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Kategorie:Betreute Dissertationen (Karl Josef Fuchs) (Quelltext anzeigen)
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{{diss
| name= Eleni Lagoudaki, BSc., MSc.
| titel = {{INFLUENCE OF SPATIAL THINKING SKILLS TRAINING USING THE ONLINE PLATFORM RIF 3.0 ON STUDENTS’ SPATIAL THINKING AND MATHEMATICAL SKILLS}}
| hochschule=Paris Lodron Universität Salzburg
| jahr = 2022
| typ =
| betreut = Karl Josef FUCHS
| begutachtet =
| download =
| sprache = Englisch
| note =
| pruefungam =
| schulart =
| stufe =
| matheduc =
}}
== Kontext ==
<!-- The importance of research that aims at the improvement of mathematics teaching and learning cannot be questioned. The various students’ misconceptions that have been identified can become an obstacle to their latter performance. For example, some students struggle with understanding the relational dimension of the equal sign and tend to perceive it as an order to "do something". This difficulty to conceptualise the equal sign a symbol of mathematical equivalence can hinder their ability to solve equations later on (Knuth et al., 2006). Issues like students’ early development of their generalizing skills, abstract thinking, observation of arithmetic and geometric patterns, and the provision of multiple representations of mathematical objects are very crucial for their future algebraic reasoning abilities (Blanton et al., 2019; Kieran, 2004; Sutherland, 2004). The aspect of students’ future mathematical competence and the role mathematics play in following a career in STEM (Science, Technology, Engineering and Mathematics) fields, is also pointed out often by Mathematics Education researchers, which is considered highly paid (Green et al., 2017; Wai et al., 2009). Consequently, the effort to amplify mathematics instruction and ensure that students are provided the best possible educational tools in order to develop their mathematical skills and later on follow that career path, is of high importance (Green et al., 2017).
Mathematics teaching and learning have been the center of interest of many studies focusing on how students perceive and understand mathematics (Skemp, 2006) or how various emotional factors affect mathematics performance (Reyes, 1984). As Schoenfeld (2001) summarizes, the scope of research that addresses Mathematics Education is, on the one hand, to understand the nature of mathematical thinking, teaching and learning and on the other hand, to utilize those findings in order to improve the teaching of the subject. Schoenfeld (2001) also notes that the nature of this research differs from the one of Mathematics themselves precisely due to the research objectives, the posed questions that are seeked to be answered and the kind of evidence and methods that are used. In addition, due to the complex themes that research regarding mathematics teaching and learning deals with, methods and findings from various disciplines as Sociology, Cognitive Psychology and a broad range of perspectives are recruited (English et al., n.d.).
Alongside the body of Mathematics Education research and the efforts to apply those findings in practice there is also a misconception found among some teachers, students and parents that mathematics is not for everyone. In other words, it is believed that some people have that kind of “intelligence” to be competent at mathematics and others that are not fit for such a career or a profession that involves mathematics.
The proposed study will focus on a specific aspect of human intelligence namely spatial thinking, the role that it plays in mathematics performance and how its training can also support mathematics learning. More specifically, the purpose of the current study is to evaluate for the first time the online spatial training platform RIF 3.0 on its effectiveness regarding the development of 11-12 year old students’ spatial and mathematical skills. This evaluation will contribute to the improvement of the spatial training tasks contained in the platform and the enhancement of the platform’s effects. The introduction of platform RIF 3.0 comes at a time when digitization in schools is expanding, which makes the scientific development of online tools a matter of high importance. In addition, platform RIF 3.0 provides the affordance of easy and free access to spatial training, allowing students to develop their spatial skills regardless of their socioeconomic background.
Furthermore, the results of the current study will contribute to the needed deepening of our understanding of the relationship between spatial and mathematical skills (Mix, 2019). Numerous researchers have stated that there’s a need for more interventional studies to better find ways to enhance students’ spatial skills and help their performance in mathematics. This is due to the small number of studies that have taken place so far and the mixed results that they have produced (Z. C. K. Hawes et al., 2022; Mix et al., 2021). In this regard, the present study will add to this experience by examining the outcomes of the platform RIF 3.0 in a broad range of spatial and mathematics skills and propose ways for effective spatial training in the context of mathematics education.
The literature review section will cover the definition of spatial intelligence, the relationship between spatial intelligence and mathematics performance and how it can be explained, interventions that aim at improving spatial abilities and then spatial interventions that specifically target mathematical skills. In the methodology section, the contribution and the importance of the study, the research questions and the method that will be followed in order to answer them are being presented.
