Reevaluating Froebel Gifts: A Tool That Embodies Three Dimensions in Space to Enhance Pre-school Children’s Geometry Skills

Abstract

Froebel Gifts are the first educational materials designed for kindergarten children in the education history. After Froebel introduced the first construction and design materials for early childhood mathematics education in 1850’s, several companies such as Lego Bricks, Lincoln Logs, and K’nex were influenced by his design. Considering the influence of Froebel Gifts on mathematics and geometry education tools for young children, it is important to analyze their impact on pre-school children’s geometry skills. This study investigated the effects of a geometry education program mediated with Froebel Gifts on 5-6 years-old children’s geometric skill development. The participants consisted of 40 pre-school children in Istanbul, Turkey. Twenty children in the experimental group received an 8-week intervention with Froebel Gifts while the control group continued their regular program. Early Geometry Skill Test (EGST) was used before and after the intervention and the collected data were analyzed with independent sample T-test. The results indicate a significant change in favor of the experimental group in the skills of building with blocks, recognizing the three-dimensional objects, predicting the surface shape of the three-dimensional objects, and recognizing the side and corner properties of two-dimensional shapes. The teacher’s instructional strategies and the physical and representational properties of Froebel Gifts are discussed and evaluated in the light of these results to provide insight about the features of an effective geometry education.

Keywords

• pre-school geometry education
• froebel gifts
• froebel approach
• early geometry skills
• shape recognition.

References

1. Aktaş-Arnas, Y., & Aslan, D. (2005). Okul öncesi dönemde geometri. Eğitim Bilim Toplum Dergisi, 3 (9), 36-46.
2. Aktaş-Arnas, Y., & Aslan, D. (2007) Okul öncesi eğitim materyallerinde geometrik şekillerin sunuluşuna ilişkin içerik analizi, Ç.Ü. Sosyal Bilimler Enstitüsü Dergisi, 16 (1), 69-80.
3. Aktaş-Arnas, Y., & Aslan, D. (2010). Children's classification of geometrıc shapes. Ç.Ü. Sosyal Bilimler Enstitüsü Dergisi, 19 (1), 254-270.
4. Aslan, D., & Arnas, Y. A. (2007). Three- to six-year-old children’s recognition of geometric shapes. International Journal of Early Years Education, 15(1), 83–104. https://doi.org/10.1080/09669760601106646
5. Baroody, A. J. (2017). The use of concrete experiences in early childhood mathematics instruction. Advances in Child Development and Behavior, 53, 43-94. https://doi.org/10.1016/bs.acdb.2017.03.001
6. Barth, H., Mont, K. L., Lipton, J., & Spelke, E. S. (2005). Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Sciences, 102(39), 14116–14121. https://doi.org/10.1073/pnas.0505512102
7. Boswell, D. A., & Green, H. F. (1982). The abstraction and recognition of prototypes by children and adults. Child Development, 53(4), 1028–1037. https://doi.org/10.2307/1129144
8. Braham, E. J., & Libertus, M. E. (2017). Intergenerational associations in numerical approximation and mathematical abilities. Developmental Science, 20(5), 1-12.

