Chapter 3 Spatial and non-spatial cognitive abilities among STEM beginners

191 Pages·2017·2.82 MB·English

ETH Library
In the minds of STEM beginners:
On cognitive abilities, working
memory, and first year
mathematics
Doctoral Thesis
Author(s):
Berkowitz Biran, Michal
Publication date:
2017
Permanent link:
https://doi.org/10.3929/ethz-b-000201896
Rights / license:
In Copyright - Non-Commercial Use Permitted
This page was generated automatically upon download from the ETH Zurich Research Collection.
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DISS. ETH NO. 24631
In the minds of STEM beginners: On cognitive abilities,
working memory, and first year mathematics
A thesis submitted to attain the degree of
DOCTOR OF SCIENCES of ETH ZURICH
(Dr. sc. ETH Zurich)
presented by
Michal Berkowitz Biran
MA, Tel-Aviv University
born on 19.01.1975
citizen of
Israel
accepted on the recommendation of
Prof. Dr. Elsbeth Stern
Prof. Dr. Klaus Oberauer
Prof. Dr. Norbert Hungerbühler
2017

Acknowledgements
I would like to thank first and foremost my supervisor Elsbeth Stern for giving me the
opportunity to carry out this research project. I am grateful for her support and advice along
the way, for allowing me a great deal of freedom to shape the project and for her confidence
in it.
I wish to thank Jessica Büetiger, Samuel Winiger, Nicole Bruegger and Anita Wildi for their
very helpful assistance with data collection and processing. I am very grateful to Martin Frick
for programming in Matlab and for invaluable assistance in setting up the working memory
battery.
I am very grateful to members and faculty from the departments of mechanical engineering,
math and physics at ETH, for their wonderful cooperation: Maddalena Velonà, Chiara
Daraio, Mirko Meboldt, Quentin Lohmeyer, Norbert Hungerbühler, Alexander Caspar,
Giovanni Felder, Joseph Teichmann, Manfred Einsiedler, Dietmar Salamon, Urs Lang,
Emmanuel Kowalski, Sara Uberi-Papapietro, Eva Künti, Marion Allemann-Kodlinsky,
Andreas Vaterlaus, Rainer Wallny and Niklas Mohr.
Many thanks to my colleagues Ursina Markwalder, Bruno Ruetsche, Peter Edelsbrunner,
Sarah Hofer and Anne Deiglmayr for discussions, methodological advice and for translations
into German.
Special thanks to Klaus Oberauer for sharing WM tasks and answering many questions; to
Alexander Caspar for sharing the School-mathematics Knowledge Test and related data; to
Claudia Quaiser-Pohl for sharing her test ‘Schnitte’ and related information; and to Emiko
Tsutsumi for sharing the Mental Cutting Test. I also thank David Uttal and Nora Newcombe
for their interest and feedback on this study.
The study was funded by the Dr. Donald C. Cooper-Fonds, to which I am very grateful.
Finally, I deeply thank my husband Paul Biran for his support and for his input as a
mathematician. I dedicate this work to our children Zohar and Schachar.
I

Abstract
This research project investigated individual differences in basic cognitive abilities of
undergraduate students in Science, Technology, Engineering and Mathematics (STEM).
Previous research has emphasized spatial thinking abilities as crucial for STEM learning. In
this study, the predictive validity of spatial abilities for STEM achievements was tested while
accounting for reasoning abilities in other domains, and with respect to several areas of
achievements. The main focus was on achievements in mathematics and math intensive areas
during the first undergraduate year, which constitute a central part in most study programs in
STEM. A main question was whether spatial abilities are important to math achievements as
they are to areas in which spatial tasks are central (e.g., in engineering design courses).
Additionally, the study examined which working memory components are related to
performance on different ability tests, and whether this has implications on achievement
prediction. Finally, the study also examined the interplay between cognitive factors and prior
knowledge in mathematics in predicting STEM achievements. A prospective cohort study
was conducted in a sample of first-year students at ETH Zurich (N=317) from the
departments mechanical engineering, math and physics. Multiple measures of cognitive
abilities and working memory were included, and structural equation modelling with latent
variables was the main method of statistical analysis. Spatial abilities uniquely predicted
achievements in an introductory to engineering design course, but not in math and
math-based courses. Mathematics was best predicted by numerical, verbal and general
reasoning abilities, and was weakly related to spatial abilities. Overall, the findings
indicated high domain-specificity of the link between spatial abilities and achievements.
Working memory was correlated with achievements in several cases. Differential patterns
of correlations were found between study groups, indicating differing cognitive
demands even within mathematics. Numerical reasoning ability was most strongly
related to working memory, even though students’ highest scores were on these
scales. Implications for research on working memory and intelligence are discussed.
Prior knowledge in mathematics explained some, but not all of the effects of cognitive
measures on achievements.
II