=== Literatur ===
<!-- Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102(2), 193–219.
Carr, M., Steiner, H. H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early emerging gender differences in mathematics competency. Learning and Individual Differences, 18(1), 61–75. https://doi.org/10.1016/j.lindif.2007.04.005
Cornu, V., Schiltz, C., Pazouki, T., & Martin, R. (2017). Training early visuo-spatial abilities: A controlled classroom-based intervention study. Https://Doi.Org/10.1080/10888691.2016.1276835, 23(1), 1–21. https://doi.org/10.1080/10888691.2016.1276835
English, L., Jones, G., Lesh, R., Tirosh, D., & Bussi, M. B. (2002). Future issues and directions in international mathematics education research. In Handbook of International Research in Mathematics Education.
Gilligan, K. A., Thomas, M. S. C., & Farran, E. K. (2020). First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years. Developmental Science, 23(4). https://doi.org/10.1111/desc.12909
Green, C. T., Bunge, S. A., Briones Chiongbian, V., Barrow, M., & Ferrer, E. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology, 157, 125–143. https://doi.org/10.1016/j.jecp.2016.12.005
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433
Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin and Review, 27(3), 465–482. https://doi.org/10.3758/s13423-019-01694-7
Hawes, Z. C. K., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of Spatial Training on Mathematics Performance: A Meta-Analysis. Developmental Psychology, 58(1), 112–137. https://doi.org/10.1037/dev0001281
Hawes, Z., Moss, J., Caswell, B., & Poliszczuk, D. (2015). Effects of mental rotation training on children’s spatial and mathematics performance: A randomized controlled study. Trends in Neuroscience and Education, 4(3), 60–68. https://doi.org/10.1016/j.tine.2015.05.001
Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139–151.
Knuth, E. J., Stephens, A. C., Mcneil, N. M., & Alibali, M. W. (2006). Does Understanding the Equal Sign Matter ? Evidence from Solving Equations. Journal for Research in Mathematics Education, 37(4), 297–312.
Kyttälä, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77–94. https://doi.org/10.1007/BF03173141
Maresch, G. (2014). Strategies for assessing spatial ability tasks. Journal for Geometry and Graphics, 18(1), 125–132.
Maresch, G., & Sorby, S. A. (2021). Perspectives on Spatial Thinking. Journal for Geometry and Graphics, 25(2), 271–293.
Mix, K. S. (2019). Why Are Spatial Skill and Mathematics Related? Child Development Perspectives, 13(2), 121–126. https://doi.org/10.1111/cdep.12323
Mix, K. S., & Cheng, Y. L. (2012). The Relation Between Space and Math. Developmental and Educational Implications. In Advances in Child Development and Behavior (Vol. 42, pp. 197–243). Academic Press Inc. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
Mix, K. S., Levine, S. C., Cheng, Y. L., Stockton, J. D. S., & Bower, C. (2021). Effects of spatial training on mathematics in first and sixth grade children. Journal of Educational Psychology, 113(2), 304–314. https://doi.org/10.1037/edu0000494
Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C., Hambrick, D. Z., Ping, R., & Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206–1227. https://doi.org/10.1037/xge0000182
Newcombe, N. (2017). Harnessing Spatial Thinking to Support Stem Learning (No. 161). Article 161. https://doi.org/10.1787/7d5dcae6-en
Publikationen – Mathematik - Materialien zu IKM und Bildungs¬standards - Nationale Kompetenzerhebung - Downloads - IQS. (n.d.). Retrieved May 29, 2022, from https://www.iqs.gv.at/downloads/nationale-kompetenzerhebung/materialien-zu-ikm-und-bildungsstandards/publikationen-mathematik
Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of Spatial Ability: Construction and Validation of the Spatial Reasoning Instrument for Middle School Students. Journal of Psychoeducational Assessment, 35(7), 709–727. https://doi.org/10.1177/0734282916659207
Reyes, L. H. (1984). Affective Variables and Mathematics Education. The Elementary School Journal, 84(5), 558–581. https://doi.org/10.1086/461384
RIF 2.0 Home english. (n.d.). Retrieved February 28, 2022, from https://www.adi3d.at/rif20/en/index.html
Schneider, M., Merz, S., Stricker, J., de Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta‐analysis. Wiley Online Library, 89(5), 1467–1484. https://doi.org/10.1111/cdev.13068
Schoenfeld, A. H. (2001). Purposes and Methods of Research in Mathematics Education. The Teaching and Learning of Mathematics at University Level, 221–236. https://doi.org/10.1007/0-306-47231-7_22
Skemp, R. R. (2006). Relational Understanding and Instrumental Understanding. Mathematics Teaching in the Middle School, 12(2), 88–95.
