Publication Date


Document Type



Mathematics, Education

Faculty Mentor

Sarah Jahn


The Discovery of Pascal’s Triangle is a great lesson for students because it gives them a glimpse into the history of mathematics, patterns in upper level math topics, and connections between real life situations using combinations and more abstract math concepts, such as Pascal’s triangle. My research dives into how Bruner’s theory on discovery learning and the concept of constructivism can motivate my differentiated learners to understand Pascal’s Triangle and enhance their understanding of combinations. Educators can use this research to promote active learning in upper level mathematics classrooms. The discovery opportunities I provided to my students not only applied constructivism and taught me about the learning needs of my students, but it also gave the students control over their learning and built leadership across the classroom as students worked together to discuss ideas and patterns. As a result, less than 5% of students in the classroom chose to not participate, and approximately 8% of them were not able to complete the given triangle because of time constraints in the classroom. Many of the students were able to fully calculate and fill out the given assessment on Pascal’s Triangle, except for a few absent students.


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