Skip to main content
SpringerLink
Log in

Transforming the established perceptions of visuospatial reasoning: integrating an ecocultural perspective

  • Original Article
  • Published:
Mathematics Education Research Journal Aims and scope Submit manuscript

Abstract

Many studies on visuospatial reasoning have drawn upon a psychological perspective. Importantly, some research has shown that spatial capabilities are developed through experiences and others emphasize the value of physical involvement. This article reports on investigations of how ecocultural experiences, that is cultural experiences in the environment, are examples of physical involvement that require thought and develop visuospatial reasoning about the environment. Such experiences and reasoning are significant in culture and in mathematical thinking. This article was developed by comparing and contrasting research reports from diverse cultural groups, my own studies and lived experiences. Most studies used ethnomethodologies through field work, unstructured interviews and yarning, that is talking about the experiences as they occur or in retrospect or in terms of cultural purpose and mathematical implications. Interestingly, many vignettes reveal close links to the traditional psychological spatial capabilities. Overarching many of the studies were cultural relationships between educators, learners and learning. These studies extend our understanding of visuospatial reasoning to show diverse approaches to many areas associated with school mathematics education. This is particularly noticeable in categorizing and using shapes and location and in the use of symmetry, measurement and proportional reasoning. Other findings were that past experiences within a particular ecocultural environment impact intentions, attention and noticing, which, in turn, affect mathematics learning and investigating. Examples of teaching from an ecocultural perspective to strengthen visuospatial reasoning in mathematics are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. A summary of this research is given in Owens (1993, pp. 32–39)

  2. I am Australian who lived in PNG for 15 years with a further 30 years of research supporting PNG colleagues.

  3. While many villagers are fluent in their own local language, other languages, and English, most are fluent like me or understand Tok Pisin, the PNG lingua franca. Interviews were held in Tok Pisin with frequent translation into the local language, Tok Ples.

  4. ACARA is the Australian Curriculum and Assessment Reporting Authority, a national government agency

  5. These were generally by invitation to visit and were agreed upon by the village Elders or community. We became guests usually because we were friends of village members.

  6. The story told with string figures is provided in a Kagua/Erave teacher’s (2007) report held at University of Goroka, Owens 2015, pp. 147, 174

  7. Two people’s two hands or hands and feet are also used.

  8. Western schools often regard a handspan from little finger tip to thumb tip but this is not practiced in most Indigenous communities where handspans are mentioned.

References

  • ACARA. (2012). Australian Curriculum - geography Retrieved from 2020 https://www.australiancurriculum.edu.au/f-10-curriculum/humanities-and-social-sciences/geography/structure/

  • ACARA. (2017). General capabilities - numeracy. Retrieved from 2020 https://www.australiancurriculum.edu.au/f-10-curriculum/humanities-and-social-sciences/geography/structure

  • Australian Museum. (~2010, update 2019). Rituals of seducation: birds of paradise. Sydney: Australian Museum.

  • Baenninger, M., & Newcombe, N. (1989). The role of experience in spatial test performance: a meta-analysis. Sex Roles, 20(5/6), 327–344.

    Article  Google Scholar 

  • Biggs, J. B. (1982). Evaluating the quality of learning: the SOLO taxonomy (structure of the observed learning outcome). New York: Academic Press.

    Google Scholar 

  • Blitz-Raith, A. H., & Liu, J. (2017). Interactivity in educational apps for young children: a multimodal analysis. International Journal of Instruction, 10(4), 237. https://doi.org/10.12973/iji.2017.10414a.

    Article  Google Scholar 

  • Booth, D. (1994). Art and geometry learning through spontaneous pattern making. Journal of Institute of Art Education, 9(2), 28–42.

    Google Scholar 

  • Burarrwanga, L., Ganambarr, R., Merrkiwayawuy Ganambarr-Stubbs, B. G., Barr, D., Maymuru, D., Wright, S., Suchet-Pearson, S., & Llloyd, K. (2013). Welcome to my country. Sydney: Allen & Unwin.

