The Importance Of Problem Based Learning

Research supports the problem based approach to learning. Various studies globally have found that problem-based learning improves student learning and engagement (Boaler, 1997, Cotic and Zuljan, 2009). A review of research has found that problem based learning ‘develops more positive student attitudes, fosters a deeper approach to learning and helps students retain knowledge longer than traditional instruction’ (Prince, 2004, p. 223). However, there are limited research studies on the effectiveness of problem based learning on conceptual understanding of mathematical concepts. An international study (Tasoglu and Bakac, 2014) compared problem based learning with traditional learning on the conceptual development of scientific concepts and found

There are many factors that can assist in conceptual understanding through problem based learning. Teachers need to pay close attention to these factors if conceptual understanding is the aim of the activity.

The nature of the problem

The main feature of the problem based learning is that it engages the students in solving authentic problems and help them build deep mathematical understanding in the process of problem solving. It is very different from the method where students complete exercises by following guided instruction to gain procedural knowledge. In problem based learning, the students are required to use more than just procedural knowledge. They need to analyse the given information and reason to make sense of the problem tasks and concepts involved. They need to identify possible ways to solve it as well as develop, justify, and evaluate arguments about the possible solutions. The choice of the problem, therefore, has a critical role in engaging and sustaining mathematical inquiry in

A real and meaningful task will engage the students and encourage them to get involved in solving the problem. A carefully chosen problem can ‘engage all of the students in the class in making and testing mathematical hypotheses’ (Lampert, 1990, p. 39). The complexity of the task should be such that it shouldn’t be too easy or too difficult for them. It should be just above their current level so that it challenges them. A problem that is too difficult can be discouraging and counter productive. Erickson (1999) states that the tasks need to focus on a particular mathematical concept and ‘present situations in which no readily known or accessible procedure or algorithm determines the method of solution’ (p. 516). It should provide opportunities for multiple strategies for solution and multiple representations of the concept. This will facilitate the learning of all kinds of learners as the concept could be understood in multiple ways (diagrams, charts, symbols, graphs etc.). For example a problem based task around cost of packaging chocolate can help students understand the concept of surface area and volume of 3D shapes. Some students might draw different kinds of packagings and even be creative and invent new type of packaging. Others might look the physical boxes of chocolates. Students will look at volume of different 3D shapes (rectangular prism, triangular prism, cylinder etc.) to calculate the most