Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

Towards Intelligent Tutoring with Erroneous Examples: A Taxonomy of Decimal Misconceptions

Abstract. In the mathematics domain of decimals, students have common and persistent misconceptions. These misconceptions have been identified, studied, and published by many researchers, spanning over 80 years of time. However, no paper discusses and brings together all of the identified misconceptions. This paper presents an initial taxonomy of decimal misconceptions, summarizing the results of past work. We also discuss the potential use and benefits of such a taxonomy in supporting the development of intelligent tutors that use erroneous examples as a learning tool for middle-school math students

Synthesis and analysis of the anticancer activity of Ru(II) complexes incorporating 2-hydroxymethylidene-indene-1,3-dione ligands

2-Hydroxymethylidene-indene-1,3-diones bearing alkoxyvinyl, pyrrolyl, and indolyl groups were synthesized by thermal decomposition of the phenyliodonium ylide of lawsone and served as ligands for the preparation of piano-stool Ru(ii) complexes. The reactivity of the new compounds with biomolecules and their stability in aqueous solution have been studied. The synthesized complexes have been tested for their anticancer activity against four human ovarian cancer cell lines (OVCAR-5, SKOV-3, UWB1.289, and UWB1.289 + BRCA1) in order to investigate their structure-activity relationships. The ruthenium complexes bearing the dihydrofuryl, the 2-(butoxy)vinyl, and the 2-(isobutoxy)vinyl substituents were the most potent compounds identified in this screen with IC50 values in the range of 22-82 μM. Complexes 11d, 11a, and 11b were found to be more active than cisplatin against the SKOV3 human ovarian cancer cells. © 2017 The Royal Society of Chemistry and the Centre National de la Recherche Scientifique

Scaffolding Collaborative Learning Opportunities: Integrating Microworld Use and Argumentation

This paper presents our research efforts to support students' collaborative process when learning mathematics and science as they interact with microworlds and engage in discussions and structured arguments. The system provides students with an environment to explore challenging problems and encourages them to collaborate using a discussion tool to argue and share their rationales and insights using specific examples from microworlds. The challenge of providing useful analysis in such a situation is to recognize, across the learning environment as a whole (both microworld and discussion tool), situations where students need support, and then to make the learners aware of these situations in a productive manner. We present a use case that demonstrates how students work within the system and how we envision the system will provide support. We conclude that the analysis and support that we propose has the potential to enhance the benefits of a combined system and offer more support than a system focused on the individual tools separately. © 2012 Springer-Verlag

To err is human, to explain and correct is divine: A study of interactive erroneous examples with middle school math students

Abstract. Erroneous examples are an instructional technique that hold promise to help children learn. In the study reported in this paper, sixth and seventh grade math students were presented with erroneous examples of decimal problems and were asked to explain and correct those examples. The problems were presented as interactive exercises on the Internet, with feedback provided on correctness of the student explanations and corrections. A second (control) group of students were given problems to solve, also with feedback on correctness. With over 100 students per condition, an erroneous example effect was found: students who worked with the interactive erroneous examples did significantly better than the problem solving students on a delayed posttest. While this finding is highly encouraging, our ultimate research question is this: how can erroneous examples be adaptively presented to students, targeted at their most deeply held misconceptions, to best leverage their effectiveness? This paper discusses how the results of the present study will lead us to an adaptive version of the erroneous examples material

Resource-bounded modelling and analysis of human-level interactive proofs

Mathematics is the lingua franca of modern science, not least because of its conciseness and abstractive power. The ability to prove mathematical theorems is a key prerequisite in many fields of modern science, and the training of how to do proofs therefore plays a major part in the education of students in these subjects