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<p>  </p> <p>Sketching is a valuable skill in engineering for representing information, developing design ideas, and communicating technical and abstract information. Design thinking is supported through sketching as a means of translating between internal and external representations, and creating shared representations of collaborative thinking. Sketching is also an important means of developing spatial abilities which are predictive of success in STEM fields. Computer-based design visualization tools have largely replaced freehand sketching in undergraduate engineering classrooms, but the shift has negatively impacted students’ design thinking and spatial reasoning skills. While many published classroom assessments of engineering and engineering design sketching skill exist, few are linked to theory of mental rotation and mental imagery, and the validity evidence for these instruments is scarce. This dissertation reports the development of a new instrument to assess sketching skills in engineering education based on spatial reasoning skills. </p> <p>The first study is a systematic literature review of engineering education literature on sketching assessment, sketching constructs and metrics were identified across existing tests, as well as cognitive theory which informed their use and wider learning contexts and purposes for sketching assessment. From content analysis after abstract and full paper sorting and review, metrics on accuracy, perspective, line quality, annotations, and aesthetics were found to be most prevalent. Cognitive skills included perceiving the sketch subject, creatively sketching ideas, using metacognition to monitor the sketching process, and communication. Sketching assessment varies by discipline and relies on feedback and scores or grades as well as expert review. </p> <p>From these findings, a new Object Assembly Test of Sketching was developed to evaluate sketching skills on 3-dimensional mental imagery and mental rotation tasks in 1- and 2-point perspective. The second study describes two rounds of pilot testing and revisions to the Object Assembly Test over Fall 2021 and Spring 2022 in two sections of an undergraduate mechanical engineering course. Initial inter-rater reliability values were low and rubric categories had inconsistent performance, and mean scores suggested line quality metrics were more difficult for students than shape quality metrics. Revisions to rubric categories were made after consulting with subject matter experts in engineering design, industrial design, and assessment, and a second round of pilot testing showed improvement in reliability between raters with similar patterns of mean scores. </p> <p>The third study presents reliability and preliminary validity evidence for the Object Assembly Test’s use in undergraduate mechanical engineering design graphics courses. Correlation and repeated-measures ANOVA were used to investigate pre-post score differences before and after sketching classroom learning intervention. A linear relationship between Object Assembly scores and intelligent tutoring software sketching metrics was also modeled for pre-post scores. Inter-rater reliability was improved through two rounds of grading and discussion. Correlations were moderately positive between scores and metrics, with more complex exercises negatively related to Speed. Post-test scores were significantly higher than pre-test scores but did not interact significantly with skill. Linear regression results showed some significant prediction of Precision and Smoothness by shape quality metrics, and a clear speed-accuracy tradeoff with negative prediction of Speed by nearly all sketching skills. </p> <p>We anticipate future use for this instrument where instructors and researchers may implement the sketching exercises and rubric in engineering classrooms alongside 3-dimensional drawing software. The Object Assembly Test can provide students with opportunities to practice perspective sketching before using computer design tools, as well as apply mental imagery and mental rotation cognition when manipulating complex solid shapes for sketching. Ongoing validation studies with this instrument will expand to a more diverse test-taking population and develop a theoretical model of mental rotation and mental imagery skills to inform object assembly sketching. </p>

The WMC-gF relationship has been attributed to attentional control by some, and to a learning-based account by others. The current study explores inconsistencies in solving structurally-identical problems and how such factors may explain the WMC-gF relationship. Participants completed multiple versions of the same visual-analogies problems, with some problems sharing surface features and others looking vastly different, to test the ability to generalize a rule. In addition, subsequent iterations were shown either immediately after the first presentation, after two intervening items (second presentation), or after at least 10 intervening items (third presentation). Performance on second-presentation items supported both attention and learning-based accounts and performance on third-presentation items supported only a learning-based account. Furthermore, surface similarities interacted with third-presentation item accuracy and WMC, with a stronger relationship for dissimilar looking items. These findings suggest that the ability to learn and generalize rules throughout a task may largely contribute to the WMC-gF relationship.

<p> In this thesis, we undertake a study of imperative reasoning. Beginning with a philosophical analysis of the distinction between imperative and functional language features, we define a (pure) imperative language as one whose constructs are inherently referentially opaque. We then give a definition of a reasoning language by identifying desirable properties such a language should have.</p> <p> The rest of the thesis presents a new pure imperative reasoning language, Assignment Calculus AC. The main idea behind AC is that R. Montague's modal operators of intension and extension are useful tools for modeling procedures in programming languages. This line of thought builds on T. Janssen's demonstration that Montague's intensional logic is well suited to dealing with assignment statements, pointers, and other difficult features of imperative languages.</p> <p> AC consists of only four basic constructs, assignment 'X := t', sequence 't; u', procedure formation 'it' and procedure invocation '!t'. Three interpretations are given for AC: an operational semantics, a denotational semantics, and a term-rewriting system. The three are shown to be equivalent. Running examples are used to illustrate each of the interpretations.</p> <p> Five variants of AC are then studied. By removing restrictions from AC's syntactic and denotational definitions, we can incorporate L-values, lazy evaluation, state backtracking, and procedure composition into AC. By incorporating procedure composition, we show that AC becomes a self-contained Turing complete language in the same way as the untyped λ-calculus: by encoding numerals, Booleans, and control structures as AC terms. Finally we look at the combination of AC with a typed λ-calculus.</p> / Thesis / Doctor of Philosophy (PhD)

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