Sorby, S. A., & Günter, M. (2009). Spatial thinking. Research in Phenomenology, 39(3), 333–343. https://doi.org/10.1163/008555509X12472022364000
Sutherland, R. (2004). A Toolkit for Analysing Approaches to Algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 71–96). Springer, Dordrecht.
Tasks to promote spatial thinking - geometry didactics. (n.d.). Retrieved May 29, 2022, from https://geometriedidaktik.at/?page_id=1882
The basic routines of spatial thinking - geometry didactics. (n.d.). Retrieved February 28, 2022, from https://geometriedidaktik.at/?page_id=1216
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. https://doi.org/10.1037/a0028446
Verdine, B. N., Irwin, C. M., Golinkoff, R. M., & Hirsh-Pasek, K. (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. Journal of Experimental Child Psychology, 126, 37–51. https://doi.org/10.1016/j.jecp.2014.02.012
Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial Ability for STEM Domains: Aligning Over 50 Years of Cumulative Psychological Knowledge Solidifies Its Importance. Journal of Educational Psychology, 101(4), 817–835. https://doi.org/10.1037/a0016127
Xu, C., & LeFevre, J. A. (2016). Training young children on sequential relations among numbers and spatial decomposition: Differential transfer to number line and mental transformation tasks. Developmental Psychology, 52(6), 854–866. https://doi.org/10.1037/DEV0000124
Young, C. J., Levine, S. C., & Mix, K. S. (2018). The connection between spatial and mathematical ability across development. Frontiers in Psychology, 9(6). https://doi.org/10.3389/fpsyg.2018.00755
<!-- Falls Sie weitere Angaben machen möchten, dann bitte im darauf folgenden Freitext. -->
{{diss
| name= Eleni Lagoudaki, BSc., MSc.
| titel = {{INFLUENCE OF SPATIAL THINKING SKILLS TRAINING USING THE ONLINE PLATFORM RIF 3.0 ON STUDENTS’ SPATIAL THINKING AND MATHEMATICAL SKILLS}}
| hochschule=Paris Lodron Universität Salzburg
| jahr = 2022
| typ =
| betreut = Karl Josef FUCHS
| begutachtet =
| download =
| sprache = Englisch
| note =
| pruefungam =
| schulart =
| stufe =
| matheduc =
}}
== Kontext ==
<!-- The importance of research that aims at the improvement of mathematics teaching and learning cannot be questioned. The various students’ misconceptions that have been identified can become an obstacle to their latter performance. For example, some students struggle with understanding the relational dimension of the equal sign and tend to perceive it as an order to "do something". This difficulty to conceptualise the equal sign a symbol of mathematical equivalence can hinder their ability to solve equations later on (Knuth et al., 2006). Issues like students’ early development of their generalizing skills, abstract thinking, observation of arithmetic and geometric patterns, and the provision of multiple representations of mathematical objects are very crucial for their future algebraic reasoning abilities (Blanton et al., 2019; Kieran, 2004; Sutherland, 2004). The aspect of students’ future mathematical competence and the role mathematics play in following a career in STEM (Science, Technology, Engineering and Mathematics) fields, is also pointed out often by Mathematics Education researchers, which is considered highly paid (Green et al., 2017; Wai et al., 2009). Consequently, the effort to amplify mathematics instruction and ensure that students are provided the best possible educational tools in order to develop their mathematical skills and later on follow that career path, is of high importance (Green et al., 2017).
Mathematics teaching and learning have been the center of interest of many studies focusing on how students perceive and understand mathematics (Skemp, 2006) or how various emotional factors affect mathematics performance (Reyes, 1984). As Schoenfeld (2001) summarizes, the scope of research that addresses Mathematics Education is, on the one hand, to understand the nature of mathematical thinking, teaching and learning and on the other hand, to utilize those findings in order to improve the teaching of the subject. Schoenfeld (2001) also notes that the nature of this research differs from the one of Mathematics themselves precisely due to the research objectives, the posed questions that are seeked to be answered and the kind of evidence and methods that are used. In addition, due to the complex themes that research regarding mathematics teaching and learning deals with, methods and findings from various disciplines as Sociology, Cognitive Psychology and a broad range of perspectives are recruited (English et al., n.d.).
