A schematic model of the blended learning approach is shown in Figure 1. Instructional design of the DVDs Each DVD covered a particular topic in the syllabus; the topic was then divided into micro lessons (parts). Each part of a DVD topic started with an introduction and definitions of the concepts, and this was followed by fully explained examples pertaining to that particular concept. The intention was to give learners an understanding of the thought processes involved in solving a problem and to help learners who would have no idea where to begin (Aminifar, Porter, Caladine & Nelson, 2007). The part ended with tutorial problems to be attempted by the learners, intended to give them a way to assess their understanding of the micro lesson. A set of comprehensive solutions followed, that could be viewed after learners had attempted the tutorial problems. This approach ensured that immediate feedback was available to any learner who struggled with the tutorial problems. The entire DVD had voice narration integrated with animated PowerPoint slides. Table 2 shows the content topics covered in the 2007 mathematics DVD series. 2The 20 mathematics DVD topics. http://pythagoras.org.za/index.php/pythagoras/article/downloadSuppFile/24/23

Production of the DVDs PowerPoint slides with animation were developed for each mathematical concept and formed the basis of the recording of the DVDs. Recordings were done in a studio by a member of the ISP team, normally a lecturer in the Mathematics and Applied Mathematics Department at the university in question. Recordings entailed using a tablet PC and presenting the PowerPoint slides with voice explanations. Other software packages like Autograph were used to illustrate sections requiring graphic drawing. Whilst recordings were being done, a second academic staff member evaluated them to ensure that the DVDs were free of mathematical errors. Re-recording of an erroneous slide took place immediately if necessary. Thereafter a technical media specialist edited the DVDs to produce master DVDs with a menu-driven system. The Saturday programme Learners attended a series of five-hour sessions held on Saturdays, during which two DVDs of one hour each were facilitated. After each session, learners engaged with tutorial problems. This was an interactive session, with discussions and assistance from facilitators as well as student tutors. The DVDs were presented to learners using a DVD player connected to a data projector. Research design Research method The research reported on in this article is part of a larger research study investigating the teaching and learning of mathematics using DVD technology within the context of blended learning. The focus of this research study was the 2007 ISP which forms part of a larger project. The 2002–2006 ISP were earlier cycles of this larger action research project. The evaluation of each cycle in this action research informed the next cycle in the project (e.g. Boshoff & Olivier, 2008). In 2007 the use of DVD technology was introduced in the ISP, and this article focuses on use of DVD technology within a blended learning environment in the 2007 ISP. Participants A total of 184 Grade 12 mathematics learners from local schools in the Nelson Mandela Metropole were selected to participate in the 2007 ISP. The best-performing learners were selected on the basis of their Grade 11 mathematics marks and their interest in pursuing studies in Science, Engineering, Technology and Mathematics and Science Education. These learners were split into four groups, with on average 46 learners to one facilitator in each group. These learners and their facilitators were the participants in this research study. Action research Action research is the methodology used in the larger research study, and this study focuses on one aspect of the action research cycle. Action research provides an important link between research and teaching, particularly when the research is actively conducted with the aim of informing teaching and learning and challenging ways of incorporating technology into the curriculum (Manchester, Ralph & Shipova, 2005). Action research was an appropriate design in the larger research study in order to reflect on the processes that were followed and to refine the ISP before the next cycle of implementation. The following steps in the action research cycle were followed in the larger study: plan and design the intervention; implement the intervention; evaluate the intervention; reflect on the evaluation; and implement the changes – and so begins another cycle. This article focuses on the third phase in the action research cycle, namely the evaluation of the ISP intervention, and in so doing concentrates on factors that contributed to a supportive and encouraging learning environment. In particular, the focus was on the experiences of learners and the impact of the blended learning approach on their mathematical ability. During the evaluation phase of the action research cycle a mixed-methods approach to collecting data was adopted, with both qualitative and quantitative methods employed. At the end of the 2007 programme 184 learners completed a questionnaire aimed at evaluating the teaching and learning approach they had experienced. The questionnaire contained open-ended questions and provided rich descriptive data with regard to the factors that provided a supportive and encouraging learning environment. Further to this, qualitative data were also collected in the form of facilitator observation of the learning process using weekly