Abstract:
Mathematical thinking and problem solving has slowly been emphasised in the primary and secondary school syllabus under the new 21st Century National Education System in Brunei Darussalam. Problem solving involves several aspects of teaching and learning. It is a powerful teaching tool that promotes multiple, creative and innovative solutions to a given mathematical problem. It also provides opportunities for students to practice a variety of concepts and skills in a meaningful context and to communicate mathematical ideas in the classroom.
A question focusing on a discovery type of problem was given to 30 secondary school teachers during a professional development course on problem solving. Each teacher represented the 30 secondary schools in Brunei Darussalam, thus representing the entire secondary school population in the country. The teachers were instructed to distribute the question to one Year 7 of his or her choice in their respective schools.
A mixed farm has some goats and chickens. The goats have 4 legs and the chickens have 2 legs. Alex counted the heads and the legs. The total was 8 heads and 22 legs. How many goats and chickens are there in the farm?
In this study, we investigated the possible strategies how Year 7 students answered this question and how teachers assessed their students' written responses. Overall, more than 600 student responses were collected, and descriptive statistics were used to analyse the data. Interestingly, majority of the Year 7 student samples were not able to answer the question articulately even though this particular question had been set in their Year 6 national primary school assessment examination administered last year in 2012. Those who did not answer the question correctly did try to make an attempt however many without any known problem-solving strategies. They simply add, multiply or divide the numbers that appeared in the question. A few others did not even made any attempt to work and answer the question. Those who attempted and responded correctly, the strategies used were mostly Estimation and Check and Drawing Pictures. This paper will discuss and elaborate further on the problem solving strategies used by the students.