Increasing the dynamics in Dynamics

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How do we make sure that our students spend quality time during the semester on actively developing a fundamental understanding as well as analytical and computational problem-solving skills? In large Bachelor classes like Dynamics, our typical format of lecturing to huge student audiences and solving simple pen-and-paper problems in exercise sessions is demonstrably of limited effectiveness and often tends to promote that students focus on studying merely for (and right before) the exam. Such learning is ineffective and little sustainable. What is missing is quality time the students spent during the semester on actively applying the new concepts and receiving continuous and prompt feedback on their progress.

In addition, the contents of Dynamics are highly mathematical and involve complex 3D visual thinking – increasingly so during the course of the semester. On the one hand, this leads to numerically complex problems that cannot be solved by pen and paper (and cannot be assessed in the classical exam format), which are hence neglected by the students, even though their solution could have the added benefit of growing computational competencies. On the other hand, the complex concepts may lead to students (with diverse educational and personal backgrounds during the early years at university) being left behind early on, the exam pressure increases, and the vicious circle begins anew.


The course: Dynamics

Dynamics is a typical course facing all of the above challenges: a mandatory class for all MAVT and BAUG students in their third semester and part of the challenging Block 1, plus a required exam for a number of Master’s students, totaling about 580 students every year. Students have a busy semester and typically focused on passing the exam with minimal time on task during the semester. The diverse student backgrounds are visible in the exam statistics. While some class topics easily qualify for pen-and-paper calculations during homework and exam, various topics – from multibody vibrations (requiring eigenvalue calculations) to integrating nonlinear equations of motion – do not admit an assessment in classical exams, which is why they remain superficial and students focus on studying other topics. Computational competences were previously not promoted, even though simple computer codes could address, e.g., the computation of eigenmodes and eigenfrequencies or numerically integrate nonlinear differential equations. Finally, the complex concepts of dynamics in 3D are hard to visualize and may lead to student frustration.


The solution: weekly online learning elements

To address the above challenges, we developed several new online learning elements in Dynamics, which the students can explore, solve, analyze, and receive feedback for on a weekly basis during the semester. The key objectives were to (1) incentivize that students study the relevant topics every week of the semester, (2) enable students to explore the course concepts more independently and in diverse ways, (3) add computational components to solve a broader range of problems, and (4) promote a deeper understanding of the course concepts rather than superficial “exam cramming”. To this end, we introduced a combination of weekly Moodle/STACK homework problems and Jupyterhub notebooks (one for each small-group exercise).

Moodle/STACK Homework & Level-Up

Weekly homework that is automatically graded provides the students with self-paced learning opportunities and immediate feedback. The set of every week contains multiple-choice questions, graphical questions (identifying points, vectors, or axes of interest), or open problems (for which the students can enter any algebraic expression including variables). Randomization of given values ensures variety and prevents copying from others. Participation is incentivized by a grade bonus in case of successful completion. Moodle’s Level-Up feature was used for gamification: students reach different levels based on their submitted responses (allowing multiple attempts per question with decreasing bonus to reduce anxiety), and the final bonus depends on the level reached at the end of the semester.

Jupyter notebooks for each exercise

A Jupyter notebook was prepared for each exercise session, which integrates (1) clicker questions for the students to complete during the exercise, (2) typical series problems whose solutions can be made available on demand, and (3) animations and visualizations of selected concepts or problems. The objective of the latter is to “make the invisible visible” with the goal of fostering intuition. This requires aligning the contents of the exercise problems with the animations and with the STACK questions. Introducing programming problems further promotes computational competences and allowed us to use numerical solution techniques where analytical solutions are out of reach.

The STACK questions are probably the best method I have ever seen to keep people engaged.
(anonymous comment from a student)

The Outcome

98% of the students completed all STACK homework problems, many commenting on their effectiveness to incentivize semester-long learning. Anonymous student comments included “STACK really helped understanding Dynamics” and “The STACK questions are probably the best method I have ever seen to keep people engaged.” 96% of the students found the clicker questions helpful, which were integrated in the Jupyter notebooks during exercises; 22% asked for even more of those. Visualizations and animations were also appreciated by the teaching assistants, who could use them effectively to explain concepts. The Jupyter notebook overall received, frankly, mixed feedback – those who liked programming praised it (“The Jupyter notebook really helps.”), while those that do not appreciate computational tasks did not appreciate the added burden (“They were a lot of jupyter things not related directly to mechanics.”). The wealth of data received from the students› responses to the online learning elements (in comparison with the exam outcomes) will assess the effectiveness of the various new types of learning elements, which is an ongoing effort. Overall, the new elements clearly and strongly increased the students’ problem-solving ability during the semester.

Course Description

Mechanics III: Dynamics
Dynamics of particles, rigid bodies, and deformable bodies: Motion of a single particle, motion of systems of particles, 2D and 3D motion of rigid bodies, vibrations, waves.
This course enables students to apply the concepts and laws governing the kinematics and kinetics of particles, rigid bodies, and elastic bodies in order to identify, formulate, and solve dynamical engineering problems. Specifically, students will be able to describe, analyze, and predict the motion of particles and bodies in space over time and to relate their motion to the applied forces for applications in (not only) mechanical and civil engineering.
MAVT (the course is taken by all 3rd semester MAVT and BAUG students)
2x2h lectures + 2h small-group exercises per week
ca. 580 students
2.5h written session exam; continuous performance assessment in the form of weekly Moodle/STACK homework problems that yield up to a 0.25 grade bonus.

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