reports. Using quantitative methods, the learners’ final Grade 11 mathematics results were compared with their final Grade 12 mathematics results to determine whether an improvement in mathematical performance had occurred as a result of this blended learning intervention. The case study of a single school of 20 learners, 6 of whom were ISP participants and 14 non-ISP participants, is also described here. There was difficulty in obtaining the results of other learners at schools that participated in the 2007 ISP. Validity and reliability Use of various methods of data collection and triangulation were vital in determination of an in-depth understanding of the programme under investigation. Strategies for promoting validity and reliability (adapted from Merriam, 2002, p. 31) used in this research study are outlined in the following section. Triangulation: The researchers used multiple sources of data and data collection methods to confirm emerging findings. Triangulation was as follows: Data triangulation: Questionnaires completed by learners and reports completed by facilitators. Methodological triangulation: Use of qualitative and quantitative methods. Member checks: The researchers took the tentative interpretations of the data back to the learners and facilitators to see if they agreed with them. Peer review: The process of the research study, congruency of emerging findings with the raw data and tentative interpretations were discussed with colleagues. Researchers’ position: The researchers undertook critical self-reflection with regard to their worldview, assumptions and relationship to this study that could have influenced bias and affected this study. Adequate engagement in data collection: It was ensured that adequate data were collected such that the data became saturated. Rich, thick descriptions: The researchers tried to supply sufficient descriptions to enable readers to determine whether this situation matches their research context or whether the findings can be transferred. Ethical considerations Denscombe (2007, p. 142) outlines three core principles that should inform the ethical choices and guide the activities of the researcher. The principles as applied in this research study were as follows: Principle 1: The interest of the participants should be protected. This research ensured the confidentiality of the participants. Data were kept safe and no personal identities were revealed in disclosure of the results. Principle 2: Researchers should avoid deception or misrepresentation. The researchers were honest and made all the processes transparent. The researchers and participants developed a relationship of trust, and the researchers presented the data in a fair and unbiased way. Principle 3: The participants should give informed consent. Ethical clearance was given by the Research Committee of the university where the ISP is based. The Department of Education gave its consent for the researchers to access participants from schools in the Eastern Cape. Written consent was obtained from all the participants and in the case of minors consent was received from their parents. All participation was voluntary. Results and discussion Analysis of the questionnaires, facilitator reports, comparisons of learners’ Grade 11 and Grade 12 mathematics marks and the case study are presented and discussed. In analysis of the data collected from learners’ questionnaires and facilitators’ weekly reports, the themes outlined below arose. Themes which arose from the data New experience More than half of the learners felt that the approach was refreshing and a different way of learning mathematics. Many learners said they found this way of learning enjoyable and exciting. A few learners said that the DVD was different from a textbook, since there was a ‘voice’ explaining the concepts. DVD as a resource Learners felt that explanations of the mathematical concepts were good and the concepts were presented well. The DVD was particularly useful to them in sections that required visual representation (drawing graphs) and in Calculus, since it was ‘not done well’ at school. Many learners said they found the DVDs helpful and that they found the mathematics easy to understand because of the many examples and illustrations on the DVDs. A few learners said that they found it easier to concentrate using this method as opposed to having someone standing in front explaining what to do. On the other hand, a few other learners found it difficult to concentrate using the DVD approach, and one said it was easy to ‘move your concentration elsewhere’ unless you had a lecturer to intervene with discussion or explanations. Many learners said the DVD approach gave more insight than school, and that they found it helpful to do a section on DVD in the Saturday project before it was done at school, and that this helped their understanding of the section. Learners also used the DVD to ‘test and check’ their understanding of a particular concept. They found that the DVD series was a good resource to consult when faced with homework or in preparation for a test or examinations. Many learners said that the DVDs allowed them to learn at their own pace and to watch a section over again until they understood the concepts. Many found that they could watch the DVDs at home and revise together with the resource material; this approach helped to enhance their understanding. However, some learners suggested that some of the DVDs did not illustrate every step of a mathematical problem, which led to confusion. They asked for more detail