Spatial Training and Calculus Ability: Investigating Impacts on Student Performance and Cognitive Style

Spatial abilities are an important, and often overlooked, component of Science, Technology, Engineering and Mathematics (STEM) education with skills like spatial visualisation and mental rotation being important for technical professions such as engineering. Individual differences in spatial abilities have been reported throughout the years. Factors such as being female or having a low-socioeconomic status are linked with lower spatial abilities level. Spatial abilities training interventions have proven to be effective, with some showing improvements, not only in spatial abilities level, but also in the success and retention of students enrolled on STEM degree programmes, especially for women. In todays’ technological society, STEM outreach activities are a common method to promote STEM for children, showing them role models in the area, and improving their self-efficacy, sense of belonging and motivation to follow careers in STEM. At the same time, the underrepresentation seen in the area (e.g., women; LGBTQ+ community; ethnic minorities; and other marginalised groups) needs to be addressed in order to enhance the inclusive environment of these fields. This concept paper discusses review work in relation to underrepresented groups and how future spatial abilities studies should consider integrating the knowledge from past spatial abilities studies into STEM outreach activities. This integration can make spatial training available to more people, revealing itself to be a useful tool in helping diminish underrepresentation in STEM.

Spatial training has been indicated as a possible solution for improving Science, Technology, Engineering, and Mathematics (STEM) achievement and degree attainment. Advocates for this approach have noted that the correlation between spatial ability and several measures of STEM achievement suggests that spatial training should focus on improving students’ spatial ability. Although spatial ability can be improved with targeted training, few studies have examined specifically the relation between spatial training and STEM achievement. In this brief report, we review the evidence to date for the effectiveness of spatial training. We argue that spatial training offers one of the many promising avenues for increasing student success in STEM fields, but research studies that show such training causally improve retention, achievement, and degree attainment remain outstanding.

Previous research has shown that psychometrically assessed cognitive abilities are predictive of achievements in science, technology, engineering and mathematics (STEM) even in highly selected samples. Spatial ability, in particular, has been found to be crucial for success in STEM, though its role relative to other abilities has been shown mostly when assessed years before entering higher STEM education. Furthermore, the role of spatial ability for mathematics in higher STEM education has been markedly understudied, although math is central across STEM domains. We investigated whether ability differences among students who entered higher STEM education were predictive of achievements during the first undergraduate year. We assessed 317 undergraduate students in Switzerland (150 from mechanical engineering and 167 from math-physics) on multiple measures of spatial, verbal and numerical abilities. In a structural equation model, we estimated the effects of latent ability factors on students’ achievements on a range of first year courses. Although ability-test scores were mostly at the upper scale range, differential effects on achievements were found: spatial ability accounted for achievements in an engineering design course beyond numerical, verbal and general reasoning abilities, but not for math and physics achievements. Math and physics achievements were best predicted by numerical, verbal and general reasoning abilities. Broadly, the results provide evidence for the predictive power of individual differences in cognitive abilities even within highly competent groups. More specifically, the results suggest that spatial ability’s role in advanced STEM learning, at least in math-intensive subjects, is less critical than numerical and verbal reasoning abilities.

The independent campus curriculum is an effort to increase competition in the 21st century, which requires competent human resources in the fields of science, technology, engineering and mathematics (STEM). STEM learning responds to the need to increase students' interest and skills in these areas. This study aims to determine the effect of using the STEM approach on spatial thinking skills in cartography learning. This research uses a quasi-experimental method with a one-group pretest-posttest Design, conducted in a single experimental class without a control class. Subjects were selected by random sampling through drawing lots, focusing on 5th-semester B students. Data were analysed using a t-test with paired samples T-Test. The results showed a sig value. (2-tailed) of 0.000, which is smaller than the significance value of 0.05. Therefore, H0 is rejected, and Hₐ is accepted. To conclude, there is an increase in the average pretest and posttest after learning using the STEM approach, indicating that the STEM approach positively affects spatial thinking skills. Each stage of the STEM approach affects the students' spatial abilities. The science stages develop spatial abilities in the form of spatial interaction. The technology stages enhance the ability to apply applications and scale on maps. The engineering stage fosters analytical, representative and comprehensive skills. The math stage improves the ability to calculate scale and its application in everyday life.Keywords: spatial skills, STEM, cartography

