Taking into account the issues that arise from the secondary-tertiary tran- sition, many universities around the world designed various programmes to
support and help first year undergraduates. These programmes aim to ad- dress students’ skills deficiencies and re-introduce mathematical topics taught at school, introduce the mathematical language used at this level, introduce the notion of proof and familiarise students with its construction, build con- fidence and trust among students, encourage good study habits that will be required at university, etc.
Leviatan (2008) describes a two-stage transition programme implemented in Beit Berl Academic College in Israel, for prospective mathematics teach- ers. The first stage of the programme is a Pre-Calculus course consisting of three components (“Introduction to advanced mathematics”, “Reading, writing and reasoning in mathematics” and “Number systems”). The second stage is a Post-Calculus course of two parts (“Definition and proofs in math- ematics” and “Topics in advanced mathematics”). With the application of innovative teaching and assessment methods (questionnaire based instruc- tion, project based learning, self study, group study, etc) the programme seeks to introduce the students to the basic concepts and tools of mathe- matics, enhance their reasoning skills, enable them to construct proofs, work individually and in groups, and experiment further with mathematical topics. Students’ feedback at the end of the year showed that the course boosted the students’ self-confidence, helped them significantly with the other courses of their mathematics curriculum, and they benefited from the use of non-routine mathematical tasks. Similarly, Hoffkamp et al. (2013) designed a bridging course for first semester students majoring in mathematics and for future mathematics teachers in the German educational context. The course was focused on the teaching and learning of mathematical reasoning, argumen- tation and proof. It consisted of three phases: Information, Cognition and Metacognition. In the first phase the students are presented with the basic
concepts of logic and the method of proof by contradiction. In the second part of this phase, which is more interactive, the students are called upon to analyse and compare two examples of proof by contradiction. And in the last part there is a discussion and reflection on the previous, which eventu- ally unveils the legitimacy of deductive reasoning. At the end of the course some of the students reported that they grasped new ways of approaching mathematics.
The aforementioned courses are just examples of the many bridging courses functioning in universities all over the world. Another initiative employed by universities which aims to help students during the first year of their studies is peer support. Cheng and Walters (2009) implemented a study of 534 first semester freshmen in order to estimate the effectiveness of a “peer assisted learning” (PAL) session, at the University of Minessota. The PAL session was complementary to one mathematics course upon which the students were enrolled (College Algebra and Probability or Precalculus I). In these sessions second year students who had completed the course successfully the previ- ous year (“the facilitators” as the authors call them) were trained before the beginning of the semester, but also during, in peer cooperative learn- ing strategies. In the 50-minute sessions, which took place once per week for a period of 13 weeks, the facilitators encouraged the students to get in- volved in the engaging activities that they have planned. The agenda was decided by the facilitators, and included worksheets, activities and material which promoted the cooperative learning among peers, but it was also open to changes giving the students the opportunity to develop it collaboratively, based mostly on the things that could trouble them. In this way the respon- sibility was shared among facilitators and freshmen. The authors found that the attendance at PAL sessions was linked to success in the completion of
the course; students who attended all the sessions had ten times higher odds of succeeding compared to those who did not attend them.
McMaster University in Canada, administered a Mathematics Review Manual for students’ voluntary preparation before entering university (Kajander & Lovric, 2005) as a part of its three stage transition programme. This is a 70-page brochure which aims to assist students during the summer months as they prepare for their mathematics courses. Students can find the Manual online and a paper copy is sent via post to all incoming students in science, engineering, and arts programmes. It consists of two parts. The first part contains information about university and the mathematics courses. The second part includes a revision of basic mathematics concepts required for the university mathematics courses (basic algebra, geometry, functions and transcendental functions). Kajander and Lovric’s (2005) study suggests that the Mathematics Review Manual did not serve eventually the purpose for which it was designed. Students considered it a “great” idea but admitted that they had not read it. Nevertheless, they usually used it for review purposes while being at university.
Bardelle and Di Martino (2012) piloted an e-learning platform available to 169 science freshmen, in the university of Piemonte Orientale in Italy. This web based platform consisted of interactive activities and resources (quizzes, lessons, tasks) which provided the opportunity to the students to work inde- pendently at different levels. In this course the students could submit any activity they worked on and receive individual feedback from their instruc- tors, but they could also work on the activities without submitting them. The course had a non compulsory character and it was made clear to the students that it was used for practice purposes. Additionally, a forum was developed where students were able to exchange ideas and pose questions.
At the end of the year the researchers found a positive correlation between the marks of the students who used the platform and the time they spent on using it. Nevertheless, a low level of participation was observed. Only 40% of the students accessed the platform. As the authors argue, more work should be put in from people that design such initiatives in order to get students engaged.
Simon Fraser University in Canada has developed numerous strategies to address the issues that arise with the transition to university mathematics (Pyke, 2012). These include initiatives that begin when students are still at high school and continue during the first year at university. For instance, the university hosts regular weekend lectures on various mathematical topics which high school students and their teachers can attend. Every summer the department of Mathematics organises a mathematics camp activity for stu- dents with a range of mathematical activities to engage with. Additionally, to give an idea of what university will look like, first year university stu- dents visit high schools as “Math Ambassadors” and share their experiences and impressions of university with the high school students. When students arrive at university they are also supported in different ways. The depart- ment offers entry-level mathematics courses, there is a wide use of technology in lectures which seeks to enhance students’ learning, dedicated spaces are provided where students can meet with tutors and/or instructors and can dis- cuss possible misunderstandings or questions on the material covered during lectures, etc.
2.1.3.2 Theoretical suggestions for alleviating the difficulties