Alongside the body of Mathematics Education research and the efforts to apply those findings in practice there is also a misconception found among some teachers, students and parents that mathematics is not for everyone. In other words, it is believed that some people have that kind of “intelligence” to be competent at mathematics and others that are not fit for such a career or a profession that involves mathematics.
The proposed study will focus on a specific aspect of human intelligence namely spatial thinking, the role that it plays in mathematics performance and how its training can also support mathematics learning. More specifically, the purpose of the current study is to evaluate for the first time the online spatial training platform RIF 3.0 on its effectiveness regarding the development of 11-12 year old students’ spatial and mathematical skills. This evaluation will contribute to the improvement of the spatial training tasks contained in the platform and the enhancement of the platform’s effects. The introduction of platform RIF 3.0 comes at a time when digitization in schools is expanding, which makes the scientific development of online tools a matter of high importance. In addition, platform RIF 3.0 provides the affordance of easy and free access to spatial training, allowing students to develop their spatial skills regardless of their socioeconomic background.
Furthermore, the results of the current study will contribute to the needed deepening of our understanding of the relationship between spatial and mathematical skills (Mix, 2019). Numerous researchers have stated that there’s a need for more interventional studies to better find ways to enhance students’ spatial skills and help their performance in mathematics. This is due to the small number of studies that have taken place so far and the mixed results that they have produced (Z. C. K. Hawes et al., 2022; Mix et al., 2021). In this regard, the present study will add to this experience by examining the outcomes of the platform RIF 3.0 in a broad range of spatial and mathematics skills and propose ways for effective spatial training in the context of mathematics education.
The literature review section will cover the definition of spatial intelligence, the relationship between spatial intelligence and mathematics performance and how it can be explained, interventions that aim at improving spatial abilities and then spatial interventions that specifically target mathematical skills. In the methodology section, the contribution and the importance of the study, the research questions and the method that will be followed in order to answer them are being presented.
=== Literatur ===
<!-- Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102(2), 193–219.
Carr, M., Steiner, H. H., Kyser, B., & Biddlecomb, B. (2008). A comparison of predictors of early emerging gender differences in mathematics competency. Learning and Individual Differences, 18(1), 61–75. https://doi.org/10.1016/j.lindif.2007.04.005
Cornu, V., Schiltz, C., Pazouki, T., & Martin, R. (2017). Training early visuo-spatial abilities: A controlled classroom-based intervention study. Https://Doi.Org/10.1080/10888691.2016.1276835, 23(1), 1–21. https://doi.org/10.1080/10888691.2016.1276835
English, L., Jones, G., Lesh, R., Tirosh, D., & Bussi, M. B. (2002). Future issues and directions in international mathematics education research. In Handbook of International Research in Mathematics Education.
Gilligan, K. A., Thomas, M. S. C., & Farran, E. K. (2020). First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years. Developmental Science, 23(4). https://doi.org/10.1111/desc.12909
Green, C. T., Bunge, S. A., Briones Chiongbian, V., Barrow, M., & Ferrer, E. (2017). Fluid reasoning predicts future mathematical performance among children and adolescents. Journal of Experimental Child Psychology, 157, 125–143. https://doi.org/10.1016/j.jecp.2016.12.005
Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. https://doi.org/10.1037/a0027433
Hawes, Z., & Ansari, D. (2020). What explains the relationship between spatial and mathematical skills? A review of evidence from brain and behavior. Psychonomic Bulletin and Review, 27(3), 465–482. https://doi.org/10.3758/s13423-019-01694-7
Hawes, Z. C. K., Gilligan-Lee, K. A., & Mix, K. S. (2022). Effects of Spatial Training on Mathematics Performance: A Meta-Analysis. Developmental Psychology, 58(1), 112–137. https://doi.org/10.1037/dev0001281
Hawes, Z., Moss, J., Caswell, B., & Poliszczuk, D. (2015). Effects of mental rotation training on children’s spatial and mathematics performance: A randomized controlled study. Trends in Neuroscience and Education, 4(3), 60–68. https://doi.org/10.1016/j.tine.2015.05.001
Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139–151.
Knuth, E. J., Stephens, A. C., Mcneil, N. M., & Alibali, M. W. (2006). Does Understanding the Equal Sign Matter ? Evidence from Solving Equations. Journal for Research in Mathematics Education, 37(4), 297–312.
Kyttälä, M., & Lehto, J. E. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77–94. https://doi.org/10.1007/BF03173141
Maresch, G. (2014). Strategies for assessing spatial ability tasks. Journal for Geometry and Graphics, 18(1), 125–132.
