Standards-Based Grading for Signals and Systems

Abstract

Standards-based grading (SBG) is gaining popularity in K-12 education as it measures students’ proficiency on a number of course objectives rather than to give a single grade that does not by itself convey how well the student understands each of the core concepts from the course. Whereas a single grade may be assigned based on the extent to which the student demonstrates proficiency on a number of course objectives, the focus is to give the student, as well as other educators, a more detailed breakdown of the assessment of individual course objectives. This paper describes the implementation of SBG in a junior-level signals and systems course. SBG has been implemented in various undergraduate engineering courses [1-5] in recent years but, to date, no one has documented its implementation in signals and systems. Because the concepts taught in a signals and systems course are fundamental to subsequent electrical and computer engineering courses, such as digital signal processing and communication systems, SBG is appealing as an assessment tool for this course. In this course, a number of course objectives have been identified from among the following key concepts: signal visualization in the time and frequency domains, system analysis in the time (convolution) and frequency (Fourier) domains, signal analysis (Fourier series and Fourier transform), and sampling (Nyquist’s theorem). Proficiency on each of these objectives is assessed using a five-point scale, and the final course grade is calculated from a weighted average of the objective assessment scores. The objectives are assessed using weekly quizzes, midterm examinations, and a final examination. This paper analyzes the effectiveness of the introduction of SBG in the signals and systems course at the author’s institution. The study consists of a comparison of course objective assessment between students who took the signals and systems course before and since the implementation of SBG. Background Standards-based grading (SBG) has gained popularity in K-12 education in recent years as it gives better granularity in determining how well students have achieved competency on a number of course objectives rather than just for the entire course. More recently, SBG has been implemented in undergraduate engineering courses, such as a fluid mechanics course [2], a firstyear introductory engineering course [3], a hybrid thermodynamics course [4], and project-based design courses [5]. Best practices [1] have been established by educators from several universities. Continuous-time signals and systems (CTSS) is a fundamental electrical and computer engineering course in which students are introduced to mathematical models for common engineering signals and systems. The CTSS course is typically prerequisite to other ECE courses, such as digital signal processing, control systems, and communication systems. The concepts found in a CTSS course are among the most conceptually difficult [7-8] in a typical ECE curriculum. To that end, many attempts have been made to improve learning in signals and systems. A Signals and Systems Concept Inventory [6] has been developed to test students’ knowledge of common CTSS concepts. Various approaches involving the use of in-class laboratory exercises [9-17] have been used to improve student learning of signals and systems. This paper marks the first known attempt to use standards-based grading to enhance learning in signals and systems. Motivation for standards-based grading Continuous-time signals and systems is a course that is fundamental to subsequent electrical and computer engineering courses such as digital signal processing, control systems, and communication systems. After attending a standards-based grading workshop [18] at a recent ASEE Annual Conference, the author was inspired to implement SBG in signals and systems because of its focus on assessing performance on individual course objectives rather than on an overall course grade. For students, SBG offers several advantages over traditional grading on a 0-100 scale. Learning objectives are clearly presented at the beginning of the course, and each lecture topic is connected to one or more learning objectives. Each assessment is labeled with one or more objectives, which are assessed according to a Likert-scale rubric to be described in a later section. Throughout the course, students can access and track their assessment scores for each objective. Students are given multiple opportunities to show improvement on each objective through quizzes, midterm examinations, and the final examination. Final grades are then computed as a weighted average of the objective assessment scores. Before the introduction of SBG, the course was taught using a traditional “chalk-and-talk” lecture style. Homework discussion sessions were offered on a weekly basis. Interactive modules for convolution and Fourier series signal and system analysis were developed [17] as additional homework assignments. The course was graded based on homework scores, midterm exam scores, and the final exam score. Students would have only been aware of their performance on a course concept by identifying the concept(s) involved with a homework or exam problem and comparing their score to the standard institutional grading scale. After the introduction of SBG, the lecture style was intentionally not changed. Homework sessions continued as before, but quizzes were added on homework due dates to give a formative assessment of the most recently covered objective. Interactive modules were retained as additional homework assignments. However, the course grading was changed to a weighted combination of mainly objective assessment scores but also a small weighting of homework assignments. The current grading scheme is described in the subsequent section. Implementation of SBG in signals and systems This study was conducted by an electrical engineering faculty member at a medium-sized, teaching-focused university. This faculty member has taught the signals and systems course for more than ten years. The typical enrollment of a section of signals and systems at the Milwaukee School of Engineering (MSOE) ranges from the high teens to the high twenties. The signals and systems course is required for students in the biomedical engineering, computer engineering, and electrical engineering programs. The course has four hours of lecture per week over a ten-week term. The following signals and systems concepts have been identified as course learning objectives: \uf0b7 Compute the output of a continuous-time, LTI system (system analysis) o Using time-domain techniques (convolution) o Using frequency-domain techniques (Fourier analysis) \uf0b7 Analyze a continuous-time signal (signal analysis) o Derive the Fourier series coefficients for a given periodic CT signal o Determine the Fourier transform of a signal by using the FT integral or a table of common pairs and properties o Compute the power or energy, as appropriate, of a CT signal using its timeor frequency-domain representation (power/energy) \uf0b7 Plot a signal in the time or frequency domain (signal visualization) o Plot a signal as a function of time (time plot) o Determine and plot the magnitude and phase spectra of a CT signal using Fourier analysis (Fourier spectrum) \uf0b7 Determine an appropriate sampling frequency and the subsequent frequency-domain representation of a sampled CT signal o Determine an appropriate sampling frequency in order to avoid aliasing of a CT signal (Nyquist) o Plot the magnitude and phase spectra of an impulse-train-sampled CT signal (sampled spectrum) Grade determination using SBG in signals and systems Each objective is graded using a Likert-scale rubric: 5 points for exceptional work, 4 for advanced, 3 for intermediate, 2 for novice, 1 for unacceptable, and 0 for incomplete. An example rubric and example quiz and exam questions are included in the Appendix. In the previous academic year, a scale of 0 to 4 was used: 4 – exceptional, 3 – advanced, 2 – intermediate, 1 – novice, 0 – unacceptable (including incomplete). An additional point was added to the bottom of the grading scale to motivate students to regularly submit homework assignments and to complete quizzes and examinations. At the end of the course, each individual objective’s overall score is computed using the following weightings: 20% from formative assessments (quizzes), 40% from intermediate assessments (midterm exams), and 40% from summative assessments (final exam). Quizzes are given weekly to provide initial feedback for each objective (one or two objectives per quiz). Midterm exams provide a second round of feedback after the completion of several objectives. Most objectives are assessed on only one quiz (or midterm exam), but for those that are assessed on multiple quizzes (or midterms), their scores may be computed as either the average or the maximum of the quiz (or midterm) scores. Institutional policy limits the score of the final exam to be worth no more than 40% of the overall course grade, hence the 40% weighting on the final exam. It should be noted that homework assignments are given but are scored only for bona fide attempts. Homework questions are typically discussed in the class section on the day before the due date. Quizzes are given on homework due dates to assess one or two of the objectives introduced in each homework assignment. Table 1 describes the weighting of each objective or assignment toward the overall course score. Table 1: Weighting of objectives and assignments toward overall course score Objective or assignments Percentage Completion of homework assignments 10% Time plot* 5% Power/energy 10% Convolution 15% Fourier series 15% Fourier spectrum 10% Fourier transform 10% Fourier analysis 10% Nyquist 10% Sampled spectrum 5% *New objective in AY 2019 Finally, the course grade is assigned based on the overall course score as described in Table 2. Table 2: Grade assignmen