Contribution: This study focuses on microcontroller circuits and aims to: 1) investigate the impact of formal reasoning on students' post-knowledge using catastrophe theory; 2) compare the different combination sequences of tangible user interface (TUI) and graphical user interface (GUI); and 3) assess the usability of both interfaces and explore potential correlations between perceived usability and students' post-knowledge. Background: Although in the existing literature, there are a few studies investigating the role of the sequence of TUI and GUI in students' post-knowledge, particularly in the microcontroller circuits there is a notable lack of related studies. Also, in this field, the effect of formal reasoning on students' post-knowledge has not been investigated. Research Questions: Does formal reasoning affect students' post-knowledge in microcontroller electronic circuits? Does interface sequence have any impact on students' post-knowledge? Does interface sequence impact students' usability perception of the TUI and GUI? Does student perceived usability correlate with their post-knowledge? Methodology: The intervention had a sample size of 134 university students who conducted four microcontroller exercises. In addition, statistical analysis employed the nonlinear Cusp catastrophe model, t-tests, and ANCOVA along with bootstrapping. Findings: Interface sequence has no impact on students' post-knowledge, while students' answers showed a significant difference in the evaluation of usability in favor of the real circuit. Cusp model showed that formal reasoning influences achievement and can act as bifurcation factor denoting that beyond a threshold value nonlinear changes in performance can occur.