    Google Scholar 

  • Capell, A. (1969). A survey of New Guinea languages. Sydney: Sydney University Press.

    Google Scholar 

  • Del Grande, J. (1992). Geometry and spatial abilities. Paper presented at the Subgroup 11.1: Geometry as a part of education in early childhood in Working Group 11: The role of geometry in general education. International Congress on Mathematical Education, ICME 7, Quebec.

  • Dreyfus, T. (1991). On the status of visual reasoning in mathematics and mathematics education. In F. Furinghetti (Ed.), Proc. 15th Conf. of Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 33–48). Italy: PME.

    Google Scholar 

  • Eliot, J. (1987). Models of psychological space: psychometric, developmental, and experimental approaches. New York: Springer-Verlag.

    Book  Google Scholar 

  • Eliot, J., & McFarlane-Smith, I. (1983). International directory of spatial tests. Windsor: NRER-Nelson.

    Google Scholar 

  • Fantinato, M. C., & Mafra, J. R. E. S. (2017). Chapter 4 Techniques and learning processes of craftswomen in Brazil. In M. Rosa, L. Shirley, M. Gavarrete, & W. Alangui (Eds.), Ethnomathematics and its diverse approaches for mathematics education (ICME-13 monographs) (pp. 69–93). Cham: Springer.

  • Furuto, L. H. L. (2014). Pacific ethnomathematics: pedagogy and practices in mathematics education. Teaching Mathematics and its Applications: An International Journal of the IMA, 33(2), 110–121. https://doi.org/10.1093/teamat/hru009.

    Article  Google Scholar 

  • Gagnier, K., & Shipley, T. (2016). Visual completion from 2D cross-sections: implications for visual theory and STEM education and practice. Cognitive Research: Principles and Implications, 1(1), 1–18. https://doi.org/10.1186/s41235-016-0010-y.

    Article  Google Scholar 

  • Gerdes, P. (1998). Women, art and geometry in southern Africa. Trenton: African World Press.

    Google Scholar 

  • Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms. Journal of Mathematical Behavior, 22(1), 73–89. https://doi.org/10.1016/s0732-3123(03)00005-1.

    Article  Google Scholar 

  • Gruenewald, D. (2008). The best of both worlds: a critical pedagogy of place. Environmental Education Research, 14(3), 308–324.

    Article  Google Scholar 

  • Guilford, J. (1966). Intelligence: 1965 Model. American Psychologist, 21, 20–26.

    Article  Google Scholar 

  • Harris, P. (1989). Mathematics in a cultural context: Aboriginal perspectives on space, time and money. Geelong: Deakin University Press.

  • Healy, L., & Fernandes, S. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77(2), 157–174. https://doi.org/10.1007/s10649-010-9290-1.

    Article  Google Scholar 

  • Hershkowitz, R. (1989). Visualisation in geometry - two sides of the coin. Focus on Learning Problems in Mathematics, 11(1), 61–76.

    Google Scholar 

  • Hutchins, E. (1995). Cognition in the wild. Cambridge: Massachusetts Institute of Technology.

    Google Scholar 

  • Izard, V., Pica, P., Spelke, E., & Dehaene, S. (2011). Flexible intuitions of Euclidean geometry in an Amazonian indigene group. Proceedings of the National Academy of Sciences of the United States of America, 108(24), 9782–9787. https://doi.org/10.1073/pnas.1016686108.

    Article  Google Scholar 

  • Jirout, J., Holmes, C. A., Ramsook, K. A., & Newcombe, N. (2018). Scaling up spatial development: a closer look at children's scaling ability and its relation to number knowledge. Mind, Brain, and Education, 12(3), 110–119. https://doi.org/10.1111/mbe.12182.

    Article  Google Scholar 

  • Johnson, M. (1987). The body and the mind: the bodily basis of meaning, imagination, and reason. Chicago: University of Chicago Press.

    Book  Google Scholar 

  • Julius, A. (2007). Mathematics of traditional 'Tabare' of the Simbu Province. In W. Other (Ed.), Ethnomathematics reports 2007 (pp. 1–11). Goroka: University of Goroka.

