Work-in-Progress: Problems in learning related to mathematical and graphical representations of signals
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Bibliographic record
Abstract
Conceptual learning of concepts that are expressed intensively in mathematical equations and processes is an ongoing challenge for engineering students. There is ample evidence in literature that electrical engineering students struggle in subjects like signals and systems because it heavily involves switching between mathematical and graphical representations of signals as well as many different domains. The purpose of this study is to identify the mistakes made by undergraduate electrical engineering students when they try to make sense of graphical and mathematical representations of different kinds of information in different contexts, for example, drawing a complex signal in time domain, drawing a frequency domain graph, drawing current-voltage characteristics of a device, and transfer characteristics of a system. The data for this study is collected from various exam responses of undergraduate electrical engineering students in two courses namely signals and systems and Electronics 1. Most of the students in Electronics 1 had already taken signals and systems course and some were co-taking signals and systems. This set up has helped to understand the learning challenges that persist even when students continue to apply similar mathematical concepts in other contexts. The responses are analyzed to identify the common mistakes. These common mistakes are further analyzed to understand students' weaknesses in solving questions related to these concepts. The results show that students struggle with understanding signals when the independent variable is not time, when the signal is complex and contains j, when the signal is a combination of more than one signals, and when the signals are abstract. The author concludes that the learning of such concepts requires continuous switching between abstract concepts and multiple domains and most of the concepts cannot be learned through sensory learning which causes students with all sorts of learning styles struggle with getting comfortable with these concepts. The mistakes identified in this work-in-progress paper is the first step to guide the protocol design for a future qualitative study to understand the reasonings students employ to make sense of these mathematical equations and representations, compare the thought processes when a question is solved correctly and when not, and investigate how students' thought processes evolve as they keep taking courses throughout their program that require similar reasonings for better learning.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it