Students’ spatial visualization ability is a key component in understanding geometry, yet many students exhibit suboptimal performance in this area. This study aimed to (1) evaluate the quality of the Geogebra-assisted 6E-IM learning model, (2) examine its effect on students' spatial visualization ability, and (3) describe students' ability levels after receiving the intervention. A sequential explanatory mixed-methods design was used. The independent variable was the Geogebra-assisted 6E-IM model, while the dependent variable was students’ spatial visualization ability. A total of 60 students participated, with 30 assigned to the experimental group and 30 to the control group. Data were collected through tests, interviews, and questionnaires. Quantitative results showed that students in the experimental group significantly outperformed the control group (p < 0.05), indicating a positive effect of the Geogebra-assisted 6E-IM model on spatial visualization ability. Qualitative analysis revealed that students with high ability met all spatial visualization indicators; those with moderate ability met two indicators, while those with low ability met only one. These findings demonstrate that the integration of Geogebra in the 6E-IM learning model can effectively enhance students’ spatial visualization skills in geometry. This study contributes to the development of innovative, technology-integrated instructional strategies in mathematics education.

The goal of this study was to investigate cognitive style (the visualizer–verbalizer dimension) and cognitive ability (spatial and verbal abilities) in terms of corresponding resource use behavior. The study further examined the potential link between cognitive style and cognitive ability based on observable behavior. A total of 67 university students participated in the study by completing an online survey containing a series of questionnaires, tests, and tasks, which assessed their cognitive style, cognitive ability, and resource use behavior. Multinomial logistic regression analyses revealed that cognitive style in general predicts resource use behavior. The findings also showed that spatial ability, particularly lower spatial ability, predicts resource use behavior. This study thus contributes to the literature with theory-based, empirical evidence that cognitive ability is reflected in cognitive style. This study further provides information needed to better understand the interplay between individuals’ cognitive style and cognitive ability and how these may be addressed in the design and implementation of learning environments.

This study investigated prospective social studies teachers’ spatial abilities. It was conducted with 234 prospective teachers attending Social Studies Teaching departments at Education Faculties of two universities in Central and Southern Anatolia. This study, designed according to the explanatory-sequential design, is a mixed research method, involving two stages. The first stage was conducted in the causal-comparative research design. The data were collected using “Mental Rotation Test” and “Surface Development Test”. Descriptive statistics, MANOVA and ANOVA were used to analyze the data. The second stage was designed as a case study. “Opinion Form for Spatial Ability Tests” was used to elicit the views of 37 prospective teachers (F:20, M:17) identified via the purposive sampling method. The qualitative data obtained were analyzed using the content analysis technique. The study results showed that spatial visualization and mental rotation abilities of the prospective teachers were low; male prospective teachers were betterqualified than female ones in mental rotation but spatial visualization ability did not vary by gender. Moreover, prospective teachers with higher academic averages had better spatial abilities. Integrating virtual environment applications such as Google Earth etc. into social studies courses and using them in these courses can help to improve prospective teachers’ spatial abilities.

Spatial reasoning is required for many topics in undergraduate mathematics as well as other STEM fields. In calculus specifically, there are few interventions that assess students’ spatial skills and provide remediation. Haptic technology is a novel approach to spatial skills remediation due to its unfamiliarity to students and its flexibility with regard to models. The purpose of this dissertation is two-fold: first, to determine what level of spatial abilities students possess upon entering an undergraduate calculus course, and second, to determine whether haptic feedback will enhance an intervention for improving spatial skills. The dissertation research was a mixed-methods study using the combination of a quantitative spatial reasoning test, semi-structured interviews, and student activities. The design of the study was pre-test – post-test matched subject, using the quantitative spatial reasoning test – the Santa Barbara Solids Test (SBST) – and other demographic information to match students of similar spatial reasoning abilities and backgrounds for the qualitative part of the study. In all, 306 students completed both the SBST pre-test and post-test. Ten of these students were selected as matched pairs, of which nine completed the pre-interview, intervention activities, and post-interview, leaving eight students in four matched pairs for the qualitative analyses. Analysis of the pre-test and post-test scores showed that the students who completed the intervention activities performed significantly better on the SBST post-test than on the pre-test. Furthermore, these students improved their scores more than the students who did not complete the intervention activities, and the difference between these groups was significant. While some differences were noted between the students who completed the intervention activities with haptic feedback and those who completed them without, there were not significant differences in performance on the post-test, nor the improvement from the pre-test to the post-test. The pre-interviews and post-interviews were coded using the spatial skills framework created by Engelke et al. (2016). Examination of the codes applied to each set of interviews showed a similar ratio of codes in each set. Both interviews contained an overwhelming majority of visualization language over orientation language. The most prominent subcategory displayed was representing objects, followed by structuring, mathematical properties, and finally measurement. The students who completed the intervention activities with haptic feedback and those who completed them without showed similar changes in their spatial language between the pre-interview and post-interview. Analysis of the scores of the interview questions did not show a significant difference between