  • Khan, S., Francis, K., & Davis, B. (2015). Accumulation of experience in a vast number of cases: enactivism as a fit framework for the study of spatial reasoning in mathematics education. ZDM, 47(2), 269–279. https://doi.org/10.1007/s11858-014-0623-x.

    Article  Google Scholar 

  • Kopi, S. (1997). Traditional beliefs, illness and health among the Motuan people of Papua New Guinea. (Unpublished doctoral thesis), University of Sydney.

  • Kosslyn, S. (1981). The medium and message in mental imagery: a theory. Psychological Review, 88(1), 46–66.

    Article  Google Scholar 

  • Kozhevnikov, M., Hegarty, M., & Mayer, R. (2002). Revising the visualizer-verbalizer dimension: evidence for two types of visualizers. Cognition and Instruction, 20(1), 47–77. https://doi.org/10.1207/S1532690XCI2001_3.

    Article  Google Scholar 

  • Krutetskii, V. (1976). The psychology of mathematical abilities in schoolchildren. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics. Survey of recent East European mathematical literature (Vol. II: The structure of mathematical abilities, pp. 5-58). Chicago: University of Chicago.

    Google Scholar 

  • Kyllonen, P. C., Lohman, D. F., & Snow, R. E. (1984). Effects of aptitudes, strategy training, and task facets on spatial task performance. Journal of Educational Psychology, 76(1), 130–145.

    Article  Google Scholar 

  • Lean, G. (1984). The conquest of space: a review of the research literatures pertaining to the development of spatial abilities underlying an understanding of 3-D geometry. Adelaide: Paper presented at the Fifth International Congress on Mathematical Education.

    Google Scholar 

  • Learmonth, A. E., Newcombe, N., Sheridan, N., & Jones, M. (2008). Why size counts: children's spatial reorientation in large and small enclosures. Developmental Science, 11(3), 414–426.

    Article  Google Scholar 

  • Lee, S. A., Sovrano, V. A., & Spelke, E. S. (2012). Navigation as a source of geometric knowledge: Young children’s use of length, angle, distance, and direction in a reorientation task. Cognition, 123(1), 144–161. https://doi.org/10.1016/j.cognition.2011.12.015.

    Article  Google Scholar 

  • Lipka, J., Wong, M., & Andrew-Ihrke, D. (2013). Alaska Native Indigenous knowledge: Opportunities for learning mathematics. Mathematics Education Research Journal, 25(1), 129–150.

  • Lipka, J., Adams, B., Wong, M., Koester, D., & Francois, K. (2019). Symmetry and measuring: Ways to teach the foundations of mathematics inspired by Yupiaq Elders. Journal of Humanistic Mathematics, 9(1), 107–157.

  • Lohman, D. F., Pellegrino, J. W., Alderton, D. L., & Regian, J. W. (1987). Dimensions and components of individual differences in spatial abilities. In S. H. Irvine & S. E. Newstead (Eds.), Intelligence and cognition (pp. 253–312). Dordrecht: Nijhoff Publishers.

    Google Scholar 

  • Mammana, C., & Villani, V. (Eds.). (1998). Perspectives on the teaching of geometry for the 21st century. New York: Springer.

    Google Scholar 

  • Mason, J. (2003). Structure of attention in the learning of mathematics. In J. Novotná (Ed.), Proceedings of the International Symposium on Elementary Mathematics Teaching (pp. 9–16). Prague: Charles University.

    Google Scholar 

  • Mason, J. (2008). Being mathematical with & in front of learners: attention, awareness, and attitude as sources of differences between teacher educators, teachers & learners. In T. Wood (Ed.), International handbook of mathematics teacher education (Vol. 4). Sense Publishers.

  • Matang, R., & Owens. (2014). The role of Indigenous traditional counting systems in children’s development of numerical cognition: results from a study in Papua New Guinea. Mathematics Education Research Journal, 26(3), 531–553. https://doi.org/10.1007/s13394-013-0115-2.

