Date of Award
Doctor of Philosophy (PhD)
STEM and Professional Studies
Instructional Design and Technology
As more students enter higher education unprepared for college level mathematics, amelioration of deficiencies may be a key barrier which, once faced, will increase overall college graduation rates (Attewell, Lavin, Domina, & Levey, 2006). Corequisite courses offer the opportunity for the underprepared learner to take the gateway mathematics course with support (Complete College America, 2012). Upon passing, mathematics and STEM courses will “unlock,” thus allowing the learner to successfully complete their degree requirements. Faculty are challenged to retain the rigor of college-level coursework while supporting learners who possess a wide range of mathematics levels (Daugherty, Gomez, Carew, Mendoza-Graf, & Miller, 2018). Implementing a corequisite curriculum requires the creation or adaptation of materials and instructional strategies to align the basic skills instruction into the college-level content. A case study was conducted with the sample population of college undergraduates (N = 43) enrolled in two sections of College Algebra and participated within a 14-week semester course. A generative learning strategy, self-explanation when combined with worked examples, was introduced during Week 5, when multi-step problems were encountered. Training within the intervention was given to one section. The other section was informed that the strategy was useful to understanding mathematics. The quality of the self-explanation produced was evaluated at the beginning and end of the intervention. Attitudinal data was captured in a pre-and post-Mathematical Attitudes and Perception Surveys (MAPS), in addition to participant semi-structured interviews and a reflection.
The sections were compared on measures of quality of the artifact produced, MAPS survey data, and through categories of ability as determined by incoming ACT score. The result indicated that those trained in self-explanation when combined with worked examples produced artifacts of higher quality. The participants who had the lowest incoming mathematical scores (ACT mathematics sub score < 17) produced higher quality self-explanations than any other mathematical score category from either case.
Attitudinal data showed that the trained section had marked increases in mathematical attitudes, with the highest increase in confidence. The untrained section’s attitudes stayed relatively consistent throughout the study. Interviews and reflections indicated that, for both sections, the intervention assisted in mathematical understanding and metacognition. Trained participants used both components to understand and identify mathematical knowledge gaps. The majority of the untrained participants devoted more attention to the worked example portion of the intervention to create mathematical meaning and identify misunderstandings.
This study found that training the learner was an important aspect of the intervention and was necessary to produce results of a higher quality along with positive mathematical attitudes.
Stapleton, Laura L..
"A Multi-Case Examination of Training of Self-Explanation when Combined with Worked Examples"
(2021). Doctor of Philosophy (PhD), Dissertation, STEM and Professional Studies, Old Dominion University, DOI: 10.25777/wf4n-mf83