Zusammenfassung
Die vorliegende Dissertation hatte zum Ziel, individuelle Unterschiede in den grundlegenden
kognitiven Fähigkeiten von neu eintretenden Studierenden an der ETH zu untersuchen.
Zahlreiche Arbeiten betonen die Wichtigkeit von räumlichem Denken für das Lernen in
MINT Fächern. In der vorliegenden Arbeit wurde unter Berücksichtigung des
schlussfolgernden Denkens und Tests zu Arbeitsgedächtnisfunktionen die
Vorhersagevalidität von räumlichem Denken für die akademische Leistung in MINT Fächern
untersucht. Dabei wurde neben der Mathematikleistung auch Inhaltsbereiche einbezogen, die
im ersten Studienjahr der ETH zur Kernausbildung gehören und die in der Basisprüfung
erfasst werden. Eine zentrale Forschungsfrage war, ob räumliches Denken für das Erlangen
von hoher Kompetenz in Mathematik ebenso zentral ist, wie es für andere Fächer postuliert
wird (beispielsweise in Maschinenbau Designkurse). Zusätzlich wurde untersucht, ob und
wie Komponenten des Arbeitsgedächtnisses mit der Leistung in unterschiedlichen
Fähigkeitstest zusammenhängen und ob ein solcher Zusammenhang Auswirkungen auf die
Leistungsvorhersage hat. Ein weiteres Ziel der Dissertation war es, das Zusammenspiel von
kognitiven Faktoren und Vorwissen in Mathematik als Vorhersagevariablen für die Leistung
in den MINT Fächern zu untersuchen. Dazu wurde eine Prospektive Kohortenstudie mit
N=317 neu eingetretenen Studierenden aus den Departementen Maschinenbau, Mathematik
und Physik der ETH Zürich durchgeführt. Es wurden diverse Messinstrumente in den
Bereichen kognitive Fähigkeiten und der Leistung des Arbeitsgedächtnisses eingesetzt. Für
die Auswertung wurden Strukturgleichungsmodelle mit latenten Variablen gewählt.
Räumliches Denken sagte zwar die Leistung für Maschinenbau Designkurse vorher, jedoch
nicht für Mathematik und ihr nahesehende Bereiche. Mathematik konnte am besten durch
numerisches, verbales und generelles schlussfolgerndes Denken vorhergesagt werden.
Lediglich ein schwacher Bezug zu räumlichem Denken konnte festgestellt werden.
Allgemein kann gesagt werden, dass die Resultate eine stark domänenspezifische Beziehung
zwischen räumlichem Denken und Leistungen im MINT-Bereich andeuten. Tests zu
Arbeitsgedächtnisfunktionen hingegen korrelierten mit Leistungen in verschiedenen MINT
Bereichen. Die zwischen den Studiengängen gefundenen Unterschiede in den
Korrelationsmustern deuten auf unterschiedliche kognitive Anforderungen an die
Mathematikleistung hin. Numerisches schlussfolgerndes Denken und die Leistungen in den
Tests zu Arbeitsgedächtnisfunktionen korrelierten erstaunlich hoch. Dies war angesichts der
hohen Durchschnittsleistung in den numerischen Tests bemerkenswert. Vorwissen in
III
Mathematik konnte zwar einen substantiellen Teil der Varianz in der Basisprüfung erklären,
aber psychometrische und kognitive Tests leisteten einen eigenständigen Beitrag.
Implikationen für die weitere Forschung werden diskutiert.

IV
Table of contents
ACKNOWLEDGEMENTS ..................................................................................................................................... I
ABSTRACT ........................................................................................................................................................ II
ZUSAMMENFASSUNG .....................................................................................................................................III
GENERAL INTRODUCTION ................................................................................................................................ 1
CHAPTER 1
SPATIAL ABILITIES FOR SCIENCE AND MATHEMATICS: A REVIEW AND EMERGING QUESTIONS ...................... 5
1.1 SPATIAL ABILITIES IN INTELLIGENCE RESEARCH .......................................................................................................... 7
1.2 MULTIDIMENSIONALITY IN ABILITY TESTS ................................................................................................................ 8
1.3 SPATIAL ABILITIES OF STEM NOVICES IN ‘SPATIAL’ DOMAINS ...................................................................................... 9
1.4 SPATIAL ABILITIES AND MATHEMATICS ................................................................................................................. 12
1.4.1 Elementary spatial cognition and elementary mathematics: The fundamental math-space link ..... 13
1.4.2 Elementary spatial cognition and school mathematics ...................................................................... 14
1.4.3 Higher order spatial cognition and mathematics: The complex math-space link ............................... 15
1.4.4 State of research on SAs and advanced mathematics ........................................................................ 16
CHAPTER 2
THE PRESENT STUDY: METHOD AND DATA SET.............................................................................................. 19
2.1 METHOD ....................................................................................................................................................... 20
2.1.1 Sample ................................................................................................................................................ 20
2.1.2 Measures ............................................................................................................................................. 22
2.1.3 Procedure ............................................................................................................................................ 32
2.2 THE DATA SET ................................................................................................................................................. 33
2.2.1 Sample ................................................................................................................................................ 33
2.2.2 Data screening and missing data ........................................................................................................ 34
2.2.3 Descriptive statistics............................................................................................................................ 35
2.2.4 Group differences ................................................................................................................................ 38
2.3 APPROACH TO DATA ANALYSIS ............................................................................................................................ 45
CHAPTER 3
SPATIAL AND NON-SPATIAL COGNITIVE ABILITIES AMONG STEM BEGINNERS:
WHAT MATTERS FOR MATHEMATICS? .......................................................................................................... 46
3.1 METHOD ....................................................................................................................................................... 47
3.2 RESULTS ........................................................................................................................................................ 48
3.2.1 Latent structure of cognitive abilities.................................................................................................. 48
3.2.2 Multiple group invariance ................................................................................................................... 53
3.2.3 Prediction of academic achievements ................................................................................................. 54
3.2.4 Post-hoc analyses ................................................................................................................................ 60
3.2 DISCUSSION.................................................................................................................................................... 66
CHAPTER 4
DOMAIN GENERAL AND DOMAIN SPECIFIC EFFECTS OF WORKING MEMORY ON COGNITIVE ABILITIES:
INSIGHTS FROM THE HIGH ABILITY RANGE. ................................................................................................... 78
4.1 INTRODUCTION ............................................................................................................................................... 78
4.2 RESEARCH QUESTIONS ...................................................................................................................................... 85
4.3 METHOD ....................................................................................................................................................... 85
4.4 RESULTS ........................................................................................................................................................ 89
V