9. Bruce, C., & Hawes, Z. (2015). The role of 2D and 3D mental rotation in mathematics for young children: What is it? Why does it matter? And what can we do about it? ZDM, 47(3), 331–343. https://doi.org/10.1007/s11858-014-0637-4
10. Bruce, T. (2012). Early Childhood Practice Froebel Today, London: Sage Publications.
11. Bruner, J. (1964). The course of cognitive growth. American Psychologist, 19, 1- 15.
12. Bruner, J. (1966). Towards a theory of instruction. Cambridge, Massachusetts: Harvard University Press.
13. Bulow, B. M. (2007). How Kindergarten Came to America: Friedrich Froebel’s Radical Vision of Early Childhood Education, Classics in Progressive Education. New Press, The, 2007. Print
14. Cetin, I., & Dubinsky, E. (2017). Reflective abstraction in computational thinking. Journal of Mathematical Behavior, 47, 70–80.
15. Charlesworth, R. (2005). Prekindergarten mathematics: Connecting with national standards. Early Childhood Education Journal, 32 (4), 229-236. https://doi.org/10.1007/s10643-004-1423-7
16. Christie, S., & Gentner, D. (2010). Where hypotheses come from: Learning new relations by structural alignment. Journal of Cognition & Development, 11(3), 356–373. https://doi-org.ezproxy.lakeheadu.ca/10.1080/15248371003700015.
17. Clements, D. H., & Sarama, J. (2000). Young children’s ideas about geometric shapes, Teaching Children Mathematics, 6 (8), 482-488.
18. Clements, D., and Sarama, J. (2000). The Earliest Geometry, Teaching Children Mathematics, 7(2), pp.82-86.
19. Clements, D. H. (1999). 'Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1 (1), 45-60.
20. Clements, D. H. (2003). Teaching and learning geometry. A research companion to principles and standards for school mathematics, Reston, VA: NCTM.
21. Clements, D. H., & Sarama J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14 (2) 133-148. https://doi.org/10.1007/s10857-011-9173-0
22. Clements, D. H., DiBiase, A.-M., & Sarama, J. (2004). Engaging young children in mathematics: Standards for early childhood mathematics education. Studies in mathematical thinking and learning series. Mahwah, N.J: In Lawrence Erlbaum Associates (Bks).
23. Connolly, S. (2010). The Impact of van Hiele-based geometry instruction on student understanding. Mathematical and Computing Sciences Masters. Paper 97. 88.
24. Correia, J., & Fisher, M. (2014). Froebel gifts: A tool to reinforce conceptual knowledge of fractions. The Ohio Journal of Science., Spring (69), 31-35.
25. Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Yearbook (National Council of Teachers of Mathematics), 1987, 1–16.
26. Dagli, Ü. Y., & Halat, E. (2016). Young children’s conceptual understanding of triangle. EURASIA Journal of Mathematics, Science & Technology Education, 12(2), 189–202. https://doi.org/10.12973/eurasia.2016.1398a
27. Dubinsky, E. (2002). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 95–126). https://doi.org/10.1007/0-306-47203-1_7
28. Eugene, F., Provenzo, Jr. (2009). Friedrich Froebel’s gifts connecting the spiritual and aesthetic to the real world of play and learning. American Journal of Play, 2 (1), 86-99.
29. Figueira-Sampaio, A. da S., Santos, E. E. F. dos, Carrijo, G. A., & Cardoso, A. (2013). Survey of mathematics practices with concrete materials used in Brazilian schools. Procedia - Social and Behavioral Sciences, 93, 151–157. https://doi.org/10.1016/j.sbspro.2013.09.169
30. Friedman, M. (2018). “Falling into disuse”: the rise and fall of Froebelian mathematical folding within British kindergartens. Paedagogica Historica, 54(5), 564–587. https://doi.org/10.1080/00309230.2018.1486441
31. Gifford, S., Griffiths, R., & Back, J. (2017). Using manipulatives in the foundations of arithmetic: Main report; examples for teachers. University of Leicester.
32. Gray, E. M., & Tall, D. O. (2001). Relationships between embodied objects and symbolic procepts: An explanatory theory of success and failure in mathematics. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of 25th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 65-72). Utrecht, The Netherlands: PME.
33. Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40. https://doi.org/10.1007/BF03217454 Hewitt, K. (2001). Blocks as a tool for learning: Historical and contemporary perspectives. Young Children, 56 (1), 6–11.
34. Hill, P. S. (1908). The value and limitations of Froebel's gifts as educative materials parts III, IV, V. The Elementary School Teacher, 9 (4) 192-201.
35. İncikabı, L., & Kılıç, Ç. (2013). İlköğretim Öğrencilerinin Geometrik Cisimlerle İlgili Kavram Bilgilerinin Analizi. Kuramsal Eğitimbilim Dergisi, 6 (3), 343-358.
36. Jones, K. (1998). Theoretical frameworks for the learning of geometrical reasoning. Proceedings of the British Society for Research into Learning Mathematics, 2(18), 29–34. https://doi.org/10.1007/BF01273689
37. Kalénine, S., Pinet, L., & Gentaz, E. (2011). The visual and visuo-haptic exploration of geometrical shapes increases their recognition in preschoolers. International Journal of Behavioral Development, 35, 18–26. https://doi.org/10.1177/0165025410367443
38. Kamina, P., & Iyer, N. N. (2009). From concrete to abstract: Teaching for transfer of learning when using manipulatives. NERA Conference Proceedings 2009, 10. Kelley, D. (1984). A theory of abstraction. Cognition & Brain Theory, 7(3-4), 329-357.
39. Kesicioğlu, O. S., Alisinanoğlu, F., & Tuncer, A.T. (2011). Okul Öncesi Dönem Çocukların Geometrik Şekilleri Tanıma Düzeylerinin İncelenmesi. Elementary Education Online, 10 (3), 1093-1111.
40. Koğ, O. U., & Başer, N. (2011). Görselleştirme yaklaşımının matematikte oğrenilmiş caresizliğe ve soyut düşümeye etkisi. Batı Anadolu Eğitim Bilimleri Dergisi, 1 (3), 89-108.
41. Koleza, E., & Giannisi, P. (2013). Kindergarten children’s reasoning about basic geometric shapes. In B. Ubuz, Ç. Haser & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education, 2118–2127.
42. Kotovsky, L., & Gentner, D. (1996). Comparison and categorization in the development of relational similarity. Child Development, 67(6), 2797. https://doi.org/10.2307/1131753
43. Loewenstein, J., & Gentner, D. (2001). Spatial mapping in preschoolers: Close comparisons facilitate far mappings. Journal of Cognition and Development, 2(2), 189–219. https://doi.org/10.1207/S15327647JCD0202_4
44. Manning, J. P. (2005). Rediscovering Froebel: A call to re-examine his life & gifts. Early Childhood Education Journal, 32 (6), 371-376. https://doi.org/10.1007/s10643-005-0004-8
45. Mistretta, R. M. (2000). Enhancing geometric reasoning. Adolescence, 35(138), 365.
46. Mitchelmore, M. C., & White, P. (1995). Abstraction in mathematics: Conflict, resolution and application. Mathematics Education Research Journal, 7(1), 50–68. https://doi.org/10.1007/BF03217275
47. Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction and generalisation. Educational Studies in Mathematics, 41(3), 209.
48. Mitchelmore, M., & White, P. (2007). Abstraction in mathematics learning. Mathematics Education Research Journal, 19(2), 1–9. https://doi.org/10.1007/BF03217452
49. Oberdorf, C. D., & Taylor-Cox, J. (1999). Shape Up! Teaching Children Mathematics, 5(6), 340–345.
50. Palmer, L. A. (1912). Montessori and Froebelian materials and methods. The Elementary School Teacher, 13(2), 66–79. https://doi.org/10.1086/454181
51. Park, H. J., & Vakalo, E. G. (2000). An enchanted toy based on Froebel s Gifts: A computational tool used to teach architectural knowledge to students. Promise and Reality - State of the Art versus State of Practice in Computing for the Design and Planning Process: 18th ECAADe Conference Proceedings, 35–39. Weimar, Germany: Bauhaus-Universitat Weimar.
52. Posnansky, C. J., & Neumann, P. G. (1976). The abstraction of visual prototypes by children. Journal of Experimental Child Psychology, 21(3), 367–379. https://doi.org/10.1016/0022-0965(76)90067-9