  • McGee, M. (1979). Human spatial abilities: Psychometric studies and environmental, genetic, hormonal, and neurological influences. Psychological Bulletin, 89, 889–918.

  • Möhring, W., Newcombe, N., & Frick, A. (2015). The relation between spatial thinking and proportional reasoning in preschoolers. Journal of Experimental Child Psychology, 132, 213–220. https://doi.org/10.1016/j.jecp.2015.01.005.

    Article  Google Scholar 

  • Muke, J. (1993). The Wahgi opo kumbo: An account of warfare in the central highlands of New Guinea. (unpublished doctoral thesis), University of Cambridge, Cambridge.

  • National Research Council Committee on Geography. (2006). Learning to think spatially: GIS as a support system in the K-12 curriculum. Washington DC: National Academies Press.

    Google Scholar 

  • Ness, D., & Farenga, S. (2007). Knowledge under construction: The importance of play in developing children's spatial and geometric thinking. Lanham: Rowan & Littlefield.

  • Newcombe, N. (2017). Harnessing spatial thinking to support STEM learning. In OECD Working Papers (Vol. 161). https://doi.org/10.1787/7d5dcae6-en.

    Chapter  Google Scholar 

  • Newcombe, N., & Stieff, M. (2012). Six myths about spatial thinking. International Journal of Science Education, 34(6), 955–971.

    Article  Google Scholar 

  • O’Hanlon, M. (1989). Reading the skin: Adornment, display and society among the Wahgi. London: Trustees of the British Museum by British Museum Publications.

  • Owens. (1992). Spatial mathematics: a group test for primary school students. In K. Stephens & J. Izard (Eds.), Reshaping assessment practices: assessment in the mathematical sciences under challenge. Australian Council for Education Research: Melbourne.

  • Owens. (1993). Spatial thinking processes employed by primary school students engaged in mathematical problem solving. (PhD), Deakin University, Geelong, Victoria, Australia. Retrieved from http://dro.deakin.edu.au/eserv/DU:30023339/author-spatialthinking-1993.pdf

  • Owens. (1999). The role of visualisation in young students' learning. In O. Zaskavsky (Ed.), 23rd annual conference of International Group for Psychology of Mathematics Education, PME23 (Vol. 1, pp. 220–234). Haifa.

  • Owens (2004). Imagery and property noticing: young students' perceptions of three-dimensional shapes. In P. Jeffery (Ed.), Proceedings of the annual conference for the Australian Association for Research in Education http://www.aare.edu.au/conf04/ File: OWE04038. Melbourne, Australia: AARE. Retrieved from http://www.aare.edu.au/conf04/ File: OWE04038.

  • Owens. (2015). Visuospatial reasoning: an ecocultural perspective for space, geometry and measurement education. New York: Springer.

  • Owens. (2016a). Culture at the forefront of mathematics research at the University of Goroka: the Glen Lean Ethnomathematics Centre. South Pacific Journal of Pure and Applied Mathematics, 2(1).

  • Owens. (2016b). The line and the number are not naked in Papua New Guinea. International Journal for Research in Mathematics Education. Special issue: Ethnomathematics: Walking the mystical path with practical feet, 6(1), 244–260.

  • Owens. (2014). The impact of a teacher education culture-based project on identity as a mathematics learner. Asia-Pacific Journal of Teacher Education, 42(2), 186–207. https://doi.org/10.1080/1359866X.2014.892568.

  • Owens, & Clements, M. (1998). Representations used in spatial problem solving in the classroom. Journal of Mathematical Behavior, 17(2), 197–218.

  • Owens,K., & Highfield, K. (2015). Chapter 9 Visuospatial reasoning in context with digital technology. In K. Owens (Ed.), Visuospatial reasoning: an ecocultural perspective on space, geometry, and measurement. New York: Springer.

  • Owens, & Kaleva, W. (2008a). Case studies of mathematical thinking about area in Papua New Guinea. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepúlveda (Eds.), Annual conference of the International Group for the Psychology of Mathematics education (PME) and North America chapter of PME, PME32 - PMENAXXX (Vol. 4, pp. 73–80). Morelia, Mexico: PME.

