Learning mathematical rules with reasoning

Date of Award


Document Type


Degree Name

Master of Education (M. Ed.)


Institute for Educational Development, Karachi


This research focused on students' learning of mathematical rules with reasoning. This includes studying the process of students' learning, how they make meanings of the mathematical rules they have learnt, how they relate, and the factors which enhance learning with reasoning. I worked with four students (grade six) with mixed ability from a private school. I engaged them in mathematical tasks for one hour outside of their classroom situation. Sessions were planned for twice a week for five weeks using the tasks designed on four basics rules of fractions, addition of fractions, subtraction of fractions, multiplication of fractions, and division of fractions. My role was dual in nature, that of a researcher as well as teacher. After determining the student’s prior knowledge of fractions in introductory sessions, I designed activities pertaining to the four rules of fractions. I used qualitative approaches for generating data. The main sources of data generation were field notes, audio tapes, observations, and students' work. My analysis started from the first day in form of analytical memos. I categorized themes through 'mapping method'. My biggest learning during this study was to learn about the factors which enhance students' leaning of mathematical rules with reasoning. This particular study provided me important insights, which influenced students learning. For example, role of teachers' questioning, role of concrete material and pictorial representations, role of conducive environment in the classroom and the role of students misconceptions and their prior knowledge. This study also discusses some of my learning as a teacher, teacher educator and as a researcher. On the basis of the findings the study makes significant recommendations to the community of teachers and teacher educators.

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