Date of Award

Fall 12-15-2020

Degree Type


Degree Name

Doctor of Education in Secondary Education



Committee Chair

Dr. David Glassmeyer

First Committee Member

Dr. Mei-Lin Chang

Second Committee Member

Dr. Rachel Gaines


The use of inquiry-based and explicit instructional methods in mathematics has been researched and have found that the most appropriate instructional method depends on many factors including the subject matter being taught, the students’ prior knowledge, and the students’ special education status. However, teachers’ use of these methods has not been investigated in two important topics in high school geometry: arc length/sector area and graphing circles – topics which reveal how several important mathematical concepts connect from elementary and middle school, to geometry, then to pre-calculus. This quasi-experimental study compared the effects of inquiry-based and explicit teaching methods on arc length/sector area and graphing circles in terms of student achievement growth and students’ assessment of their learning gains. One group of students was taught arc length and sector area using inquiry-based methods while the other group was taught using explicit methods. An independent samples t-test compared growth in procedural fluency and conceptual understanding for all students as well as for certain subgroups based on prior achievement and special education status. The procedure was repeated with graphing circles with the instructional methods swapped for each group. Overall, results showed significantly higher student achievement growth in arc length and sector area procedural fluency under explicit instruction, but other overall differences were not significant. Therefore, teachers can use either instructional method to promote student achievement growth in conceptual understanding of arc length/sector area, conceptual understanding of graphing circles and procedural fluency in graphing circles. Teachers should consider using explicit instruction to teach arc length and sector area procedural fluency.