An analysis of the nature of visualisation objects in three Namibian grade 9 mathematics textbooks: a case study in Namibia - Nghifimule, Selma Ndilipomwene (Rhodes University, Faculty of Education, Department of Education, 2017)
Textbooks are a universal and central element of teaching and learning mathematics (Namibia. Ministry of Education [MoE], 2008). Steenpaß and Steinbring (2014) state that diagrams in mathematics textbooks are often used as Visualisation Objects (VOs) to enhance learning of mathematical concepts. VOs in textbooks are thus important teaching and learning tools (Fotakopoulou and Spiliotopoulou, 2008). This Namibian interpretive case study analysed the nature of VOs used in the three approved grade 9 Namibian mathematics textbooks namely: y=mx+c to success, Maths for Life 9 and Discover Mathematics 9. The VOs were analysed by using an analytical framework adapted from Fotakopoulou and Spiliotopoulou (2008). This analytic tool was specifically used to interrogate the following categories: the type of VOs, the roles of VOs, the relation of VOs to mathematical content, the relation of VOs to reality, and their properties. The 266 VOs under study were collected from the Algebra and Geometry chapters of each book. This study also included survey questionnaires with the 50 selected mathematics teachers, which sought their views and perceptions on the use of the identified VOs. In addition, the authors' rationale in selecting the identified VOs used in their textbooks was sought through interviews. This research study is part of the "Visualisation in Namibia and Zambia" (VISNAMZA) project which seeks to research the effective use of visualisation processes in the mathematics classroom in Namibia and Zambia (Schäfer, 2015). It is hoped that this study contributes towards improving the quality of textbook evaluations, and design of suitable and more comprehensive assessment procedures in Namibia. It is also hoped that it creates a critical awareness of the roles of VOs in textbooks amongst teachers, inspiring them to help their learners interpret VOs effectively. It should also inspire potential authors to use suitable and appropriate VOs that enhance conceptual teaching and learning of mathematics. The study discovered that most of the VOs used in the selected textbooks align well with the mathematical content. The VOs can help make abstract ideas concrete, stimulate learning, simplify and clarify written texts. In addition, VOs can also be used as a tool for reasoning and an instrument for problem solving. The findings however also indicate that some of the VOs used are not self-explanatory; they are vague, unfamiliar and confusing, leading to misinterpretations by some learners. Another interesting finding was that some of the learners found it difficult to interpret VOs on their own without the help of the teacher.
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