Grade two students' approach to solving problems

Abstract

Mathematical problem solving has been a primary goal of the Singapore Primary School curriculum since the 1990s (N. H. Lee et al., 2014). Mathematical problems are prominent in mathematics education but often an area of struggle for students across the grade levels (Di Martino, 2019; Silver & Thompson, 1984). In response, educators have created various instructional strategies to better support students’ understanding and application in problem solving tasks. Despite so, problem solving remains to be a key area of concern for educators and students alike in mathematical learning (Di Martino, 2019). Yet, it is notable how problem solving skills and informal mathematics are naturally inherent in young children (Cobb, 1986). This should reasonably lead to well equipped problem solvers as they gain more formal knowledge in mathematical problem solving.<br><br>Di Martino's (2019) study found that kindergarten to Grade 1 students could effectively solve a non-routine problem that Grade 3 to Grade 5 students struggled to relate to and solve. As such, in complement to the existing problem-solving classroom strategies and pedagogical methods, it is perhaps valuable to consider the role of the learner, another element in the didactic triangle of education. The learner could come with prior pre-conceived notions on how to solve a problem and these could be relevant ideas to be encouraged in a problem-solving lesson.<br><br>Inspired by the above study, this exploratory study thus examined Grade Two students’ approach in solving a non-routine mathematical problem before they are exposed to any formal heuristic or cognitive strategy instruction. A group of 10 Grade Two students in a neighbourhood primary school in Singapore was individually engaged in solving a problem task. Their written and verbal responses were captured with interview prompts.<br><br>The study findings indicate that participants were able to solve the problem successfully using informal strategies. Metacognition and attempts to check accuracy of answers were observed. They were also confident of their solutions. However, as expected, they were unable to capture the thought processes formally. Some also failed to recognise the form(s) of Mathematics involved in the solving process.<br><br>The study, while limited in scope, adds to the ever-growing research base offering educators suggestions on how to improve their students’ problem solving abilities. The study results recommend that teachers invite students to share their informal problem solving methods and demonstrate how formal notations can capture these mathematically. This is in addition to existing pedagogy of teaching heuristics and metacognitive strategies and will convince students that mathematics is connected to the real world, a recurrent theme in today’s mathematics curriculum.