Chapter 2: Literature Review
2.6 Mathematics Enrichment Program (MEP)
2.6.5 Enrichment Framework
2.6.5.2 Contextual Teaching and Learning (CTL)
For the success of this enriched content, a specific view of teaching and learning supports engaging problems that develop and use problem-solving strategies and encourages mathematical thinking. Pape, Bell and Yetkin, (2003) stated that for students to be successful problem solvers, they need to be creative, confident, and autonomous. This means that teaching should move away from teacher-centered practice. Based on the literature, when teacher-centered the classroom, the students’
expectations of mathematics focus on activities that are concerned with procedures, accuracy, and lead by the teacher without social activity involvement. This limited interaction is likely to result in little learning gains compared to learning opportunities as students feel autonomous and independent where the teacher’s role is a facilitator.
This curriculum addition of the contextual problems to the students' learning is in line with Correl’s (1978) definition of “enrichment” as any experience that substitutes, supplements, or extends instruction beyond that normally offered. NCTM (2014) asserted that effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow many entry points and varied solution strategies.
Additionally, the effective use of enrichment opportunities means that some students require more support than others. Therefore, an appropriate scaffolding and differentiation of content are emphasized. Though, Swan (2008) stressed the crucial role of students’ collaboration, building on the knowledge that students previously studied, and creating tension and cognitive conflict to be resolved drawing on collective knowledge and discussion for multiple solution pathways.
Thus, as the second component of the mathematical enrichment, the classroom environment and teaching should facilitate constructive approaches through social interaction between students and teachers. The teacher's role is to provide the appropriate tasks, create an atmosphere in which students are not passive and use interventions that do not perform but extract mathematics from students by making mathematical connections and helping them bridge the knowledge gaps (Piggott, 2004). Constructivism emphasized, as a learning theory, the role of students rather than that of the teacher. In constructivism, students can use their prior knowledge and experience in testing ideas and apply these ideas to a new situation (Berns & Ericson, 2001).
Students' achievement in mathematics is based on building skills on top of one another. Mathematics skills are important across the school year as with other basic subjects, such as reading and writing, because performance depends on what the student learned previously and apply it to new concepts and applications.
Unfortunately, the UAE students failed to apply their school learning of mathematics to new contexts from real life as revealed by the PISA results. To bridge this gap, teachers need to present mathematics in a real-world context. Thus, teachers can apply Contextual Teaching and Learning (CTL) which is a method that helps the teachers to
relate subject content to real-world application and motivate students to make connections (Berns & Ericson, 2001; Hudson & Whistler, 2007).
This CTL method could help the students to improve the students' mathematical literacy because “among mathematical problems, those which have some applications in other branches of science and technology or the ones which have been essentially derived from real-life problems might be more attractive for students, since they bring life to the abstract concepts of mathematics which they learn, and make the concepts more tangible” (Adams, 2003, p. 794). Students in classes are taught the basic knowledge of mathematics but as abstract concepts. To give more meaning to what they have learned, students need to apply these concepts to real-life problems. This CTL provides the means for reaching learning goals that require higher-order thinking skills (Satriani, Emilia & Gunawan, 2012).
There are five strategies suggested by Crawford (2002) that could be used in contextual learning are; 1) relating; 2) experiencing; 3) applying; 4) cooperating or study group; and 5) transferring (REACT) (Satriani, Emilia, & Gunawan, 2012). These strategies are relevant to the skills of mathematics literacy. Moreover, Crawford stated that the REACT strategy affected student’s motivation and their learning outcomes in both mathematics and science (Maryani & Widjajanti, 2020). There are several connections between the steps and components of learning with indicators of mathematical literacy abilities (Maryani & Widjajanti, 2020). Hence, Mathematical literacy could be improved through the application of contextual learning. The connections between the steps and components of learning with indicators of mathematical literacy abilities are illustrated in Figure 8 (Maryani & Widjajanti, 2020, p. 7) below.
To apply CTL, there are five teaching approaches have emerged where context is its critical component to engage students in an active learning process. These approaches could be used individually or in combination with one or more others.
These approaches are; Problem Based Learning, Cooperative Learning, Project-based learning, Service Learning, and Work-based learning (Berns & Ericson, 2001).
In this study, students were provided with extracurricular mathematical problems that give the students the chance to be exposed to contextual problems in a Problem Based Learning (PBL) as one of the CTL approaches. PBL is believed to promote the use of deep processing that means connecting different subjects together, and self-regulation and thus aims to stimulate high-quality learning (Wijnen, Loyens, Smeets, Kroeze & Van der Molen, 2017). This is because the learning strategies of students can be influenced by the instructional educational method applied in the study
Figure 8: CTL and mathematical literacy
Contextual Teaching and Learning (REACT)
Relating : The teacher provides material related to students’ daily lives
Experiencing: Students are given exercises so students are accustomed to solving problems using the knowledge they have
Applying : Students apply concepts in problem solving activities and the teacher motivates by providing realistic and relevant exercises
Cooperating : The teacher forms an effective group then prepares relevant assignments, observe well and provides information needed by students
Transforming : Students are given the context of a problem or a new situation to be solved
Mathematical Literation Skills Formulate
• Using Symbolic
• Using Mathematics Tools
Interpret
• Representation
• Communicating Apply
• Devising Strategies for Solving Problem
• Reasoning and Argument
• Mathematising
program (Vermunt, 2007). In addition, based on research that is supporting the use of PBL in education classrooms (Capon & Kuhn, 2004) and its correspondence with NCTM's Process Standards that make PBL a natural fit for the curriculum used in this study as an “enrichment” content.
Each of the NCTM standards can be found within the PBL goals. Hmelo-Silver (2004) stated that "PBL is designed to help students: (1) construct an extensive and flexible knowledge base, (2) develop effective problem-solving skills, (3) develop self- directed lifelong learning skills (4) become effective collaborators, (5) become intrinsically motivated to learn" (p. 240). The first four goals of PBL are also considered as core components to Process Standards (Communications, Reasoning &
Proof, Problem Solving, and Connections) stated by the NCTM (2000) as described in their Principles and Standards. These Process Standards are important to describe ways to understand and apply mathematical content knowledge.
This approach reflects the constructive perspectives of learning through social interaction (Confrey, 1990). This knowledge building implies that learning builds on a student's prior knowledge, his interaction with resources, and interaction with members of their practice community. Additionally, the structure of a “good” problem itself requires the students to interact and build solution plans, revisit ideas, closely link with building on prior knowledge, and building mental patterns associated with a rational view of knowledge (Piggott, 2004). Each lesson in the “enrichment unit” was designed as such where the students are active in their learning with the teacher's guidance. In PBL, ill-structured and nonroutine problems let the students think of more than one solution using more than one strategy, while the students work together and
use their prior experience to gain new information in the process of problem-solving, the teacher's role is to facilitate this collaboration.