Maresch, G., & Sorby, S. A. (2021). Perspectives on Spatial Thinking. Journal for Geometry and Graphics, 25(2), 271–293.
Mix, K. S. (2019). Why Are Spatial Skill and Mathematics Related? Child Development Perspectives, 13(2), 121–126. https://doi.org/10.1111/cdep.12323
Mix, K. S., & Cheng, Y. L. (2012). The Relation Between Space and Math. Developmental and Educational Implications. In Advances in Child Development and Behavior (Vol. 42, pp. 197–243). Academic Press Inc. https://doi.org/10.1016/B978-0-12-394388-0.00006-X
Mix, K. S., Levine, S. C., Cheng, Y. L., Stockton, J. D. S., & Bower, C. (2021). Effects of spatial training on mathematics in first and sixth grade children. Journal of Educational Psychology, 113(2), 304–314. https://doi.org/10.1037/edu0000494
Mix, K. S., Levine, S. C., Cheng, Y.-L., Young, C., Hambrick, D. Z., Ping, R., & Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206–1227. https://doi.org/10.1037/xge0000182
Newcombe, N. (2017). Harnessing Spatial Thinking to Support Stem Learning (No. 161). Article 161. https://doi.org/10.1787/7d5dcae6-en
Publikationen – Mathematik - Materialien zu IKM und Bildungs¬standards - Nationale Kompetenzerhebung - Downloads - IQS. (n.d.). Retrieved May 29, 2022, from https://www.iqs.gv.at/downloads/nationale-kompetenzerhebung/materialien-zu-ikm-und-bildungsstandards/publikationen-mathematik
Ramful, A., Lowrie, T., & Logan, T. (2017). Measurement of Spatial Ability: Construction and Validation of the Spatial Reasoning Instrument for Middle School Students. Journal of Psychoeducational Assessment, 35(7), 709–727. https://doi.org/10.1177/0734282916659207
Reyes, L. H. (1984). Affective Variables and Mathematics Education. The Elementary School Journal, 84(5), 558–581. https://doi.org/10.1086/461384
RIF 2.0 Home english. (n.d.). Retrieved February 28, 2022, from https://www.adi3d.at/rif20/en/index.html
Schneider, M., Merz, S., Stricker, J., de Smedt, B., Torbeyns, J., Verschaffel, L., & Luwel, K. (2018). Associations of number line estimation with mathematical competence: A meta‐analysis. Wiley Online Library, 89(5), 1467–1484. https://doi.org/10.1111/cdev.13068
Schoenfeld, A. H. (2001). Purposes and Methods of Research in Mathematics Education. The Teaching and Learning of Mathematics at University Level, 221–236. https://doi.org/10.1007/0-306-47231-7_22
Skemp, R. R. (2006). Relational Understanding and Instrumental Understanding. Mathematics Teaching in the Middle School, 12(2), 88–95.
Sorby, S. A., & Günter, M. (2009). Spatial thinking. Research in Phenomenology, 39(3), 333–343. https://doi.org/10.1163/008555509X12472022364000
Sutherland, R. (2004). A Toolkit for Analysing Approaches to Algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The Future of the Teaching and Learning of Algebra: The 12th ICMI Study (pp. 71–96). Springer, Dordrecht.
Tasks to promote spatial thinking - geometry didactics. (n.d.). Retrieved May 29, 2022, from https://geometriedidaktik.at/?page_id=1882
The basic routines of spatial thinking - geometry didactics. (n.d.). Retrieved February 28, 2022, from https://geometriedidaktik.at/?page_id=1216
Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. https://doi.org/10.1037/a0028446
Verdine, B. N., Irwin, C. M., Golinkoff, R. M., & Hirsh-Pasek, K. (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. Journal of Experimental Child Psychology, 126, 37–51. https://doi.org/10.1016/j.jecp.2014.02.012
Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial Ability for STEM Domains: Aligning Over 50 Years of Cumulative Psychological Knowledge Solidifies Its Importance. Journal of Educational Psychology, 101(4), 817–835. https://doi.org/10.1037/a0016127
Xu, C., & LeFevre, J. A. (2016). Training young children on sequential relations among numbers and spatial decomposition: Differential transfer to number line and mental transformation tasks. Developmental Psychology, 52(6), 854–866. https://doi.org/10.1037/DEV0000124
Young, C. J., Levine, S. C., & Mix, K. S. (2018). The connection between spatial and mathematical ability across development. Frontiers in Psychology, 9(6). https://doi.org/10.3389/fpsyg.2018.00755