Technological University Dublin ARROW@TU Dublin Doctoral Engineering 2017-9 Spatial Thinking in the Engineering Curriculum: an Investigation of the Relationship Between Problem Solving and Spatial Skills Among Engineering Students. Gavin Duffy Technological University Dublin, [email protected] Follow this and additional works at: https://arrow.tudublin.ie/engdoc Part of the Other Electrical and Computer Engineering Commons Recommended Citation Duffy, G. (2017) Spatial Thinking in the Engineering Curriculum: an Investigation of the Relationship Between Problem Solving and Spatial Skills Among Engineering Students. Doctoral thesis, DIT, 2017. This Theses, Ph.D is brought to you for free and open access by the Engineering at ARROW@TU Dublin. It has been accepted for inclusion in Doctoral by an authorized administrator of ARROW@TU Dublin. For more information, please contact [email protected], [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License Spatial thinking in the engineering curriculum: an investigation of the relationship between problem solving and spatial skills among engineering students. A thesis submitted to Dublin Institute of Technology in fulfilment of the requirements for the degree of Doctor of Philosophy By Gavin Duffy, BE (Chem.), M. Eng. Sc., M. Sc. Applied e-Learning School of Electrical & Electronic Engineering, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland September 2017 Supervisor: Professor Brian Bowe, College of Engineering & Built Environment, DIT Abstract Long considered a primary factor of intelligence, spatial ability has been shown to correlate strongly with success in engineering education, yet is rarely included as a learning outcome in engineering programmes. A clearer understanding of how and why spatial ability impacts on performance in science, technology, engineering and mathematics (STEM) subjects would allow educators to determine if spatial skills development merits greater priority in STEM curricula. The aim of this study is to help inform that debate by shedding new light on the role of spatial thinking in STEM learning and allow teaching practice and curriculum design to be informed by evidence based research. A cross cutting theme in STEM education – problem solving – is examined with respect to its relationship with spatial ability. Several research questions were addressed that related to the role and relevance of spatial ability to first year engineering education and, more specifically, the manner in which spatial ability is manifest in the representation and solution of word story problems in mathematics. Working with samples of engineering students in Ireland and the United States, data were collected in the form of responses to spatial ability tests and problem solving exercises in the areas of mathematics and electric circuits. Following a pilot study to select and refine a set of mathematical story problems a mixed methods design was followed in which data were first analysed using quantitative methods to highlight phenomena that were then explored using an interpretive approach. With regard to engineering education in general, it was found that spatial ability cannot be assumed to improve as students progress through an engineering programme and that spatial ability is highly relevant to assessments that require reasoning about concepts, novel scenarios and problems but can remain hidden in overall course grades possibly due to an emphasis on assessing rote learning. With regard to problem solving, spatial ability was found to have a significant relationship with the problem representation step but not with the solution step. Those with high levels of spatial ability were more able to apply linguistic and schematic knowledge to the problem representation phase which led to higher success rates in translating word statements to mathematical form. ii Declaration I certify that this thesis which I now submit for examination for the award of PhD, is entirely my own work and has not been taken from the work of others, save and to the extent that such work has been cited and acknowledged within the text of my work. This t hesis was prepared according to the regulations for postgraduate study by research of the Dublin Institute of Technology (DIT) and has not been submitted in whole or in part for another award in any other third level institution. The work reported on in this thesis conforms to teh principle s and requirements of the DIT's guidelines for ethics in research. DIT has permission to keep, lend or copy this thesis in whole or in part, on condition that any such use of the material of the thesis be duly acknowledged. 9-Feb-2018 Signature: ______________________________ Date: _______________ Gavin Duffy, BE (Chem.), M. Eng. Sc., M. Sc. Applied e-Learning iii Acknowledgements To Brian for his always insightful comments, probing questions and support; to Sheryl for her kindness and generosity in all matters, research and otherwise; to Steve for his kindness and assistance in collecting data and moving couches; to colleagues in CREATE for collaborations and discussions; to the students who participated in this study; and to colleagues in my school for the various ways I was supported during the project. I am indebted to my own family who were uprooted to spend a year in Ohio while I worked on this project; it was a lot to ask and I very much appreciate the sacrifice they made for me. As always, my parents were extremely supportive in so many ways and I am very grateful to them. I gratefully acknowledge the support of the National Science Foundation for this work through grant number DRL-1535356. I gratefully acknowledge the fee support I have received from DIT while registered as a PhD student. iv Table of contents Abstract .......................................................................................................................................... ii Declaration .................................................................................................................................... iii Acknowledgements ....................................................................................................................... iv Table of contents ........................................................................................................................... v Table of illustrations and figures ................................................................................................... x Chapter 1 Introduction ................................................................................................................. 1 1.1 Background and rationale ................................................................................................... 2 1.2 Context and outline of thesis .............................................................................................. 6 Summary ................................................................................................................................... 9 Chapter 2 Literature Review ....................................................................................................... 11 2.1 Spatial ability and intelligence/Factors of intelligence ..................................................... 12 Defining spatial ability ......................................................................................................... 16 Measuring spatial ability ..................................................................................................... 21 2.2 Spatial ability in the STEM curriculum .............................................................................. 27 Weak visualizers and malleability of spatial skills ............................................................... 30 STEM curriculum components related to spatial ability ..................................................... 31 2.3 Problem solving ................................................................................................................. 43 Problem solving in mathematics ......................................................................................... 47 Problem solving in physics .................................................................................................. 53 Spatial ability and solving word problems in mathematics ................................................ 56 v Conclusions ............................................................................................................................. 59 Chapter 3 Research Design ......................................................................................................... 62 3.1 Philosophical considerations in social science research ................................................... 63 Epistemology ....................................................................................................................... 64 Ontology – the role of prior assumptions ........................................................................... 68 A mixed methods design ..................................................................................................... 69 3.2 Procedure/Research process ............................................................................................ 72 Spatial ability vs. Problem representation, quantitative work ........................................... 74 Spatial ability vs. Problem representation - qualitative work............................................