and more examples on the DVDs. The blended learning environment Although most of the learners agreed that the DVD was a useful resource, many said they needed facilitators and tutors for further explanations and discussions. They needed the facilitators’ explanations to bridge gaps where the DVD skipped steps or where they had problems understanding. According to the learners, tutors, facilitators and discussions with other learners helped them see concepts from different viewpoints. Learners felt that their English improved as a result of the blended learning approach, although one learner suggested that DVDs be produced in other languages. Learners said that they liked the way the ISP presentations blended the tutorials, DVDs and discussions, and that this made it easier for them to concentrate for longer periods. The issue that stands out and which was pointed out by almost all learners was the ease with which learners could view the DVD and replay and pause whenever they wanted to. However, some learners mentioned that whilst watching the DVD there were questions that needed explanation, and that the DVD should not be used alone. A few learners also said that their teacher used these DVDs at their schools to teach certain topics, like Calculus, for example. Some learners formed study groups and watched the DVDs in these groups over weekends. The blended learning approach using DVDs presented a new way of learning mathematics to or for the learners, and most of them were positive that the method benefited their understanding of the subject. The approach allowed them the freedom to access a variety of different resources, and allowed them to work at their own pace and to revise at home. Facilitators’ observations The facilitators’ observations of learners’ experiences of the blended learning environment were positive and encouraging. All four facilitators felt that the learners’ confidence improved as a result of this approach. In addition, one facilitator noted that as the project progressed, communication and engagement with the facilitators and learners, tutors and learners, and amongst the learners improved. A facilitator said that the level of mathematics questions posed by the learners improved with time, and the learners’ test performances improved steadily as the project progressed. All the facilitators agreed that the interaction in the blended learning approach was lively, although learners found it (i.e. DVD technology) strange at first. One facilitator said that the ‘DVD is a powerful resource allowing learners to work at their own pace and review solutions and procedures until they understood the concept’. All four facilitators said that they believed that DVDs should be used in conjunction with other face-to-face methods of teaching and learning. They believed that used in isolation, the DVDs would not prove such a successful resource in the teaching and learning of mathematics. Evidence is provided which suggests that DVD technology impacted on the mathematics learning and enhanced the mathematics performance of the ISP learners. In addition, the learners responded favourably to use of the DVD technology within the blended learning environment. However, some learners said that at first they needed to adjust to this new learning environment. They also indicated that once they had adjusted, they could see the advantages of being exposed to different modes of delivery. The majority of the learners agreed that this blended environment of teaching and learning mathematics fostered a deeper understanding of the subject for them. The most important point raised by learners was the fact that DVDs alone were not sufficient to ensure success. They believed that the DVDs together with facilitators’ and tutors’ explanations and discussion coupled with the hard copy resources were the best blended approach for their learning of mathematics. Improvement in marks Statistical analysis was undertaken to investigate whether differences between the final Grade 11 mathematics marks and final Grade 12 mathematics marks of the ISP learners were significant. The descriptive statistics comparing the final Grade 11 marks with the final Grade 12 marks are shown in Table 3. 3Descriptive statistics for Grade 11 and Grade 12 mathematics marks (N = 184). http://pythagoras.org.za/index.php/pythagoras/article/downloadSuppFile/24/24

The observed difference of 2.96 between the mean scores shows a statistical significance; however, no practical significance is noted. Figure 2 illustrates that the distribution for Grade 11 marks peaks with the majority of scores between 40 and 59, whereas the distribution for Grade 12 is evenly spread, having moved from the middle to the other categories. The Kolmogrov–Smirnov Test (K–S D = 0.245, p < 0.01) confirms a significant difference in distribution. It is pleasing to note that in higher intervals from 60 upwards there is clearly an improvement of marks from Grade 11 to Grade 12. In the category of 70+ there is an increase from Grade 11 to Grade 12, from 4% to 22%. Unfortunately, there also are more students who performed badly in Grade 12 compared to Grade 11: there is an increase in the under-40 intervals; in fact, there is an increase in the interval 0−39, from 14% in Grade 11 to 26% in Grade 12. Figure 3 confirms that the distribution for Grade 11 is flatter, with more results between 40 and 69, whereas the distribution for Grade 12 is more evenly spread. Table 4 and Figure 3 reflect the difference in distribution between Grade 11 and Grade 12. The relationship between the categories of marks for Grade 11 and Grade 12 is depicted in Table 4. 4Contingency table of Grade 11 and Grade 12 mathematics marks. http://pythagoras.org.za/index.php/pythagoras/article/downloadSuppFile/24/25