  • Owens, & Kaleva, W. (2008b). Indigenous Papua New Guinea knowledges related to volume and mass. In Paper presented at the International Congress on Mathematics Education ICME 11, Discussion Group 11 on The Role of Ethnomathematics in Mathematics Education. Monterray, Mexico. https://researchoutput.csu.edu.au/en/publications/indigenous-papua-new-guinea-knowledges-related-to-volume-and-mass. Accessed 2020.

  • Owens, Doolan, P., Bennet, M., Logan, P., Murray, L., McNair, M., et al. (2012). Continuities in education: pedagogical perspectives and the role of Elders in education for indigenous students. Journal of Australian Indigenous Issues, 15(1), 20–39.

  • Owens, K., Lean, G., Paraide, P., & Muke, C. (2018). The history of number: evidence from Papua New Guinea and Oceania. New York, NY: Springer.

  • Paivio, A. (1986). Mental representations: a dual coding approach. New York: Oxford University Press.

    Google Scholar 

  • Paraide, P., Owens, K., Clarkson, P., Muke, C., & Owens, C. (forthcoming). History of mathematics education in Papua New Guinea (working title). Cham: Springer nature.

  • Paraide, P. (2018). Chapter 11: Indigenous and western knowledge. In K. Owens & G. Lean, G. with P. Paraide & C. Muke (Ed.), History of number: Evidence from Papua New Guinea and Oceania. New York: Springer.

  • Pellegrino, J. W., & Hunt, E. B. (1991). Cognitive models for understanding and assessing spatial abilities. In H. Rowe (Ed.), Intelligence: reconceptualization and measurement. Lawrence Erlbaum and Australian Council for Educational Research: Hillsdale, NJ.

    Google Scholar 

  • Penn Museum. (1997). Traditional navigation in the Western Pacific: a search for pattern. Retrieved from http://www.penn.museum./sites/Navigation/Intro.html

  • Pinxten, R., & François, K. (2011). Politics in an Indian canyon? Some thoughts on the implications of ethnomathematics. Educational Studies in Mathematics, 78(2), 261–273. https://doi.org/10.1007/s10649-011-9328-z.

    Article  Google Scholar 

  • Pirie, S., & Kieren, T. (1991). Folding back: dynamics in the growth of mathematical understanding. In F. Furinghetti (Ed.), Proceedings of the 15th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 169–176). Italy: Program Committee for the International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Pylyshyn, Z. (1981). The imagery debate: analogue media versus tacit knowledge. Psychological Review, 88, 16–45.

    Article  Google Scholar 

  • Pylyshyn, Z. (1994). Some primitive mechanisms of spatial attention. Cognition, 50(1–3), 363–384. https://doi.org/10.1016/0010-0277(94)90036-1.

    Article  Google Scholar 

  • Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: a semiotic-cultural perspective on mathematical thinking. In Paper presented at the 29th Conference of the International Group for the Psychology of Mathematics Education (PME29). Melbourne.

  • Ramful, A., & Lowrie, T. (2015). Cognitive style, spatial visualization and problem solving performance: perspectives from grade 6 students. In Paper presented at the 39th conference of the International Group for the Psychology of Mathematics Education. Hobart.

  • Reid, J.-A. (2007). Literacy and environmental communications: towards a 'pedagogy of responsibility'. Australian Journal of Language and Literacy, 30(2), 118–133.

    Google Scholar 

  • Ribiero, S., Palhares, P., & Salinas, M. J. (2019). Ethnomathematical study of folk dances: linking to school mathematics (Working Group 5: Connections with Culture). In Paper presented at the CIEAEM71. Braga.

  • Royal Society, & Joint Mathematical Council. (2001). Teaching and learning geometry Pre-19. Retrieved from London: 2016.

  • Saxe, G. (2012). Cultural development of mathematical ideas: Papua New Guinea studies. New York: Cambridge University Press.

