Knowledge Spaces and Learning Spaces

How to design automated procedures which (i) accurately assess the knowledge of a student, and (ii) efficiently provide advices for further study? To produce well-founded answers, Knowledge Space Theory relies on a combinatorial viewpoint on the assessment of knowledge, and thus departs from common, numerical evaluation. Its assessment procedures fundamentally differ from other current ones (such as those of S.A.T. and A.C.T.). They are adaptative (taking into account the possible correctness of previous answers from the student) and they produce an outcome which is far more informative than a crude numerical mark. This chapter recapitulates the main concepts underlying Knowledge Space Theory and its special case, Learning Space Theory. We begin by describing the combinatorial core of the theory, in the form of two basic axioms and the main ensuing results (most of which we give without proofs). In practical applications, learning spaces are huge combinatorial structures which may be difficult to manage. We outline methods providing efficient and comprehensive summaries of such large structures. We then describe the probabilistic part of the theory, especially the Markovian type processes which are instrumental in uncovering the knowledge states of individuals. In the guise of the ALEKS system, which includes a teaching component, these methods have been used by millions of students in schools and colleges, and by home schooled students. We summarize some of the results of these applications

Antimatroids and Balanced Pairs

We generalize the 1/3-2/3 conjecture from partially ordered sets to antimatroids: we conjecture that any antimatroid has a pair of elements x,y such that x has probability between 1/3 and 2/3 of appearing earlier than y in a uniformly random basic word of the antimatroid. We prove the conjecture for antimatroids of convex dimension two (the antimatroid-theoretic analogue of partial orders of width two), for antimatroids of height two, for antimatroids with an independent element, and for the perfect elimination antimatroids and node search antimatroids of several classes of graphs. A computer search shows that the conjecture is true for all antimatroids with at most six elements.Comment: 16 pages, 5 figure

ANALYSIS OF ALEKS MATHEMATICS PLACEMENT TEST DATA

In Fall 2014, Michigan Technological University (MTU) began using an online mathematics placement test provided by ALEKS Corporation. This study answers three questions that accompanied this implementation: (1) Do the cut scores being used for Precalculus and Calculus I result in the expected pass rates for those courses?, (2) Does the path by which a student becomes eligible for Calculus I – via a single placement test attempt, via multiple placement test attempts, or by beginning in Precalculus at MTU – influence their likelihood of success in Calculus I?, and (3) Does a mathematical background weak in any particular curriculum area correlate with a lower chance of success in Calculus I? ALEKS placement test scores, Calculus I exam scores, and Precalculus and Calculus I final grade data from students who took the ALEKS placement test during the 2015 testing cycle were examined. A conditional probability analysis indicated that the current cut scores result in a probability of a C grade or better of at least 0.64 in each course examined. Tabulation of DFW rates showed that students right at the cut score threshold have higher DFW rates than the overall rate for the course. Odds ratios revealed that students who placed into Calculus I on their first testing attempt were the most likely to receive a final grade of C or better. ALEKS subscore data indicated that most incoming students exhibited knowledge gaps in trigonometry. Logistic regression showed that a 1% increase in trigonometry subscore increased the odds of earning a C or better in Calculus I by 3%

Multi-scenario modelling of learning

International audienceDesigning an educational scenario is a sensitive and challenging activity because it is the vector of learning. However, the designed scenario may not correspond to some learners’ characteristics (pace of work, cognitive styles, emotional factors, prerequisite knowledge, …). To personalize the learning task and adapt it gradually to each learner, several scenarios are needed. Adaptation and personalization are difficult because it is necessary on the one hand to know in advance the profiles and on the other hand to produce the multiple scenarios corresponding to these profiles. Our model allows to design many scenarios without knowing the learner profiles beforehand. Furthermore, it offers each learner opportunities to choose a scenario and to change it during their learning process. The model ensures that all announced objectives have enough resources for acquiring knowledge and activities for evaluation

Examining Students’ Perceptions About an Adaptive-Responsive Online Homework System and its Influence on Motivation and Learning

Advances in technological education have made online homework an integral part of science courses in general which is especially true for general chemistry courses. Online homework, if used correctly, has the potential to improve students’ experience, and learning and performance in general chemistry courses. The purpose of this research investigation is to study students’ levels of perceptions about an adaptive-responsive online homework in terms of (1) examining students’ motivation, learning, and understanding of concepts, (2) determining the aspects of adaptive-responsive online homework that are useful to students’ learning, and (3) understanding the features in online homework that causes improvement in students’ motivation. The investigation took place at an urban, commuter, minority serving, and public college. The study subjects were recruited from student enrolled in general chemistry courses consisting of 207 research participants (N = 207). Our data suggest that students display positive levels of perceptions about the adaptive-responsive online homework and its use. Students also hold perceptions that show positive attitudes towards the online homework system and that it positively affected their motivation. Also, students list several useful aspects of the online homework system such as explanations of concepts, knowledge checks, review questions for tests, and tutorials. The adaptive-responsive online homework, according to the participants in our study, helped motivate students by helping them learn the concepts, continuously assessing their learning, checking their knowledge, and updating the topics accordingly

Tutores inteligentes en la enseñanza: una revisión y análisis en la educación secundaria

Uno de los ámbitos más afectados por la crisis sanitaria ocasionada por la pandemia de COVID 19 fue la educación, debido a la interrupción de la enseñanza presencial durante los años 2020 y 2021, transformando las trayectorias de aprendizaje de más de 1.600 millones de estudiantes en todo el mundo. En las pruebas Aprender 2019, el 72% de los alumnos terminó la secundaria con deficiencias en Matemática y anticipan que la pandemia agravó los resultados. Es por esto, que la utilización de sistemas tutores inteligentes, puede resultar oportuno para acompañar el proceso de enseñanza y aprendizaje en el área de matemática, con el fin de ayudar a mejorar el nivel académico de los estudiantes. En este trabajo se realiza un análisis comparativo de sistemas tutores inteligentes orientados a la educación secundaria para matemática.XXI Workshop Tecnología Informática aplicada en Educación (WTIAE)Red de Universidades con Carreras en Informátic