Pemahaman murid Tingkatan Satu tentang pembahagian pecahan / Fan Siong Peng - Fan, Siong Peng (2011)
This study was conducted within the framework of radical constructivism. The purpose of the study was two-fold. The first was to indentify children’s patterns of thought on proper fractions, improper fractions, and meanings of division based on languages, verbal and actions when they attempted to give meanings to fractional situations. The second was to investigate children’s understanding on division of fractions which refers to Form One Student’s patterns of thought by constructing specific ways to solve fractional division problems involving whole numbers, fractions, or combination of both using knowledge of proper fractions, improper fractions, and meanings of division. Six types of fractional tasks involving regions and collections were presented to each of the five children in one-to-one clinical interviews. Each interview session was recorded with audio and video recorder. Data analyses started with transcription of the interviews, written answers, sketches of diagrams, and marked on the given objects. Within case synthesis were inferred as individual’s forms of thought and cross case synthesis on the forms of thought were inferred as participants’ patterns of thought collectively. Participants’ patterns of thought on proper fractions were single partitioning, single grouping, single splitting, fragmenting region diagrams, and simplified fractions. First, third, and fourth applied to regions and second and third applied to collections. Participants’ patterns of thought on improper fractions were based on mixed numbers, denominator of improper fractions, and one whole. First and third applied to regions and collections, where as second only applied to regions. Participants’ patterns of thought on meaning of division were partitioning to produce several objects, partitioning to produce several parts of a whole, and partitioning to produce several objects and parts of a whole, measurement to produce several parts, measurement to produce several objects and portioning to produce several parts of a whole. Specific methods used by participants to solve problems on division of fractions involving application of fractional knowledge were single partitioning and measurement, single grouping and splitting, tenth numbers, and hundredth numbers. Four types of operations, such as addition, subtraction, multiplication, and division were used by participants to solve problems on division of fractions. Participants applied both meanings of division, such as partitioning to produce several whole and parts of objects and measurement to produce several parts of a whole objects.