In this study, we explored the relationship between two predictors of engineering success: spatial ability and self-efficacy. Spatial ability, especially mental rotation, has been linked to successful performance in engineering. Self-efficacy is an individual’s belief in his or her ability to perform successfully [1] and has received increased attention as a predictor of persistence in STEM fields. We examined the possible relationships between mental rotation, spatial visualization, engineering self-efficacy, and self-efficacy for two subsets of skills important in engineering majors: tinkering and design. Tinkering refers to the hands-on ability to construct, take apart, modify, and repair mechanical devices while design refers to the ability to develop a system, component or set of processes to solve a specific problem. We also investigated the possible role of previous design or tinkering related experience such as certain hands-on hobbies. We found spatial ability was correlated with multiple forms of engineering self-efficacy in less experienced, but not more experienced engineering students. Tinkering and design related hobbies were not related to spatial ability, but were related to tinkering and design self-efficacy. They also predicted performance on a measure of mechanical reasoning. Gender differences in engineering students on spatial ability and general engineering self-efficacy were small. The largest and most consistent gender differences were on tinkering-related experience and tinkering self-efficacy, although the latter appeared to be mitigated by the amount of engineering experience. Individual differences in tinkering-related experience is an understudied possible source of individual and gender differences in STEM fields such as engineering.

Spatial skills are associated with mathematics skills, but it is unclear if spatial training transfers to mathematics skills for preschoolers, especially from underserved communities. The current study tested (a) whether spatial training benefited preschoolers' spatial and mathematics skills, (b) if the type of feedback provided during spatial training differentially influenced children's spatial and mathematics skills, and (c) if the spatial training's effects varied by socioeconomic status (SES). Preschoolers (N = 187) were randomly assigned to either a 'business-as-usual' control or one of three spatial training groups (modeling and feedback [MF]; gesture feedback [GF]; spatial language feedback [SLF]). Three-year-olds were trained to construct puzzles to match a model composed of various geometric shapes. New models were created similar to the 2-dimensional trials of the Test of Spatial Assembly (TOSA). Training was given once per week for 5 weeks. Preschoolers were pretested and posttested on 2D and 3D TOSA trials, spatial vocabulary, shape identification, and 2 mathematics assessments. Results indicate that first, any spatial training improved preschoolers' 2D TOSA performance, although a significant interaction with SES indicated improvement was driven by low-SES children. Furthermore, low-SES children showed greatest gains on the 2D TOSA with MF and GF. Second, MF and GF improved low-SES children's performance on the 3D TOSA. Third, only low-SES children with MF saw improvements in far-transfer to mathematics (Woodcock-Johnson: Applied Problems, but not the Test of Early Mathematical Ability). Results indicate that, especially for low-income learners, spatial training can improve children's early spatial and mathematics skills. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

Can spatial training improve long-term outcomes for gifted STEM undergraduates?

Culture affects people’s spatial memory, mental representations, and spatial reference frameworks. People with different cultural backgrounds show different degrees of spatial ability. However, the current research does not reveal the shaping of spatial ability by culture from the perspective of visual cognition. In this study, we used eye tracking and designed mental rotation, spatial visualization, spatial orientation, and spatial correlation tasks to compare the spatial ability of Chinese and Malaysian Chinese people. The results showed that there were some minimal differences between them. Chinese participants had higher accuracy in the mental rotation task, showed more fixation to landmarks in spatial orientation, showed more fixation to the main map, and switched more frequently between the two thematic maps when judging spatial relationships. As “cultural citizens” of China, Malaysian Chinese people’s spatial ability is not only shaped by their own ethnic culture in terms of language but also influenced by foreign races in terms of education, wayfinding tendency, and cognitive style. This study can contribute to the understanding of the influence of culture on spatial ability and its possible causes.