It is interesting to note that no learners from the 0−39 category in Grade 11 moved to the 70+ category in Grade 12, and none of the learners in the category 70 in Grade 11 moved to the 0−39 category in Grade 12. It is also noteworthy that 25% of the learners in the 40−49 category in Grade 11 moved to the 70+ category in Grade 12. The quantitative data indicated statistical significance, and it seems that there was an improvement from the Grade 11 to the Grade 12 mathematics marks in many cases. However, it became clear from the quantitative data that not all learners responded positively to the blended learning approach. Case study A school in the Uitenhage district was used as a case study. There were 20 learners in this Grade 12 mathematics class. Six of these learners participated in the 2007 ISP. For all 20 learners, their 2007 final Grade 12 mathematics marks were compared with their 2006 Grade 11 end-of-year mathematics marks. Results of the learners who were on the ISP improved, whilst those learners not on the ISP generally presented lower Grade 12 final results. To determine whether the difference was statistically significant, a Mann-Whitney U Test (z = 3.38, p = 0.001, d = 3.20) was conducted. A Cohen’s D test was conducted for practical significance. It was found that the difference in means was highly significant, since d > 0.8 reflects a large difference. The results are summarised in Table 5 and Table 6.5Case study Grade 11 and Grade 12 end-of-year marks for mathematics. http://pythagoras.org.za/index.php/pythagoras/article/downloadSuppFile/24/26

6 Case study – Difference in means of Grade 11 and Grade 12 end-of-year marks for mathematics. http://pythagoras.org.za/index.php/pythagoras/article/downloadSuppFile/24/27

ConclusionThe research question addressed in this article was ‘how can a blended learning approach that incorporates DVD technology contribute to improving the quality of teaching and learning in secondary school mathematics?’ From the study it is clear that this blended approach offers a workable teaching approach with definite advantages. One of the advantages of using DVD technology within a blended approach is accessibility of the subject content and presentation outside the classroom. Qualitative results indicated that both learners’ and teachers’ experiences were largely positive, with concerns identified that offer opportunity for improvement. Most learners attributed their better understanding of mathematical concepts taught to the DVD approach that was used in conjunction with other traditional modes of delivery. Quantitative results indicated statistical significance when comparing the mean scores for Grade 11 and Grade 12 results, although not of practical value. According to Calldo and Du Plooy (2008), the percentage of students passing mathematics on higher grade declined from 7.2% in 2006 to 6.9% in 2007. In the face of declining performance in mathematics in South Africa in the 2007 matriculation examination, our results seem to suggest that the DVD approach of blended learning could in some way have contributed to the improvement in mathematics results that was noted amongst many of the ISP learners, especially the better students. It is disappointing that a large group of the borderline students did not seem to benefit from this blended learning approach. This finding is reason for concern, since these are the students that should be targeted – and the reason for this disappointing deterioration has to be investigated. The fact that the DVD technology is easily accessible and affordable supports a case that the DVD approach could also help to address the shortage of adequately qualified teachers and lack of teaching resources at previously disadvantaged schools in South Africa. Harding, Kaczynski and Wood (2005) say that in order to be successful in using blended learning, one has to not only implement learning reforms but also, importantly, evaluate these reforms, and in so doing provide students with the best possible outcomes. The ISP saw the implementation of DVD technology for the first time in 2007, and this research aimed to evaluate its value to the teaching and learning of mathematics. In order to provide learners with the best possible outcomes, ‘it is important that we continue to identify successful approaches of blended learning at institutional, programme, course and activity levels that can be adapted to work in contexts’ (Graham, 2004, p. 19). Our DVD blended learning approach still requires further development and refinement, especially with regard to the skills of facilitators within such a blended learning environment and the development of materials. These and other issues will be looked at in future research initiatives. Acknowledgements We are grateful to SASOL for the funding that supported the 2007 ISP and this research. Competing interests We declare that we have no financial or personal relationships which may have inappropriately influenced us in writing this article. Authors’ contributions H.B. was the project leader whilst H.B. and W.O. were responsible for the project design. H.B. collected the data. A.H. made conceptual contributions. P.P. performed the qualitative and statistical analysis, made conceptual contributions and wrote the manuscript. 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