oHMint: An Online Mathematics Course and Learning Platform for MINT Students Helena Barbas1, Franz Konieczny2, Alexander Lohse1, Thomas Schramm3* 1Universität Hamburg, Fachbereich Mathematik, Bundesstraße 55, 20146 Hamburg, Germany. 2integral-learning GmbH, Clausewitzstraße 2, 10629 Berlin, Germany. 3HafenCity Universität Hamburg, Überseeallee 16, 20457 Hamburg, Germany. *[email protected] an opportunity to test new didactical approaches for Abstract. The oHMint project is an initiative with the goal of mathematics online courses as well as innovative types providing an online course and learning platform for STEM stu- of exercises addressing the specific needs of the current dents of higher mathematics. Its flexible design allows it to be student generation. used for self-study as well as blended learning scenarios including In this article we recall some information from [1, 2], flipped classrooms. In a pilot project in 2017/18 the chapter where the general scope of the oHMint project was Differential Calculus is being produced as a prototype of an described (Sections 2, 3), and focus on using oHMint in oHMint unit. This pilot is organized and funded through the a flipped classroom learning scenario (Section 4). Hamburg Open Online University, with technical support and implementation by integral-learning GmbH. It is intended as a catalyst for the future development of the full oHMint course 1 Background of oHMint spanning four semesters. A unique characteristic of oHMint is its broad supporting base among a variety of German institutions in 1.1 OMB+ mathematics bridging course the form of the OMB+ consortium. The OMB+ consortium has developed and maintains the well-accepted “Online Mathematics Bridging Course Plus” OMB+ [3] under the auspices of the TU9, a group Introduction of nine important German technical universities. The course is based on the recommended cosh catalogue [4], Engineering mathematics is the main tool to describe which sets a standard of mathematical requirements for the world and to simulate its processes. A profound freshmen in STEM studies, and should also give an mathematical education is therefore essential for future orientation for school teachers in mathematics. engineers and scientists. Digitalization is becoming The OMB+ is text oriented, but includes a large amount increasingly important in teaching and studying at uni- of questions, interactive elements, videos and examples versity level. More and more online learning tools are with standard solutions, which can be uncovered sys- being developed to address the current need for educa- tematically. As of today, around 50 German institutions tional resources that go well beyond the classical text- use and recommend the OMB+, which is available in book by providing high temporal and spatial flexibility German and English and currently being translated into for users while at the same time offering an interactive Chinese. Supplementary chapters covering e.g. stochas- learning environment. In this spirit, the oHMint project tics, complex numbers and formal logic have been add- was initiated through the OMB+ consortium, a group of ed and further educational videos are in the making. The 14 German institutions of higher education. The acro- oHMint project uses the same enriched text oriented nym stands for online Higher Mathematics (for m)int. It style and shares similar features. For more information is the aim of oHMint to provide university students of on OMB+ see [3] and [5]. STEM degree programmes with a modern way of transi- tioning smoothly from a high school level of mathemat- 1.2 The Hamburg Open Online University ics to a bachelor degree level. The OMB+ consortium has already developed the online mathematics bridging The acronym HOOU stands for Hamburg Open Online course OMB+, which is widely used and recommended University (www.hoou.de), a joint initiative of six insti- as a preparation for those interested in a STEM univer- tutions of higher education in Hamburg: Universität sity degree programme. This experience is a valuable Hamburg (UHH), Hamburg University of Applied Sci- asset for oHMint. ences (HAW), Hamburg University of Technology Currently, in a pilot project with a lifespan of 14 months (TUHH), HafenCity University Hamburg (HCU), one base unit of oHMint is being created. This serves as Hochschule für bildende Künste (HFBK) and the Hochschule für Musik und Theater (HFMT). The Ham- plemented by videos where important concepts or ideas burger Senat (Senate of Hamburg) founded it in 2015 as are also shown. Each chapter starts with a motivation the educational branch of “Strategie Digitale Stadt” for the new mathematical concepts taught such that (Strategy Digital City), an initiative to bundle processes students develop a sense for the importance of the con- of digitalization within the city. tent they are supposed to learn. Moreover, many interac- The HOOU focuses on learners and collaboration for tive elements are being implemented in oHMint, some problem solving and develops study material at academ- are discussed in more detail below. ic level. Its target groups are not only the custom uni- versity students but also interested non-academic per- 2.2 Content of the first-semester course sons. Thus, all study material is open as Open Educa- The learning material from which a lecturer can choose tional Resource and is distributed under a CC license. for a first-semester oHMint course consists of the fol- The production of the first chapter of oHMint is funded lowing units: by the HOOU and running from November 2017 - Three base units: numbers and functions, differential through December 2018. calculus, integral calculus. - Four supplementary units: differential calculus, inte- gral calculus, sequences, series. 