-CPU user interface and disconnections in the pedagogy that impede learning story problem categorization and solution preparation. The study was conducted over two iterations where identification of obstacles and change plans (mitigations) produced a qualitative data table used to modify the first version systems (MS-CPU 1.1). Mitigation corrections produced the second version of the MS-CPU 1.2, and the next iteration of the study was conducted producing a second set of obstacle/mitigation tables. Pre-posttests were conducted in each iteration to provide corroboration for the effectiveness of the mitigations that were performed. The study resulted in the identification of a number of learning obstacles in the first version of the MS-CPU 1.1. Their mitigation produced a second version of the MS-CPU 1.2 whose identified obstacles were much less than the first version. It was determined that an additional iteration is needed before more quantitative research is conducted. / Dissertation/Thesis / Doctoral Dissertation Educational Technology 2018

V předložené práci se zabýváme hledáním řešení lineární diferenciální maticové rovnice se zpožděním x'(t)=A0x(t)+A1x(t-tau), kde A0, A1 jsou konstantní matice, tau>0 je konstantní zpoždění. Dále se zabýváme odvozením podmínek stability řešení systému a řiditelnosti daného systému. Pro řešení tohoto systému byla použita metoda "krok za krokem". Řešení bylo nalezeno jak v rekurentní formě tak i v obecném tvaru. Je provedena analýza stability a asymptotické stability řešení systému. Jsou zformulovány podmínky stability. Hlavní roli v analýze stability měla metoda Lyapunovových funkcionálů. Jsou zformulovány nutné a postačující podmínky řiditelnosti pro případ systémů se stejnými maticemi a je zkonstruována řídící funkce. Jsou odvozeny postačující podmínky pro řiditelnost v případě komutujících matic a v případě obecných matic a je sestrojena řídící funkce. Všechny výsledky jsou ilustrovány na netriviálních příkladech.