Mathematical modelling problems are embedded in written, representational, and graphic text. For students to actively engage in the mathematical-modelling process, they require literacy. Of critical importance is the comprehension of the problems' text information, data, and goals. This design-research study investigated the application of top-level structuring; a literary, organisational, structuring strategy, to mathematical-modelling problems. The research documents how students' mathematical modelling was changed when two classes of Year 4 students were shown, through a series of lessons, how to apply top-level structure to two scientifically-based, mathematical-modelling problems. The methodology used a design-based research approach, which included five phases. During Phase One, consultations took place with the principal and participant teachers. As well, information on student numeracy and literacy skills was gathered from the Queensland Year 3 'Aspects of Numeracy' and 'Aspects of Literacy' tests. Phase Two was the initial implementation of top-level structure with one class of students. In Phase Three, the first mathematical-modelling problem was implemented with the two Year 4 classes. Data was collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. During Phase Four, the top-level structure strategy was implemented with the second Year 4 class. In Phase Five, the second mathematical-modelling problem was investigated by both classes, and data was again collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. The key finding was that top-level structure had a positive impact on students' mathematical modelling. Students were more focussed on mathematising, acquired key mathematical knowledge, and used high-level, mathematically-based peer questioning and responses after top-level structure instruction. This research is timely and pertinent to the needs of mathematics education today because of its recognition of the need for mathematical literacy. It reflects international concerns on the need for more research in problem solving. It is applicable to real-world problem solving because mathematical-modelling problems are focussed in real-world situations. Finally, it investigates the role literacy plays in the problem-solving process.

The study explores Mathematics educators’ use of students’ out-of-school experiences in the teaching of Transformation Geometry. This thesis focuses on an analysis of the extent to which students’ out-of-school experiences are reflected in the actual teaching, textbook tasks and national examination items set and other resources used. Teachers’ teaching practices are expected to support students’ learning of concepts in mathematics. Freudenthal (1991) argues that students develop their mathematical understanding by working from contexts that make sense to them, contexts that are grounded in realistic settings. ZIMSEC Examiners Reports (2010; 2011) reveal a low student performance in the topic of Transformation Geometry in Zimbabwe, yet, the topic has a close relationship with the environment in which students live (Purpura, Baroody & Lonigan, 2013). Thus, the main purpose of the study is to explore Mathematics teachers’ use of students’ out-of-school experiences in the teaching of Transformation Geometry at secondary school level. The investigation encompassed; (a) teacher perceptions about transformation geometry concepts that have a close link with students’ out-of-school experiences, (b) how teachers are teaching transformation geometry in Zimbabwe’s rural secondary schools, (c) the extent to which students’ out-of-school experiences are incorporated in Transformation Geometry tasks, and (d) the extent to which transformation geometry, as reflected in the official textbooks and suggested teaching models, is linked to students’ out-of-school experiences. Consistent with the interpretive qualitative research paradigm the transcendental phenomenology was used as the research design. Semi-structured interviews, Lesson observations, document analysis and a test were used as data gathering instruments. Data analysis, mainly for qualitative data, involved coding and categorising emerging themes from the different data sources. The key epistemological assumption was derived from the notion that knowing reality is through understanding the experiences of others found in a phenomenon of interest (Yuksel & Yildirim, 2015). In this study, the phenomenon of interest was the teaching of Transformation Geometry in rural secondary schools. In the same light, it meant observing teachers teaching the topic of Transformation Geometry, listening to their perceptions about the topic during interviews, and considering how they plan for their teaching as well as how students are assessed in transformation geometry. The research site included 3 selected rural secondary schools; one Mission boarding high school, a Council run secondary school and a Government rural day secondary school. Purposive sampling technique was used carefully to come up with 3 different types of schools in a typical rural Zimbabwe. Purposive sampling technique was also used to choose the teacher participants, whereas learners who sat for the test were randomly selected from the ordinary level classes. The main criterion for including teacher participants was if they were currently teaching an Ordinary Level Mathematics class and had gained more experience in teaching Transformation Geometry. In total, six teachers and forty-five students were selected to participate in the study. Results from the study reveal that some teachers have limited knowledge on transformation geometry concepts embedded in students’ out-of-school experience. Using Freudenthal’s (1968) RME Model to judge their effectiveness in teaching, the implication is teaching and learning would fail to utilise contexts familiar with the students and hence can hardly promote mastery of transformation geometry concepts. Data results also reveal some disconnect between teaching practices as espoused in curriculum documents and actual teaching practice. Although policy stipulates that concepts must be developed starting from concrete situations and moving to the abstract concepts, teachers seem to prefer starting with the formal Mathematics, giving students definitions and procedures for carrying out the different geometric transformations. On the other hand, tasks in Transformation Geometry both at school level and the national examinations focus on testing learner’s ability to define and use procedures for performing specific transformations at the expense of testing for real understanding of concepts. In view of these findings the study recommends the revision of the school Mathematics curriculum emphasising pre-service programmes for teacher professional knowledge to be built on features of contemporary learning theory, such as RME theory. Such as a revision can include the need to plan instruction so that students build models and representations rather than apply already developed ones. / Curriculum and Instructional Studies / D. Ed. (Curriculum Studies)