Mathematics is as much an aspect of culture as it is a collection of algorithms.
~ Carl Boyer
Many of the students that attended the Ukuqonda Post Matric year in Rustenburg, come from backgrounds where progress and success in individuals’ life is not commonly observed and therefore they lack the presence of mentors and role models whom they personally know and with whom they can engage.
As an Institute we partake in the further journey of the students that have started their tertiary studies after completing their post matric year in Rustenburg. Our initial engagement with these students, that started in Rustenburg, and for some even earlier in the Ukuqonda school projects, puts us in a place where we will try to stay in touch with each student..
Undergraduate students communicate clearly a definite need for effective and good mentoring in order to guide them to learn more successfully. We believe effective mentoring depends on an engagement with the undergraduate student that is based on a clear understanding of the responsibility that lies with the student to take responsibility for their own studies. It is essential that the student is allowed and guided to take ownership of their learning which will enable them to take the initiative in terms of making sense of learning, maintaining a self directed approach to their studies and be aware of establishing reasonable timelines within which they are aiming to achieve their individual goals identified. Doing so will enable them to measure their progress and be aware of their successes and failure so that they can proactively make the necessary adjustments when needed.
Our first aim is to establish Ukuqonda post matric communities on the different campuses so that they can start to develop relationships that can help to facilitate the peer mentoring amongst each other.
We are also continually keeping contact with the students by communicating with individuals and the group via e-mail, phone calls and campus visits. This engagement with students seems to be very necessary and they respond very positively to the contact made.
Ukuqonda has on two previous occasions presented holiday support courses to some of the former Impala Post-Matric (bridging year) students when they were studying at university. We were hoping to continue with – and formalise – such tertiary academic support for former post-matric students in 2010, but have not (yet) obtained funding for that purpose.
We did conduct a tertiary academic support program during the mid-year holidays in 2010, but for a different funder and not for bridging-year students. This project took shape very quickly, after an introductory meeting in February 2010 between staff of Ukuqonda and the Sasol Inzalo Foundation. This foundation was created by Sasol in 2009 to contribute to science, technology, engineering and mathematics education in South Africa, and is planning to invest in education on larger scale than any of our current funders. During the meeting it emerged that Ukuqonda and Inzalo have common interests and beliefs, and soon afterwards Inzalo proposed that Ukuqonda present an academic support course to first year students in engineering and science.
Inzalo has for the first time in 2010 awarded about 90 scholarships to first year students in engineering and science. The students were chosen according to school marks and financial need, and the group of students were chosen to be demographically representative of the South African population, both in terms of ethnicity and gender.
It was agreed between Ukuqonda and Inzalo that the aim of the support course would be to present a curriculum that is parallel to the curriculum followed at university, and not to directly help students with their studies. This aim corresponds to a focus on problematic concepts that are essential prerequisites (thresholds) for the further learning. These are concepts that students typically would struggle to understand when lectured on, especially for students with limited language skills. We believe an understanding of such concepts can be developed through a (slow) process of investigation and reasoning.
Our aim in the classroom is to manage the process of investigation and reasoning in such a way that students come to understand the need for critical independent thinking, and that they develop their capacity to make sense of problems and make sense of the procedures that can help to solve problems. We would further prefer to use problem contexts that give students experiences in multi-step problem solving.
During the March/April holidays, Ukuqonda conducted two week long pilot courses with small numbers (10 and 5) of the Inzalo students. These courses targeted threshold concepts in algebra and calculus.
We selected materials from the post-matric programme and the grade 10-12 holiday schools, but modified the materials to make it more challenging and to speed up the learning trajectory. We found the calculus learning trajectory to work well, but that the algebra activities seemed to be fragmented and not sufficiently challenging for the students. We also found that there were a small number of students who were much stronger than the students whom we have experience with in the post-matric programme.
During June/July, we presented a support course to all of the Inzalo first-year students. This time the course was 11 days long, so as to give sufficient time to deal with concepts in geometry and physics in addition to those in algebra and calculus. The geometry part was especially important because geometry has effectively been removed from the school curriculum.
We completely redesigned the algebra part of the course so that it now consisted of two challenging contexts with which students engage one full day each. The calculus activities remained mostly unchanged.
The geometry part of the course consisted of three parts: practical activities to develop spatial reasoning, geometry activities involving proof, and application of trigonometry and matrix notation to transformations. These activities were designed and presented by three university lecturers with whom we have worked before.
The physics part of the course focused on the development of models to explain physical phenomena, and on the use on experimentation in this model development. This was an extension of learning material that has been used with post-matric students.
Our most striking observation during the course was the diversity of students in terms of skills, conceptual understandings and dispositions. The distribution was so wide within certain classes that a single ‘learning trajectory’ could not be followed by the whole class. The top 13% of Inzalo students are much stronger than the strongest post-matric students, and the bottom 8% are weaker than the weakest post-matric students. We had to engage the strongest students with more challenging problems at times, and the bottom 8% of students with remedial teaching on basic skills and understanding (of fractions).