PhD Oral Exam - Alexandra N. Kindrat, Education
When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
Study 1 examined the relational thinking of seventh-graders before and after a 15-day mental mathematics intervention. Students from two classes were assessed at three time points on their ability to solve equivalence problems and their reasoning about true-false number sentences. Results indicated that the students’ performance improved on both measures. Maintenance of performance on the equivalence problems was observed four weeks after the conclusion of the intervention. The results suggested a link between mental mathematics and relational thinking.
Study 2 replicated Study 1 using three intact classes, but also extended it by examining long-term effects and including a measure of students’ mental computation. Results indicated that students in the second class improved and maintained their performance on the equivalence assessment through to the final time point, but there was no improvement after the intervention in either Class 1 or Class 3. Students in all three classes reduced their reliance on computation when reasoning about true-false number sentences. Performance was maintained on the relational thinking measure through all subsequent time points, including on a delayed posttest. Mental mathematics performance for two of the three classes increased significantly after the interventions, and remained at the same levels at all subsequent time points for the students in these two classes.
Study 3 examined whether the effects on relational thinking of a mental mathematics intervention could be augmented beyond what was observed in Studies 1 and 2 if students were permitted to write down parts of their mental computation strategies, thereby reducing their cognitive load. Students from two seventh-grade classes were randomly assigned to a Regular Mental Mathematics (RMM) condition and a Reduced Cognitive Load (RCL) condition. All students received the same instruction over an eight-day period, but students in the RCL condition were permitted to write down specifically-identified elements of their computations. Students were assessed before and after the intervention on the same measures as Study 1 and 2, and the nature of their mental computation strategies was documented at posttest. The results indicated that both conditions improved on their performance on all assessments, but there were no condition effects.