    Book  Google Scholar 

  • Schinazi, V. R., Nardi, D., Newcombe, N., Shipley, T. F., & Epstein, R. A. (2013). Hippocampal size predicts rapid learning of a cognitive map in humans. Hippocampus, 23(6), 515–528. https://doi.org/10.1002/hipo.22111.

    Article  Google Scholar 

  • Shah, P., & Miyake, A. (2005). The Cambridge handbook of visuospatial thinking. New York: Cambridge University Press.

    Book  Google Scholar 

  • Shepard, R., & Metzler, J. (1971). Mental rotation of three dimensional objects. Science, 171, 701–703.

    Article  Google Scholar 

  • Sinclair, N., & Patterson, M. (2018). The dynamic geometrisation of computer programming. Mathematical Thinking and Learning, 20(1), 54–74. https://doi.org/10.1080/10986065.2018.1403541.

    Article  Google Scholar 

  • Sinclair, N., Bartolini Bussi, M. G., de Villiers, M., Jones, K., Kortenkamp, U., Leung, A., & Author. (2016). Recent research on geometry education: an ICME-13 survey team report. ZDM, 1–29. https://doi.org/10.1007/s11858-016-0796-6.

  • Stieff, M., Dixon, B., Ryu, M., Kumi, B., & Hegarty, M. (2014). Strategy training eliminates sex differences in spatial problem solving in a STEM domain. Journal of Educational Psychology, 106(2), 390–402.

    Article  Google Scholar 

  • Tartre, L. (1990). Spatial skills, gender, and mathematics. In E. L. G. Fennema (Ed.), Mathematics and gender. New York: Teachers College Press.

    Google Scholar 

  • Thornton, S. (2014). Slow maths - a metaphor for connectness for school mathematics. (PhD thesis), Australian National University, Canberra. Retrieved from 2020 http://hdl.handle.net/1885/111190. Accessed 2020.

  • Thornton, M., & Watson-Verran, H. (1996). Living maths. Abbotsford: Yirrkala Community School and Boulder Valley Films.

    Google Scholar 

  • Thurstone, L., & Thurstone, T. (1941). Factor studies of intelligence. Psychological Monographs, 2.

  • Towers, J., & Martin, L. (2014). Building understanding through collective property noticing. Canadian Journal of Science, Mathematics, and Technology Education, 14(1), 58–75.

    Article  Google Scholar 

  • Tuan, Y.-F. (1977). Space and place: the perspective of experience. London: Edward Arnold.

    Google Scholar 

  • Uttal, D., Fisher, J., & Taylor, H. (2006). Words and maps: developmental changes in mental models of spatial information acquired from descriptions and depictions. Developmental Science, 9(2), 221–235.

    Article  Google Scholar 

  • Uttal, D., et al. (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402. https://doi.org/10.1037/a0028446.

    Article  Google Scholar 

  • van Hiele, P. (1986). Structure and insight: a theory of mathematics education. New York: Academic Press.

    Google Scholar 

  • Vandendriessche, E. (2016). String figures as mathematics: an anthropological approach to string figure-making in oral traditional societies. Dortrecht: Springer.

  • Were, G. (2003). Objects of learning: an anthropological approach to mathematics education. Journal of Material Culture, 8(25), 25–44. https://doi.org/10.1177/1359183503008001761.

    Article  Google Scholar 

  • Were, G. (2010). Lines that connect: rethinking pattern and mind in the Pacific. Honolulu: University of Hawai'i Press.

    Book  Google Scholar 

  • Witherspoon, G., & Peterson, G. (1995). Dynamic symmetry and holistic asymmetry in Navajo and western art and cosmology. New York, New York: Peter Lang Publishing.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Charles Sturt University, Locked Bag 49, Dubbo, NSW, Australia

    Kay Owens

Authors
  1. Kay Owens
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kay Owens.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Owens, K. Transforming the established perceptions of visuospatial reasoning: integrating an ecocultural perspective. Math Ed Res J 32, 257–283 (2020). https://doi.org/10.1007/s13394-020-00332-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13394-020-00332-z

Keywords

Search

Navigation