Date of Publication


Document Type


Degree Name

Doctor of Philosophy in Science Education Major in Mathematics

Subject Categories

Science and Mathematics Education


Br. Andrew Gonzalez FSC College of Education


Science Education

Thesis Advisor

Auxencia A. Limjap

Defense Panel Chair

Minie Rose C. Lapinid

Defense Panel Member

Voltaire M. Mistades
Celina P. Sarmiento
Levi E. Elipane
Rosie L. Conde


Mathematics instruction seeks to help students make sense of and take meaning from their learning. It is essential to make mathematics topics meaningful to learners through in-depth comprehension of how they should function and by diving into different mathematical concepts as a platform for other work and thought. Mathematics investigation entails the fundamental nature of mathematical activity: problem formulation; dealing with circumstances for which no possible solution exists; formulating and justifying conjectures; and generalizing. To reinforce students' learning from their mathematical exploration, educators should carefully design activities incorporating real-world situations, requiring learners to think critically, explore situations, and decide on the most appropriate solution to the problem. Hence, the researcher employed two design-based research cycles involving three MI teachers to develop problem-based learning modules in a mathematical investigation. This study also examined how the developed material promoted the mathematical investigation proficiency of the 35 pre-service mathematics education students who participated in the study. The students’ hypothetical learning trajectory was crafted, analyzed, and considered along with the PBL design principles in developing the module. The teachers' class observations, student learning logs, interviews, and investigation reports were gathered during the teaching experiment to analyze students' learning of MI through online PBL. Reflections from such an analysis aided in HLT revision and module enhancement. The results revealed that the learning goals, reminders, guide questions, and instructions provided in the module aided students in regulating their learning by setting their own goals, designing their learning strategies, and managing their time effectively and efficiently. It was also found that solving the PBL tasks engaged students in collaborative discourse to share and explain their thoughts, listen to and analyze others' ideas, and resolve learning issues. Furthermore, the module provided direction for student learning and aided the teacher in devising a strategy to select appropriate conditions for students to perform the tasks. It was further revealed that students were equipped with the required content knowledge to carry out the investigation. They obtained a high level of knowledge on the concepts consisting of multiples, factors, greatest common factors, and prime numbers. Students perform fairly well in their investigative procedures. They showed improvement in analyzing the problem as shown in the depth, complexity, and originality of their investigation. Also, they demonstrated fair reasoning ability. They had difficulty in constructing precise and valid reasoning to justify their conjectures. Relative to the communication process, students have shown great communication abilities in presenting their investigation. Thus, learning activities assisted students in promoting their mathematical investigation proficiency in terms of the foundational knowledge and investigation and communication processes.

Keywords: Mathematical investigation, PBL module, problem-based learning, mathematics content knowledge, mathematical investigation process, mathematical investigation proficiency

Abstract Format






Physical Description

257 leaves


Mathematics—Study and teaching; Problem-based learning

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