Mid Sweden University

Research has identified several aspects that influence students’ transitionto mathematics studies at university, but these aspects haveoften been studied separately. Our study contributes to the field’sunderstanding of the transition between upper secondary and universitymathematics by taking a multifaceted perspective not previouslyexplored. We analyse experiences and attainment in mathematicsof 154 engineering students with respect to known aspectsof this transition, and our results show that it is important to considerseveral aspects together in order to understand the full complexity ofthe transition. It is revealed that students with previous experiencesof university studies, when compared with new first year undergraduates,perceive a larger difference between studying mathematics atthe upper secondary level and university. Our results also show thatthe engineering students enrolled in distance programmes experiencelarger differences between secondary and tertiary levels thanengineering students enrolled in campus programmes. Furthermore,our analyses show that students’ success in mathematics is relatedto their perceptions of the rift experienced in the transition. In all,our results highlight the importance of taking a student perspectivein the development of explanatory and useful models of students’transition between upper secondary and university mathematics.

We present the conceptual design, implementation, testing and initial validation results for the Horn of ODin (HOD), a new generation mobile learning object for undergraduate mathematics in the form of a viking age adventure. Our serious game is specifically designed to encourage extended student engagement with the mathematical topics to be mastered, thus permitting prolonged reflection upon the subtleties of the often abstract concepts involved and through this making it more possible that students reach the deeper levels of learning needed to meet the underlying Learning Outcomes (LOs).

HOD is a novel learning object developed within our scalable, modular and extensible software framework Quest for Wisdom (Q4W), built on smart amalgamation of cutting edge web technologies. Virtual community building technologies in particular play an important role in Q4W for synchronous and asynchronous learner collaboration, enabling students throughout immersive gameplay to interact individually with the maths on a cognitive level, but also in a social setting. Our framework follows open access principles and can potentially be knowledge-transferred to other subjects.

Traditionally, undergraduate mathematical topics are taught through self-study of books, supported by lectures, workshops on well-chosen illustrative problems and sometimes formative assessment. Students often criticise textbooks as boring or not helpful in their learning, class attendance is not always at ideal levels, and it is not uncommon for the majority of a cohort to fail one or more LOs on a course due to lack of student engagement.

Well-constructed serious computer games are widely accepted as good learning tools for student engagement and deeper learning. However, it is a challenge to construct such games so they methodically cover all aspects of complex LOs in tertiary mathematics without the resulting object resembling a common maths lesson. A multidisciplinary team of games specialists and educators have designed the learning activities of HOD so they make up an immersive game for sustained student engagement while still aligning with all aspects of the LOs regarding the topics covered.

HOD teaches mathematical relations, a common subject in first year undergraduate mathematics throughout the world. The game is based on an original story in which players get to be heroes and go on a quest for wisdom where they interact with colourful characters and creatures from Norse mythology. Players progress through the game levels by learning more and more about relations and work towards a final goal of assembling a magical horn. On their way they prepare potions, find runes in a maze, defeat giants in strength contests and more. Each game level is a story chapter and involves puzzles and problems designed to illustrate one particular bite-sized aspect of a LO. HOD gives continuous personal feedback on all hero actions, and formative assessment is integrated in the narrative with correct answers giving the player advantages for game progression.

For testing, a group of first year discrete mathematics students were invited to play HOD as an add-on curricular activity. Initial results are very encouraging, showing students persevering with HOD until the quest is complete, thus actively engaging with all aspects of the LOs covered. Analysis of exam results achieved also shows that student attainment in relevant exam questions compares favourably to that of earlier cohorts.

I detta kapitel beskrivs en nätbaserad matematikkurs med stödmaterial, såsom datorrättade quiz, diskussionsforum, inspelade föreläsningar och nätbaserade träffar samt nätbaserad examination. Det överordnade målet är att skapa en lärgemenskap. 

A triple array is a row-column design which carries two balanced incomplete block designs (BIBDs) as substructures. McSorley et al. (Des Codes Cryptogr 35: 21–45, 2005), Section 8, gave one example of a triple array that also carries a third BIBD, formed by its row-column intersections. This triple array was said to be balanced for intersection, and they made a search for more such triple arrays among all potential parameter sets up to some limit. No more examples were found, but some candidates with suitable parameters were suggested. We define the notion of an inner design with respect to a block for a symmetric BIBD and present criteria for when this inner design can be balanced. As triple arrays in the canonical case correspond to SBIBDs, this in turn yields new existence criteria for triple arrays balanced for intersection. In particular, we prove that the residual design of the related SBIBD with respect to the defining block must be quasi-symmetric, and give necessary and sufficient conditions on the intersection numbers. This, together with our parameter bounds enable us to exclude the suggested triple array candidates in McSorley et al. (Des Codes Cryptogr 35: 21–45, 2005) and many others in a wide search. Further we investigate the existence of SBIBDs whose inner designs are balanced with respect to every block. We show as a key result that such SBIBDs must possess the quasi-3 property, and we answer the existence question for all known classes of these designs.