This study explores the learners’ strategies for heuristic ability in mathematics at the secondary level. The study is qualitative, and the method adopted for obtaining information about the learner’s strategies is a case study. The site selected is Govt. Girls Higher Secondary School Rustam, Mardan, Khyber Pakhtunkhwa, Pakistan. Participants of the study were six in number, selected from science group students of the 9th class based on their interests. A test of non-routine problems was used for the collection of data. Six non-routine problems were given to the students to check their heuristic ability. Non-routine problems were analysed through cognitive strategies. No scoring of students was considered in this study. The researchers categorized the learner’s responses so that students who solved questions by applying complete strategy were marked with the word excellent, the half strategy was marked very good, and unsatisfactory solutions were marked satisfactory. The study investigated learners’ strategies such as making tables, using formulas, guessing, making diagrams, doing trial and error, logical reasoning, non-logical reasoning and looking for patterns. Results show that students who are interested, motivated and have a positive attitude toward learning practice various methods for solving non-routine problems.

This study makes an effort to investigate learner mathematics-related beliefs at the secondary level. The study was qualitative and the method adopted for the in-depth information about the belief was a single case study. The site were selected for this investigation were Government Girls Higher Secondary School Rustam in District Mardan. The number of participants was six from class 10th science students. In-depth interviews were scheduled for the collection of data. Interview items were 9 in number.  Thematic analysis of the transcripts exposed learner beliefs about mathematics. The main findings of the study showed that those students who understand the concept of mathematics possessed the positive beliefs about mathematics, and they also like the book and course materials and satisfied with it. They feel easy during mathematics classrooms, enjoy, and excited to learn something new in this subject. In contrast, the learners who do not understanding level is low they hold negative beliefs they did not like the book and course materials and not satisfied and feel hesitation during mathematics classroom. The study further showed that in the construction of beliefs that are positive or negative about the mathematics classroom environment play a great role especially mathematics teacher, her methods, and her beliefs. If the teacher involves the students in activities, keep good and interesting method and motivate the students time to time, then the learners will possess positive beliefs and will take interest in such a very important mathematics class.