Zone of proximal development and scaffolding required by junior high school students in solving mathematical problems

Introduction. Mathematics comprises grading concepts. It means that one specific concept can be interrelated to another concept, which embodies a continuous process. Mathematics instruction at schools is ordinarily delivered from the easiest to the hardest concepts and requires a considerably deep understanding of each concept. By acquiring the understanding, it is quite certain that students can solve mathematical problems effectively.

Aim. The current research aimed to analyse and describe the Zone of Proximal Development (ZPD) and scaffolding required by junior high school students in mathematical problem-solving. There is also an attempt to describe the actual level of competence possessed by students, and to determine the level of scaffolding needed to develop students’ learning competencies.

Methodology and research methods. The present research employed a qualitative method within the descriptive approach. The research sample consisted of six students who attended the ninth grade at Muhammadiyah Junior High School 1 in Malang, Indonesia. The participants were grouped based on their mathematical competence levels, i.e. two high-achievers, two average-achievers, and two low-achievers. The data collection technique is done by giving tests, interviews, and observations. As for the teaching material, geometry was chosen as the main theme, covering the topic “Volumes of a Tube and a Ball”.

Results. This research revealed that ZPD of the high-achievers was effective to help them solve mathematical problems independently. Conversely, the average- and low-achievers were found to be problematic at solving mathematical problems independently. The teachers must review and restructure the scaffolding strategies, dealing intensively with students who are less competent in solving mathematical problems.

The scientific novelty of the work lies in the fact that previous studies have described efforts to improve the quality of learning through scaffolding (Siyepu S., 2013). This study describes in full the scaffolding process in the classroom: identification of students’ actual abilities and potential abilities after implementing instructional scaffolding.

Practical significance. Referring to the results of the research, it is suggested that teachers should be so heedful about their students’ ZPD and thus more appropriate scaffolding treatments can be applied. In addition, teachers are strongly recommended doing self-training in scaffolding and keeping the instruction for their students to analyse their answers repeatedly to avoid a fallacy in operations. Besides, teachers should prepare their students to be good problem-solvers by exposing them to various exercises. For further studies, it is highly expected that more relevant research should be conducted from different viewpoints, i.e. investigating the effective scaffolding strategies.

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