Empirical evidence in literature identified significant association between spatial ability and educational performance particularly in science, technology, engineering and mathematics (STEM). The purpose of this study was to explore pre-service teachers’ spatial skills in solving mathematics problems, in the context of coordinate geometry. It is envisaged that spatial skills allow for the perception of visual information and, therefore, spatial cognition has been considered as a key skill in teaching mathematics. However, literature asserts that teachers are ill prepared to teach mathematics, hence there is limited use and misuse of spatial skills in teaching the subject. This study, therefore, examines the spatial orientation of pre-service teachers in teaching coordinate geometry. This is a mixed methods study in which pre-service teachers answered a coordinate geometry test to explore their content knowledge and their ability to interpret, analyse and apply visual spatial models to solve mathematical problems in coordinate geometry. The study established that the spatial orientation skills of pre-service teachers determine their performance in mathematics, especially coordinate geometry.

In the realm of virtual reality (VR) research, the synergy of methodological advancements, technical innovation, and novel applications is paramount. Our work encapsulates these facets in the context of spatial ability assessments conducted within a VR environment. This paper presents a comprehensive and integrated framework of VR, eye-tracking, and electroencephalography (EEG), which seamlessly combines measuring participants’ behavioral performance and simultaneously collecting time-stamped eye tracking and EEG data to enable understanding how spatial ability is impacted in certain conditions and if such conditions demand increased attention and mental allocation. This framework encompasses the measurement of participants’ gaze pattern (e.g., fixation and saccades), EEG data (e.g., Alpha, Beta, Gamma, and Theta wave patterns), and psychometric and behavioral test performance. On the technical front, we utilized the Unity 3D game engine as the core for running our spatial ability tasks by simulating altered conditions of space exploration. We simulated two types of space exploration conditions: (1) microgravity condition in which participants’ idiotropic (body) axis is in statically and dynamically misaligned with their visual axis; and (2) conditions of Martian terrain that offers a visual frame of reference (FOR) but with limited and unfamiliar landmarks objects. We specifically targeted assessing human spatial ability and spatial perception. To assess spatial ability, we digitalized behavioral tests of Purdue Spatial Visualization Test: Rotations (PSVT: R), the Mental Cutting Test (MCT), and the Perspective Taking Ability (PTA) test and integrated them into the VR settings to evaluate participants’ spatial visualization, spatial relations, and spatial orientation ability, respectively. For spatial perception, we applied digitalized versions of size and distance perception tests to measure participants’ subjective perception of size and distance. A suite of C# scripts orchestrated the VR experience, enabling real-time data collection and synchronization. This technical innovation includes the integration of data streams from diverse sources, such as VIVE controllers, eye-tracking devices, and EEG hardware, to ensure a cohesive and comprehensive dataset. A pivotal challenge in our research was synchronizing data from EEG, eye tracking, and VR tasks to facilitate comprehensive analysis. To address this challenge, we employed the Unity interface of the OpenSync library, a tool designed to unify disparate data sources in the fields of psychology and neuroscience. This approach ensures that all collected measures share a common time reference, enabling meaningful analysis of participant performance, gaze behavior, and EEG activity. The Unity-based system seamlessly incorporates task parameters, participant data, and VIVE controller inputs, providing a versatile platform for conducting assessments in diverse domains. Finally, we were able to collect synchronized measurements of participants’ scores on the behavioral tests of spatial ability and spatial perception, their gaze data and EEG data. In this paper, we present the whole process of combining the eye-tracking and EEG workflows into the VR settings and collecting relevant measurements. We believe that our work not only advances the state-of-the-art in spatial ability assessments but also underscores the potential of virtual reality as a versatile tool in cognitive research, therapy, and rehabilitation.

Spatial ability is discussed in terms of psychometric factors and information processing research. Reanalysis of major psychometric studies suggests two major spatial factors — spatial relations and spatial visualization ability. Apparent differences between these factors in speed versus power and cognitive complexity are verified by process analyses of individual differences in spatial relations and visualization ability. Information processing studies suggest multiple sources of individual differences such as process execution speed, quality and capacity of representation, process coordination and strategies for problem solution. Consideration is also given to additional issues for research as well as implications for testing.