Chapter 2: Literature Review
2.6 Mathematics Enrichment Program (MEP)
2.6.4 Paradigmatic Positions of Mathematics Enrichment
two types of enrichment; either by broadening or deepening. Enrichment by broadening represents learning additional topics rather than what is normally studied at school as courses out of school, while enrichment by deepening enhances the depth and complexity of the subject being studied in the school (Schnell & Prediger, 2017).
Enrichment by deepening the tasks and topics are mostly chosen because they are in line with the regular curriculum unlike broadening by extracurricular activities (Sheffield, 2003). For this study, enrichment by deepening is chosen because it suits the needs of advanced students, including those gifted in mathematics, in regular classes by deepening what they are already studying through an emphasis on problem- solving and mathematical reasoning (Piggott, 2004). When all students engage in this type of task, those with potential are expected to expand their expertise, skills as well as the rest of the students in the class depending on the level of each student.
Teachers should raise the ceiling of expectations when interacting with gifted students so that students can compete with their potential rather than with the norm.
To maximize the potential of gifted students, teachers need to differentiate the materials, assignments, and products in the level of complexity, abstraction, and depth (Rief & Heimburge, 2006). The enrichment method for treating the gifted students is considered perfect for the high achievers, especially that some of these high achievers are also gifted too. This research aims to study the impact of enrichment on the mathematical literacy of tenth grade students in the UAE.
of mathematics. From the enrichment literature, four paradigmatic positions can be identified to reflect their educational views and priorities. Feng (2006) listed enrichment positions as follows:
• development of exceptional mathematical talent;
• popular contextualisation of mathematics;
• enhancement of mathematics learning processes, and
• outreach to the mathematically underprivileged.
All of these mathematics enrichment positions are motivated to provide high- quality mathematics learning experiences. However, opposing views arose from differing perceptions of how best to achieve this and on whom it should be applied to achieve the most benefit. Nevertheless, the following three positions are directed at all students with a different focus for each of them.
According to Feng (2006), the first position is directed to few students, only gifted, as it aims to identify and develop (mathematical) talent and views enrichment as a method to meet their academic needs, and to cultivate an elite group to become leaders in civic, commercial and industrial contexts. This position was supported by many researchers, for example, Clendening and Davies (1983).
The second position applies to all students where its focus is on the application of mathematics as a means of engaging students in mathematics. This will make students appreciate the applications of mathematics to life, not just as an academic discipline. This is expected to break the negative stereotypes of mathematics by deepening students' understanding of mathematics and its applications.
The Third position of enrichment is best described as student-and experience- centered (Feng, 2006). This type of enrichment is an approach of the ongoing process that should infuse all aspects of teaching and learning as an integral part of education for all students, whether in regular classrooms or beyond. According to Feng (2006)
“using this interpretation of enrichment, the engagement of all students in meaningful mathematical practices is an essential and worthwhile part of education; this also forms the main goal of mathematics enrichment”. This conceptualization promotes the linking of mathematical content presented separately in the curriculum with mathematical content and other fields of study. By providing students with a stimulating experience in mathematics, enrichment promotes mathematical thinking and problem-solving. It is important to note that depending on the different levels of students in the classroom, students will need different levels of support to take advantage of enrichment opportunities. Thus, enrichment in this sense emphasizes appropriate scaffolds and content differentiation: enrichment tasks are often designed to use mathematical concepts and techniques at various levels of difficulty and may lead to qualitatively different endpoints (Feng, 2006; Piggott, 2004).
The fourth position calls for social justice and equity, educators that support this view not only believe that enrichment should be open to all students, but also make proactive efforts to ensure mathematics enrichment for students who have not traditionally benefited from such provisions (Feng, 2006).
The focus of this study is mainly on the third position to enhance the mathematics learning process while using contextual mathematics which will lead also to the satisfaction of the second position of enrichment as popular contextualization of mathematics. If mathematics enrichment includes "mathematical problem solving and
mathematical logic linked to mathematical contexts" (Piggott, 2004), enrichment should be the basis for many, if not all, aspects of the curriculum, and all students should be able to benefit from this experience (Feng, 2006).
In the next sub-section, the basic concepts including problems, problem- solving, and thinking will be put together in a meaningful enrichment framework based on mathematical literacy and its major components, mathematical problem solving and reasoning.