2 Modularisation and scope - Eight optional units: continuity, determination of ze- ros, L’Hospital’s rule, partial fraction decomposition, 2.1 Course structure approximate integration, sequences, series, Fourier The OMB+ consortium designed the preliminary struc- analysis. ture of the curriculum for the full oHMint course. It The scope of the content of each unit has been roughly spans four semesters and aims to cover all the mathe- assessed in terms of the European Credit Transfer and matics typically taught in STEM studies at German Accumulation System (ECTS) which is commonly used institutions of higher education. The curriculum was at European institutions of higher education. ECTS carefully structured, keeping in mind that different points measure the volume of learning based on work- (types of) universities have different needs for their load and desired learning outcome. In Germany, one respective degree programmes. The course will be ECTS point is equivalent to 25-30 hours of studying. available in English and German. With oHMint we aim The oHMint working group has made an assignment to create a course that consists of units which can be between the content of the chapters of the first-semester combined in various ways to cover these needs. The fact course and ECTS points. The base units are assigned 1 that a broad spectrum of institutions is represented in ECTS point each, the supplementary units and optional the OMB+ consortium justifies our hope that the final units are assigned 0.5 ECTS points. The workload for course will be widely accepted within the relevant the corresponding units is estimated to be within the community. This clearly distinguishes oHMint from given range. existing higher mathematics online courses in Germany. These values are used as an orientation for the lecturers There are three types of units in oHMint: base units who use the material for their courses. The actual as- cover standard content and are expected to be included signment of credit points to the course is made by the in every higher mathematics course, regardless of the lecturer or their institution. institution it is taught at. Supplementary units go deeper into the (theoretical) background of a base unit, and include more abstract views on base unit concepts as 3 Didactical concepts of oHMint well as more involved parts. Finally, optional units exist for subjects that are not necessarily always part of a 3.1 Didactical methods higher mathematics course, depending in particular on The oHMint materials are designed to be used for a the study programme and/or institution. The idea is that wide range of blended learning environments up to fully lecturers will be able to choose and combine the units web-based self-learning courses. We selected our didac- that are relevant for their classes to provide students tical methods to specifically suit these environments. with everything they need (but not more). Our guiding principles are a spiral curriculum (after J. Parallel to the development of the content of oHMint, a Bruner, see [6]), the development of intuitive under- data base is being created that keeps track of all the standing, awareness, and knowledge of mathematical interconnections between mathematical concepts and thinking (see e.g. [7], [8], [9]), and in general an appli- results in the units and which will help to ensure the cation oriented approach. We follow the ideas of cogni- desired modularity of the course. tive load theory [10] which focuses on the limited ca- The units themselves are text-based and consist of lec- pacity of working memory of students. New ideas and tures, exercises, trainings and final tests. They are sup- concepts are introduced incrementally, always keeping the cognitive load small and focused. The formally student helpers also from the HafenCity University who exact representation is the result of the teaching process provide valuable feedback from the target group of and not as often a starting point, making the construc- oHMint. tive process of mathematical knowledge visible to the students and fostering the awareness between intuitive 3.3 The advantage of the oHMint concept thinking and correct formulation of mathematics. Because of the modularisation (see 2.1) lecturers can Our database of mathematical interconnections (see 2.1) design their own course by selecting units depending on supports the development of the spiral curriculum as their programme-level.