This thesis focuses on a year-long project of implementing active learning in undergraduate dynamics courses at Cal Poly San Luis Obispo from 2012-2013. The purpose is to increase conceptual understanding of critical dynamics concepts and to repair misconceptions of the students. Conceptual understanding in Dynamics is vital to understanding the big picture, building upon previous knowledge, and better understanding the behavior of engineering systems. Through various hands-on activities, students make predictions, test their conceptions, and solve real world problems. These active learning methods allow students to improve their learning of Dynamics concepts. Education research on active learning is present in Physics and Mathematics disciplines, yet is still growing in Engineering. Four Inquiry-Based Learning Activities (IBLAs) and two Model-Eliciting Activities (MEAs) are discussed in this thesis. Inquiry-Based Learning Activities feature student prediction and experimentation in which the physical world acts as the authority. On the other hand, Model-Eliciting-Activities prompt students to solve real world problems and deliver results to a client. From the results, some activities yield an increase in conceptual understanding, as measured by assessment items, while others do not yield a significant increase. These activities not only help to promote conceptual gains, but also to motivate students and offer realistic engineering contexts. In conclusion, the six total IBLA and MEAS will continue in practice and be improved in their implementation. This thesis work will contribute to engineering education research of active learning methods, and improve the undergraduate dynamics curriculum locally at Cal Poly.

The aim of this study was to explore the effects of a problem-solving heuristic instructional method on Grade 6 learners’ achievements in algebra. Two main theories inspired the design of this teaching method, namely the modelling and modelling perspective, and action, process, object, schema (APOS) theory. Modelling and modelling perspectives guided the development of modelling-eliciting activities used in the teaching method and the APOS theory guided the sequence of activities used to develop Grade 6 learners’ conceptions in algebra. The impact of the problem-solving heuristic instructional method was investigated with 198 Grade 6 learners from four different primary schools in the Zululand district of Kwazulu-Natal that were conveniently sampled. A mixed-method approach was used in this study and a hypothesis was formulated to investigate the effects of the teaching method on the learners’ achievements in algebra. The qualitative component consisted of a pre-intervention class observation of mathematics lessons of all four mathematics educators in the schools used for this study. The design and implementation of the problem-solving heuristic instructional method and the quantitative component employed non-equivalent control group design with pre-test and post-test measure. The main instruments for data collection were an observation schedule to document sequence of events in the classroom during the class observation, a standardized achievement test in algebra used to measure effects of the problem-solving heuristic instructional method and modelling-eliciting activities used as a medium of interaction between learners and the researcher during the implementation of the problem-solving heuristic instructional method. Findings from the class observation indicated all four schools made use of comparable traditional methods of instruction. The implementation of the problem-solving instructional method gave insights into how a problem-solving heuristic instructional method can be developed and used in Grade 6 algebra lessons, and the factors that could influence learners’ conceptual development in algebra. The findings from the quantitative component supported the initial hypothesis that improved scores in algebra are achieved through participation in the problem-solving heuristic instructional method. Quantitative data was analysed using the t-test, analysis of covariance, Johnson-Neyman (J-N) technique and the effect size. / Mathematics Education / D. Phil. (Mathematics Education)