53. Ramatlapana, K., & Berger, M. (2018). Prospective Mathematics Teachers’ Perceptual and Discursive Apprehensions when Making Geometric Connections. African Journal of Research in Mathematics, Science and Technology Education, 22(2), 162–173. https://doi.org/10.1080/18117295.2018.1466495
54. Ransbury, M. K. (1982). Friedrich Froebel 1782–1982: A re-examination of Froebel’s principles of childhood learning. Childhood Education, 59(2), 104–106. https://doi.org/10.1080/00094056.1982.10520556
55. Read, J. (1992). A Short History of Children’s Building Blocks. In Pat Gura (Ed.), Exploring learning: Young children and block play. (pp. 1-12). London: Paul Chapman Publishing Ltd.
56. Reinhold, S., Downton, A., & Livy, S. (2017). Revisiting Friedrich Froebel and his Gifts for Kindergarten: What are the benefits for primary mathematics education? In A. Downton, S. Livy & J. Hall (Eds.), 40 years on: We are still learning! Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp.434-441) Melbourne: MERGA.
57. Sarama, J. and Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19 (1), 181-189.
58. Sarama, J. and Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York, NY: Routledge. https://doi.org/10.4324/9780203883785
59. Schmitt, S. A., Korucu, I., Napoli, A. R., Bryant, L. M., & Purpura, D. J. (2018). Using block play to enhance preschool children’s mathematics and executive functioning: A randomized controlled trial. Early Childhood Research Quarterly, 44, 181–191. http://dx.doi.org/10.1016/j.ecresq.2018.04.006
60. Sezer, T., & Güven, Y. (2016) Erken geometri beceri testi'nin geliştirilmesi ve çocukların geometri becerilerinin incelenmesi. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 33, 1-22.
61. Son, J. Y., Smith, L. B., & Goldstone, R. L. (2008). Simplicity and generalization: Short-cutting abstraction in children’s object categorizations. Cognition, 108(3), 626–638. https://doi.org/10.1016/j.cognition.2008.05.002
62. Stiny, G. (1980). Kindergarten grammars: designing with Froebel's building gifts. Environment and Planning B, 7 (4), 409-462.
63. Tovey, H. (2016). Bringing the Froebel approach to your early years practice, Series Edited by Sandy Green, A David Fulton Book, Routledge
64. Walker, C., Hubachek, S. Q., & Vendetti, M. S. (2018). Achieving abstraction: Generating far analogies promotes relational reasoning in children. Developmental Psychology, 54(10), 1833–1841. https://doi-org.ezproxy.lakeheadu.ca/10.1037/dev0000581.
65. Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76–95. https://doi.org/10.1007/BF03217546
66. White, H., Jubran, R., Heck, A., Chroust, A., & Bhatt, R. S. (2018). The role of shape recognition in figure/ground perception in infancy. Psychonomic Bulletin & Review, 25, 1381–1387. doi: 10.3758/s13423-018-1476-z
67. Wiggin, K.D., & Smith, N.A. (1895) Froebel’s Gifts, Houghton, Mifflin and Company, Boston & New York.
68. Willingham, D. T. (2009). Why don’t students like school? A cognitive scientist answers questions about how the mind works and what it means for the classroom (1st ed). San Francisco, CA: Jossey-Bass.
69. Wilson, S. (1967). The “Gifts” of Friedrich Froebel. Journal of the Society of Architectural Historians, 26(4), 238. https://doi.org/10.2307/988449
70. Woodard, C. (1979). Gifts from the father of the kindergarten. The Elementary School Journal, 79 (3), 136-141.
71. Yaman, H., & Şahin, T. (2014). Somut ve sanal manipülatif destekli geometri oğretiminin 5. sınıf oğrencilerinin geometrik yapıları inşa etme ve cizmedeki başarılarına etkisi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 14 (1), 202-220. https://doi.org/10.17240/aibuefd.2014.14.1-5000091509
72. Yuan, L., Uttal, D., & Gentner, D. (2017). Analogical processes in children’s understanding of spatial representations. Developmental Psychology, 53(6), 1098–1114.
73. Zuckerman, O. (2006). Historical Overview and Classification of Traditional and Digital Learning Objects. Cambridge, MA: MIT Media Lab. http://llk.media.mit.edu/courses/readings/classification-learning-objects.pdf.