To scaffold or not to scaffold mathematics learning : that is the question

Abstract

The purpose of this research is to study the effects of scaffolding on the conceptual and procedural knowledge of the students. It investigates how scaffolding affects the learning results and learning process in mathematical problem-solving in a teacher-to-classroom interaction. Mathematical competence development relies on conceptual and procedural knowledge. Learning of procedures must be connected to the learning of concepts and vice versa. Scaffolding assists the teacher to construct a learning trajectory which capitalises on the growth of student development. It also assists the students to develop both types of knowledge by focusing on the role of prior knowledge, self-efficacy, and sequencing of the study materials.

In this study, sixth-grade students (n = 31) solved the questions related to algebraic problem-solving. This was done on a pre-structured worksheet which scaffolded their mathematical learning process and displayed the process to reach the learning results. The research questions were as follows: (1) What kind of difference is there in students’ knowledge level between the prior knowledge test and after the main activity worksheet? (2) How did scaffolds affect the learning results and learning process of the students? (3) How did self-efficacy develop across different thinking levels during the learning process?

The data was collected over the period of two days. On the first day, students completed the prior knowledge test in a ten-minute session and then the teacher instructed on an algebraic problem-solving in a forty-five-minute session. After the instruction, the students were provided with a problem-solving worksheet which had seven algebraic questions based on three thinking levels of revised Bloom’s Taxonomy; remembering, understanding and applying. It also had the elements of embedded and optional scaffolds namely self-assessment box and access to teacher’s and peer’s help during the learning process. On the second day, eight students were selected for an interview, based on their different performance in terms of the prior knowledge test and main activity? The findings show that there was a significant difference between the conceptual knowledge the prior knowledge test and the main activity. Self-efficacy beliefs (measured by self-assessment) of the students developed in a dynamic manner as the thinking levels in the worksheet progressed indicating that students’ zone of proximal development change according to the situation they face.

To conclude, the structured tasks can help teachers to know where students lie on a zone of proximal development during classroom interaction. Self-assessment embedded in the worksheet allows the students to evaluate their understanding. When students’ mathematical understanding progress is traceable, it is possible for teachers to design the activities and tasks which support student learning in mathematics as well as help the teachers to adjust and target their assistance precisely.