Relation of Spatial Skills to Calculus Proficiency: A Brief Report

Cromley, Jennifer G.; Booth, Julie L.; Wills, Theodore W.; Chang, Briana L.; Tran, Nhi; Madeja, Michael; Shipley, Thomas F.; Zahner, William

doi:10.1080/10986065.2017.1258614

Cited by 16 publications

(12 citation statements)

References 45 publications

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“…To expand on this instrument, we added items to the survey about what "being good at math in engineering" means to students. To answer the second research question, we added a conceptual calculus assessment [127,128]. This instrument requires no calculations, only graphical evaluations of functions and derivatives and concept knowledge of integrals and limits.…”

Section: Methodsmentioning

confidence: 99%

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Mathematical Maturity for Engineering Students

Faulkner

Earl

Herman

2019

Int. J. Res. Undergrad. Math. Ed.

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This dissertation presents four studies on the mathematical education of engineering students. The first study is a qualitative analysis of the beliefs of engineering faculty at a single institution regarding what constitutes "mathematical maturity" for engineering students. Faculty emphasized the need for mathematical modeling skills, fluent symbolic representation skills, and a combination of effortless algebraic fluency and ability to use computational tools. The second study is an analysis of the beliefs of engineering faculty at a variety of institutions. These faculty also emphasized modeling, representation, and computation, corroborating the results of the first study. The third study is an analysis of the mathematical content of engineering circuits and statics homework problems. Just 8% of statics problems and 20% of circuits problems use calculus, and in a much more limited way than what is taught in calculus. The fourth study presents a quantitative survey of engineering sophomores' perceptions of the relevance of mathematics to their engineering studies. The students have somewhat favorable views of the relevance of mathematics, but some high-performing students view mathematics as irrelevant.ii To David Pierce, for starting me on the path to becoming an educator.And to Caitlin McGuire, for helping me complete that journey.iii

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Section: Methodsmentioning

confidence: 99%

“…This instrument is taken from Cromley et al [128]. Directions: Solve each of the following problems, using any available space for scratch work.…”

Section: Appendix D Conceptual Measure Of Calculus Knowledgementioning

confidence: 99%

Mathematical Maturity for Engineering Students

Faulkner

Earl

Herman

2019

Int. J. Res. Undergrad. Math. Ed.

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“…This makes understanding the core processes which allow students to engage in problem solving, and which are enhanced through problem solving, of paramount importance for increasing the efficacy of pedagogical practices. In STEM education, spatial ability has been shown to correlate with academic performance in multiple sub-disciplines including biology (Rochford 1985;Russell-Gebbett 1985), chemistry (Small and Morton 1983;Wu and Shah 2004), physics (Kozhevnikov et al 2007), mathematics (Cheng and Mix 2014;Cromley et al 2017;Pittalis and Christou 2010;Sorby et al 2013), computer programming (Jones and Burnett 2008), design (Lin 2016), engineering graphics (Marunic and Glazar 2013), geometry (Suzuki et al 1990), and engineering (Alias et al 2002;Sorby 2009). Furthermore, a number of longitudinal studies examining the association between spatial ability and STEM across multiple subdisciplines provide evidence which categorically demonstrates its importance (Shea et al 2001;Wai et al 2009;Webb et al 2007).…”

Section: Introductionmentioning

confidence: 99%

Investigating the use of spatial reasoning strategies in geometric problem solving

Buckley

Seery

Canty

2018

Int J Technol Des Educ

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A core aim of contemporary science, technology, engineering, and mathematics (STEM) education is the development of robust problem-solving skills. This can be achieved by fostering both discipline knowledge expertise and general cognitive abilities associated with problem solving. One of the most important cognitive abilities in STEM education is spatial ability however understandings of how students use this ability in practice are currently underdeveloped. Therefore, this study aimed to investigate how levels of spatial ability impacted both performance and approaches to problem solving. In the context of graphical education, selected due to its significant overlap with technological, mathematical and engineering knowledge, a repeated cross-sectional study design was implemented to gather longitudinal data of student approaches to problem solving. A battery of psychometric tests of spatial ability was administered to two cohorts and problem solving was examined through a variety of graphical problems. The findings illustrate a relationship between attaining higher levels of spatial ability and performance. Participants with lower levels of spatial ability evidenced the utilisation of models to a greater extend with a particular emphasis on models with the capacity to alleviate the need for spatial reasoning.

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“…Albeit with a gifted sample of participants who had scored within the top .5% on SAT tests, Lubinski and Benbow (2006) concluded that participants who pursued STEM majors and later held STEM careers exhibited talent in mental rotation as early as age 13. Unlike previous studies, however , Cromley et al (2017) compared the relative predictive value of mental rotation to paper folding. After accounting for the degree of shared variance between the two tasks, mental rotation emerged as a unique predictor of performance on AP calculus exam questions, which tend to reflect AP textbook content and respective classroom instruction.…”

Section: Overview Of Findingsmentioning

confidence: 99%

Predictability of Visual Processes on Performance in Geometry

Weckbacher¹,

Okamoto²

2018

JEL

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There is a consensus that certain cognitive abilities and mathematics performance are related. This link also extends to geometry. Surprisingly, however, little research has examined specific aspects of cognition that may contribute to successful performance in geometry, particularly at the secondary level. In this study, we explored in what ways, if any, three types of cognitive abilities (spatial visualization, mental rotation, and imagery ability) and one’s preferred cognitive style (a visualizer or verbalizer style) might be related to geometry. High school students who have already taken at least two quarters of geometry participated in the study (N = 114). The results showed that the two spatial measures, not cognitive style, were significantly correlated to geometry performance. Of the two spatial measures, paper folding, not mental rotation, emerged as a significant predictor of geometry performance. The interpretations of the current findings as well as educational implications are discussed.

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Relation of Spatial Skills to Calculus Proficiency: A Brief Report

Cited by 16 publications

References 45 publications

Mathematical Maturity for Engineering Students

Mathematical Maturity for Engineering Students

Investigating the use of spatial reasoning strategies in geometric problem solving

Predictability of Visual Processes on Performance in Geometry

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